Jointly Organised by Message

Prof. Hrushikesha Mohanty Vice-Chancellor, KIIT-Deemed to be University Message

Dr. Shashank Chaturvedi Director Message Message

Prof. Jnyana Ranjan Mohanty Registrar, KIIT-Deemed to be University Message

It gives me immense pleasure to convey you that two days Plasma Scholars Colloquium (PSC 2020) is organized by our Department of Physics, School of Applied Sciences, KIIT Deemed to be University, Bhubaneswar, and the Plasma Science Society of India (PSSI) from October 8-9, 2020 on Virtual platform.

In the 21st Century, one of the most important applications of the technology is based on Plasma Science in all the sector of like industries, agriculture, energy as well as health. This PSC 2020, especially in this COVID 19 pandemic situation where the whole world is struggling to get the new normal life. Young Students/Researchers Colloquium will be very much beneficial for the students working in the field of Plasma.

I am confident the deliberations and discussion will open a new path to take forward the Plasma research in the next level

I wish Colloquium (PSC 2020) is a grand success.

Dr. Puspalata Pattojoshi Dean SAS, KIIT-Deemed to be University Message

(Dr. Paritosh Chaudhuri) General Secretary Plasma Science Society of India (PSSI) Message

Dr. S. K. S. Parashar Convener SAS, KIIT-Deemed to be University 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

CONTENTS Code Title Page No. Basic Plasma Experiments and Simulations OL1-1 Cross-field charge particle transport inside a void created by an obstacle 8 inserted in a magnetized plasma column, Satadal Das, IPR

OL1-2 Probing Ne ECR plasma to study the gas mixing and anomalous effect, 9 Puneeta Tripathi, IUAC, New Delhi

OL1-3: Electrical conductivity of a plasma confined in a dipole magnetic field: 10 systematic experiments and theory, A. Nanda, IIT Kanpur

OL1-4: Floating potential fluctuations in atmospheric pressure micro-plasma jets, D. 11 Behmani, IIT Kanpur

OL1-5: Comparative study of plasma antenna and monopole metal antenna, 12 Manisha Jha, IPR

OL1-6: Magnetic field effects on 13.56 MHz capacitive coupled 13 radio-frequency sheaths, S. Binwal, Jamia Millia Islamia, Delhi

OL1-7: Does the fate of 2D incompressible high Reynolds number turbulence 14 depend on initial conditions? : A revisit! Shishir Biswas, IPR

OL1-8: Study on ion re-circulation and potential well structure in an inertial 15 electrostatic confinement fusion device using 2D-3V PIC simulation, D. Bhattacharjee, CPP-IPR

OL1-9: Molecular dynamics simulation of collisional cooling of He and its binary 16 mixtures with Ne, Ar, Kr and Xe for creating strongly coupled cryo plasmas, S. S. Mishra, IIT Kanpur

OL1-10: Effects of flow Velocity and Density of Dust Layers on the 17 Kelvin-Helmholtz Instability in Strongly Coupled Dusty Plasma: Molecular Dynamic Study, Bivash Dolai, Guru Ghasidas Vishwavidyalaya, Bilaspur

1 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL1-11: Simulation Study of Planar Anode Micro Hollow Cathode Discharge Using 18 Dielectric Layer, Khushboo Meena, CEERI, Pilani

Fusion Science and Technology OL2-1: Impact of Energetic Particles in the First-Wall Erosion in Fusion Power 20 Reactors, P. N. Maya, IPR

OL2-2: Disruptions study in Aditya-U Tokamak, Suman Dolui, IPR 21

OL2-3: Simulation of runaway electron generation in fusion grade tokamak and 22 suppression by impurity injection, Ansh Patel, PDPU, Gandhinagar

OL2-4: Simultaneous measurement of thermal conductivity and thermal diffusivity 24 of ceramic pebble bed using transient hot-wire technique, Harsh Patel, IPR

OL2-5: A DDPM-DEM-CFD flow characteristic analysis of pebble bed for fusion 25 blanket, Chirag Sedani, IPR

OL2-6: Initial results of Laser Heated Emissive Probes operated in cold condition in 28 Aditya-U Tokamak, A. Karnik, VIT Chennai

OL2-7: Evidence Of Non-local Transport in ADITYA-U Tokamak, 29 T. Macwan, IPR

OL2-8: Parametric Study of SMBI CD Nozzle for ADITYA-U Tokamak, 30 K. Singh, IPR

OL2-9: Study of Sawtooth Induced Heat Pulse Propagation in the ADITYA 31 Tokamak, S. Patel, PDPU, Gandhinagar

OL2-10: Calculation of Toroidal and Poloidal Rotation in Aditya-U Tokamak, 32 A. Kumar, IPR Basic Plasma Theory OL3-1: Electron-Acoustic Solitary waves in Fermi Plasma with Two-Temperature 34 Electrons, Ankita Dey, Lady Brabourne College, University of Calcutta

OL3-2: Quantum Electro-static Shock Fronts in Two Component Plasma with 35 Non-thermal Distributive Ion, Subhangi Chakraborty, JIS University, Kolkata

OL3-3: Thermal Instability of Two-Component Plasma with Radiative Heat-Loss 36 Functions Frictional Effect of Neutrals and Hall Current, Sachin Kaothekar, Mahakal Institute of Technology & Management, Ujjain

2 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL3-4: Target Shape Effects on the Energy of Ions Accelerated in Radiation 37 Pressure Dominant (RPD) Regime, S. Jain, University of Kota, Kota

OL3-5: Study of slow mode solitons in a negative ion plasma with superthermal 38 electrons, X. Mushinzimana, University of Rwanda

OL3-6: Effect of the non-thermal electrons on ion-acoustic cnoidal wave in 39 un-magnetized plasmas, P. C. Singhadiya, Seth RLS Govt. College, Rajasthan.

OL3-7: Formation of shock fronts in inner magnetospheric plasma, 40 J. Sarkar, Jadavpur University

OL3-8: Slow and fast modulation instability and envelope soliton of ion acoustic 41 waves in fully relativistic plasma having nonthermal electrons, Indrani Pal, Jadavpur University

OL3-9: To Study the Growth Rates of Waves between Piezoelectric and Ferroelectric 42 Semiconductor Using QHD Model In Quantum Plasma, Manisha Raghuvanshi, Govt. M.V.M college Shivaji nagar, Bhopal

OL3-10 Diagnostics of Ar-CO2 mixture plasma using CR model, 44 N. Shukla, IIT Roorkee

OL3-11 Large amplitude ion-acoustic compressive solitons in plasmas with 45 positrons and superthermal electrons S. K. Jain1, P. C. Singhadiya and J. K. Chawla 1Govt. College, Dholpur, Rajasthan, India-328001 Dusty Plasma, Laser Plasma, Plasma Applications OL4-1: Study of Arc Fluctuations of a DC Transferred Arc Plasma, 47 S. P. Sethi, CSIR-IMMT, Bhubaneswar

OL4-2: Inductive Energy Storage System with Plasma opening Switch: A review, 48 Kanchi Sunil, BARC, Mumbai

OL4-3: Role of plasma sheath in the energy management during plasma surface 49 modification of polymer, Bivek Pradhan Sikim Manipal University

OL4-4: Dynamics of dust ion acoustic waves in the Low Earth Orbital (LEO) plasma 50 region, Siba Prasad Acharya, SINP, Kolkata

OL4-5: Effect of negative charge dust on ion-acoustic dressed solitons in 51 un-magnetized plasmas, J K Chawla, Govt. College Tonk, Rajasthan

OL4-6: Effect of collision on dust–ion acoustic shock wave in dusty plasma with 52 negative ions, Jyotirmoy Goswami, Jadavpur University.

3 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL4-7: Equilibrium configuration of self gravitating dusty plasmas, M. Shukla, 53 Jawaharlal Nehru College, Pasighat.

OL4-8: Strong and collimated terahertz radiation by photo mixing of Hermite Cosh 54 Gaussian lasers in collisional plasma, Sheetal Chaudhary, CCSU, Meerat

OL4-9: Effect of laser pulse profile on controlling the growth of 55 RayleighTaylor instability in radiation pressure dominant regime Krishna Kumar Soni, University of Kota, Kota

OL4-10: Laser-driven radially polarized terahertz radiation generation in hot Plasma, 56 Manendra, CCSU, Meerat

FULL PAPER PSC-1 Simulation of runaway electron generation in fusion grade tokamak 58 and suppression by impurity injection Ansh Patel1, Santosh P. Pandya2 1School of Liberal Studies, PanditDeendayal Petroleum University, Gandhinagar, India 2Institute for Plasma Research, Bhat, Gandhinagar, India.

PSC-2 Effects of flow Velocity and Density of Dust Layers on the 63 Kelvin-Helmholtz Instability in Strongly Coupled Dusty Plasma: Molecular Dynamic Study Bivash Dolai and R. P. Prajapati Department of Pure and Applied Physics, Guru Ghasidas Vishwavidyalaya, Bilaspur-495009 (C.G.), India

PSC-3 Study on ion re-circulation and potential well structure in an inertial 70 electrostatic confinement fusion device using PIC simulation D. Bhattacharjee1, S. Adhikari2 and S. R. Mohanty1, 3 1Center of Plasma Physics-Institute for Plasma Research, Sonapur, Kamrup(m), Assam, 782402, India 2Department of Physics, University of Oslo, PO Box 1048 Blindern, NO-0316 Oslo, Norway 3Homi Bhabha National Institute, Anushaktinagar, Mumbai, Maharashtra, 400094, India

PSC-4 Slow and fast modulation instability and envelope soliton of ion 75 acoustic waves in fully relativistic plasma having nonthermal electrons Indrani Paul1, Arkojyothi Chatterjee2 and Sailendra Nath Paul1,2 1 Department of Physics, Jadavpur University, Kolkata-700032, India 2East Kolkata Centre for Science Education and Research P-1, B.P.Township, Kolkata-700 094, India

4 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

PSC-5 Effect of negative charge dust on ion-acoustic dressed solitons in 80 unmagnetized plasmas J. K. Chawla, P. C. Singhadiya1, A. K. Sain and S. K. Jain2 Department of Physics, Govt. College Tonk, Rajasthan, India-304001 1Seth RLS Govt. College, Kaladera, Rajasthan, India-303801 2Govt. College, Dholpur, Rajasthan, India-328001

PSC-6 Inductive Energy Storage System with Plasma Opening Switch: A 85 review Kanchi Sunil1, Rohit Shukla1,2, Archana Sharma1,2 1Homi Bhabha National Institute, Mumbai-400094, 2Pulsed Power & Electro-Magnetics Division, Bhabha Atomic Research Centre Facility, Atchutapuram, Visakhapatnam, Andhra Pradesh, India-531011

PSC-7 Simulation Study of Planar Anode Micro Hollow Cathode Discharge 91 Using Dielectric Layer Khushboo Meena1, R P Lamba1 1CSIR-Central Electronics Engineering Research Institute (CSIR-CEERI), Pilani-333031, Rajasthan, India.

PSC-8 Effect of laser pulse profile on controlling the growth of 96 Rayleigh-Taylor instability in radiation pressure dominant regime Krishna Kumar Soni, Shalu Jain, N.K. Jaiman, and K.P. Maheshwari Department of Pure & Applied Physics, University of Kota, Kota-324005 (Rajasthan)

PSC-9 Effect of the nonthermal electrons on ion-acoustic cnoidal wave in 101 unmagnetized plasmas P. C. Singhadiya1, J. K. Chawla2, S. K. Jain 1Seth RLS Govt. College, Kaladera, Rajasthan, India-303801 2Department of Physics, Govt. College Tonk, Rajasthan, India-304001 Govt. College, Dholpur, Rajasthan, India-328001

PSC-10 Target Shape Effects on the Energy of Ions Accelerated in the 106 Radiation Pressure Dominated (RPD) Regime S. Jain, K. K. Soni, N. K. Jaiman, K. P. Maheshwari Department of Pure & Applied Physics, University of Kota, Kota-324005 (Rajasthan)

PSC-11 Effect of magnetic field on the sheath width of a 13.56 MHz radio 111 frequency capacitive argon discharge S Binwal1, S K Karkari2, L Nair1 1Jamia Millia Islamia (A Central University), Jamia Nagar, New Delhi, 110025, India 2Institute for Plasma Research, HBNI, Bhat Village, Gandhinagar, Gujarat, 382428, India

5 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

PSC-12 Dynamics of dust ion acoustic waves in the Low Earth Orbital (LEO) 116 plasma region S. P. Acharya1, a, A. Mukherjee2, b, and M. S. Janaki1, c 1Saha Institute of Nuclear Physics, Kolkata, India 2National University of Science and Technology, “MISiS”, Moscow, Russia

PSC-13 Large amplitude ion-acoustic solitons in plasmas with positrons and 122 two superthermal electrons S. K. Jain1, P. C. Singhadiya2 and J. K. Chawla 1Govt. College, Dholpur, Rajasthan, India-328001 2Seth RLS Govt. College, Kaladera, Rajasthan, India-303801 Department of Physics, Govt. College Tonk, Rajasthan, India-304001

6 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Basic Plasma Experiments & Simulations

7 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL1-1

Cross-field charge particle transport inside a void created by an obstacle inserted in a magnetized plasma column

Satadal Das1, S.K.Karkari2 1 Institute for Plasma Research, Bhat, Gandhinagar, Gujarat 382428, India, HBNI 2 Institute for Plasma Research, Bhat, Gandhinagar, Gujarat 382428, India, HBNI

e-mail: [email protected]

Voids are created inside plasma when a macroscopic object blocks the transmission of charge particles from a high density region to a low density region or during a situation where primary source of ionization is annulled by an obstacle. The phenomena leads to a creation of local space charge, which intern can affect the ion dynamics in the region around the obstacle. Such effects are commonly seen in the case of dusty plasma and around cosmic objects such as commentary tail or an artificial satellite revolving in geo-stationary orbits around the earth. The void formation is common in laboratory plasmas; for example a shadow gets created behind an electrostatic probe or a limiter in a magnetized plasma. The formation of particle free regions in rf discharges under microgravity conditions is also a well-known phenomenon. It was commonly accepted that the ion drag force is responsible for the formation of particle free region in the central part of discharge. The ion drag force is driven by an outflow of positive ions from an ionizing region towards the surrounding particle free diffused region. If the plasma is strongly magnetized, the electric potential created by the void can strongly affect the dynamics of charge particles around the obstacle. In this talk, a study on radial potential and density variation inside a void created in a partially magnetized plasma column shall be presented. The void is created by partially blocking the anode of a hot cathode filament discharge produced in argon. It will be shown that the filling rate of charge particles inside the ionization free region increases with application of magnetic field. With increasing the axial magnetic field strength, the collision probability between charged particles and neutrals increases, which leads to higher drag force. The increase in drag force towards the center leads to faster filling of charged particles inside void. A simple force balance equation in combination with short-circuiting effect is adequate to describe the void formation matching precisely with our experimental data.

References [1] Khrapak, S. A., Ivlev, A. V., Morfill, G. E., & Thomas, H. M. (2002). Ion drag force in complex plasmas. Physical review E, 66(4), 046414. [2] Zafiu, C., Melzer, A., & Piel, A. (2002). Ion drag and thermophoretic forces acting on free falling charged particles in an rf-driven complex plasma. Physics of plasmas, 9(11), 4794-4803. [3] Akdim, M. R., & Goedheer, W. J. (2001). Modeling of voids in colloidal plasmas. Physical Review E, 65(1), 015401. [4] Simon, A. (1955). Ambipolar diffusion in a magnetic field. Physical Review, 98(2), 317. [5] Das, Satadal, and Shantanu K. Karkari. "Positive ion impediment across magnetic field in a partially magnetized plasma column." Plasma Sources Science and Technology (2019). [6] Lieberman, M. A., & Lichtenberg, A. J. (2005). Principles of plasma discharges and materials processing. John Wiley & Sons.

8 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL1-2

Probing Ne ECR plasma to study the gas mixing and anomalous effect

Puneeta Tripathi*, Sushant Kumar Singh, Pravin Kumar Inter-University Accelerator Centre, New Delhi, India-110067

*E-mail: [email protected]

The Electron Cyclotron Resonance (ECR) ion source [1] is well known for producing multiply charged ions with relatively high intensity especially for particle accelerators. The first ECR ion source built by the inventor, (Late) Richard Geller, was reported in early 1970’s. Since then, there have been substantial improvements in its performance due to new emerging technologies. The 4th generation superconducting ECR ion sources show beam intensities in the order of emA, which are remarkable, and have opened up new channels of their applications. Apart from design technologies, the gas mixing experiments [2, 3] also help to build high intensity of highly charged ions in ECR plasmas. In continuation of earlier efforts for understanding the gas mixing and subsequent anomalous effect with Xe and Kr plasma, we recently performed an experiment with pure and mixed (with oxygen and helium gases at various levels) Ne ECR plasma using LEIBF [4] at IUAC, New Delhi, India. The new results are quite interesting and shed more light on the understanding of these two important plasma processes. The charge state distribution of pure, oxygen and helium mixed Ne ECR plasma will be discussed to address the important findings of gas mixing effect and isotope anomaly.

References: [1] R. Geller, Electron Cyclotron Resonance Ion Sources and ECR Plasmas, IOP, Bristol (1996) [2] A G Drentje, Nucl. Instr. and Meth. in Phys. Res. B, 9 (1985) 526 [3] A. G. Drentje, A. Kitagawa, and M. Muramatsu, Rev. Sci. Instrum. 81 (2010) 02B502 [4] P. Kumar, G. Rodrigues, U.K. Rao, C.P. Safvan, D. Kanjilal, A. Roy, Pramana-Ind. J. Phys. 59 (2002)805

9 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL1-3

Electrical conductivity of a plasma confined in a dipole magnetic field: systematic experiments and theory

A. Nanda and S. Bhattacharjee Department of Physics, Indian Institute of Technology Kanpur, India

e-mail: [email protected]

The plasma confined by a dipole magnetic field emerges as the host to a multitude of fascinating physics phenomena, due to its unique confinement scheme while relies on plasma compressibility. For understanding of the underlying transport mechanisms in dipole plasmas, investigation on one of the fundamental properties such as electrical conductivity is inevitable. There have been some reports of earlier works primarily on theoretical progress in conductivity; and their applications to both laboratory and space plasma [1,2]. However, unlike a true dipole field, most of the works consider the magnetic field along a particular direction only [3,4]. One of these pioneering works in the ionospheric plasma assumes a plasma sheet surrounding the earth, by taking the angle of dip into account, and neglecting normal components of the associated electric field [4]. However, despite such advancements, the magnetic geometry and the physics of the real problem do not seem to have been addressed in totality. Therefore, electrical conductivity in a bidirectional (r,) magnetic dipole field still remains unexplored, by including possible couplings between the all the magnetic and the electric field components.

The present study relies on the measurements from a compact dipole plasma device [5,6] having plasma size size of the magnet, and thus the conventional approximations of plasma sheet and unidirectional magnetic field may not hold in the voluminous plasma. To address the problem, a mathematical≫ model is formulated using the momentum equation, by considering the net velocity due to all possible particle drifts. The statistical nature of plasma is preserved by modifying the collision parameter by averaging it over the experimentally measured electron energy distribution function [7]. The Ohm’s law is derived, from which the conductivity dyad is obtained. The dyad constitutes of one Pedersen, two Hall and three longitudinal terms in contrast to the previous works having single terms for each type of conductivity. A unique finding which has not been reported earlier is the explicit magnetic field dependence (both individual and coupled component wise) in the longitudinal terms of the conductivity.

In the colloquium, results of the above-mentioned investigation will be presented. The reason behind the existence of multiple Hall and longitudinal terms, and the explicit field dependence observed in the longitudinal terms will be discussed.

References [1] V. Rohansky, Rev. Plasma Phys., 24, 1-52 (2008). [2] R. A. Trueman et al., Front. Phys.: Space Phys., 1, 31 (2013). [3] P. Porazik et al., Phys. Plasmas, 24, 052121 (2017). [4] K. I. Maeda, Journal of Atmospheric and Terrestrial Physics, 39, 1041 (1977). [5] A. R. Baitha et al., Plasma Res. Express, 1, 045005 (2019). [6] A. R. Baitha et al., AIP Advances, 10, 045328 (2019). [7] G. G. Lister et al., J. Appl. Phys., 79, 12 (1996).

10 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL1-4

Floating potential fluctuations in atmospheric pressure micro-plasma jets

D. Behmani, K. Barman, and S. Bhattacharjee Department of Physics, Indian Institute of Technology, Kanpur, Uttar Pradesh: 208016

e-mail: [email protected]

Potential fluctuations play an important role in the transport of charged particles, and are known to give rise to instabilities in the plasma. Characterization of fluctuations in atmospheric micro-plasma jets is crucial due to its broad applications in biomedicine [1], surface treatment of tissues, cancer cells, and wounds [2], and surface alteration of polymers [3]. Fluctuations and non-uniformities in the potential (or the electrical field) can disrupt the transport and heating of particles penetrating the target surface, which is further known to control the activation energy and adhesive properties of the surface. Therefore, fluctuations of the above-mentioned parameters in the plasma jet must be analysed for the reliability of the applications.

The objective of the current work is to analyse potential fluctuations in atmospheric pressure micro-plasma jets. The plasma is generated inside a glass capillary tube by applying high voltage and charge particles emerge from the capillary in the atmospheric air as a fine plasma jet of ~10 mm in length and ~0.8 mm in diameter. A two-pin probe with a diameter of 0.18 mm and a length of 2 mm each is used to measure the floating potential at two neighbouring points (separated by 0.267 mm) inside the jet.

Conventional techniques such as Fast Fourier transform (FFT) and synchro squeezed time-frequency analysis (TFA) are used to analyse the fluctuations [4]. It is found that most of the fluctuations are of low frequency and lie in the range 0 – 20 kHz. The dependence of fluctuations on the operating parameters such as applied voltage, gas flow-rates, and working gas mixture ratio (helium and argon) has been studied. It has been observed that at a constant flow rate (1 l/min), the fluctuation increases with increase in the applied voltage (from 7 kV to 11 kV), then achieves a maximum value at 11 kV, owing to the high discharge current at that particular voltage and then decreases. At a fixed applied voltage of 14 kV, when the gas flow rate is increased, the plasma jet becomes turbulent at a flowrate of 3 l/min and the turbulent regime has a significantly higher level of fluctuations. In the case of a gaseous mixture of He and Ar, various general properties of argon gas, e.g. poor thermal conductivity and lower ionization potential relative to helium gas, make the argon jet extremely unstable than the helium jet. Time-frequency analysis also helps to understand the fluctuating behavior of the micro-plasma jet, where the temporal behavior of the frequencies can be observed. The present research is helpful in choosing suitable operating parameters and gas as per the requirements of the application.

References [1] Sousa J S, Niemi K, Cox L, Algwari Q T, Gans T and O'connell D J. Appl. Phys. 109 123302 (2011). [2] Tian W, Lietz A M, and Kushner M J Plasma Sources Sci. Technol. 25 055020 (2016). [3] Penkov O V, Khadem M, Lim W S and Kim D E J. Coat. Technol. Res. 12 225-235 (2015). [4] Tu X, Yan J, Yu L, Cen K and Cheron B Appl. Phys. Lett. 91 13 (2007).

11 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL1-5

Comparative study of plasma antenna and monopole metal antenna

Manisha Jha1, Nisha Panghal, Dr. Rajesh Kumar 1Institute for Plasma Research, Gujarat

e-mail: [email protected]

Plasma antenna is a column of ionized gas which can be used to receive and transmit electromagnetic waves for communication, stealth and radar purpose. The change in the plasma density can help to reconfigure the antenna electrically rather than mechanically. This property of plasma antenna makes it more attractive than a conventional metal antenna. In this paper, a monopole plasma antenna is designed in CST for communication in VLF range. Further a comparative study between the monopole metal and plasma antenna is done in terms of return loss, VSWR, gain, Bandwidth which shows that the metal can be replaced by plasma column in antennas.

References [1]Rajneesh Kumar,Study of RF Produced Plasma Columns thesis by, Gujarat University, and Ahmedabad [2]Theodore Anderson, Plasma Antennas

12 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL1-6

Magnetic field effects on 13.56 MHz capacitive coupled radio-frequency sheaths

S Binwal1, S K Karkari2, L Nair1 1Jamia Millia Islamia (A Central University), Jamia Nagar, New Delhi, 110025, India 2Institute for Plasma Research, HBNI, Bhat Village, Gandhinagar, Gujarat, 382428, India

e-mail: [email protected]

Radio-frequency discharges produced by capacitive driven parallel plate electrodes are widely popular in semi-conductor industries for the processing of silicon substrates. The ion energy and ion flux are the two important parameters in the discharge which governs the physical and chemical processes happening at the substrate. The ions are mainly accelerated inside the sheaths where almost the entire rf voltage is concentrated. The sheath region depends on the plasma parameters namely the electron density, electron temperature and the potential drop across the sheaths. External means of controlling the plasma parameters is necessary by means of which the plasma processes at the substrates can be tailored. This may be achieved by introducing an external magnetic field, which can enhance the discharge efficiency by influencing the collision rate [1]. Not only will the magnetic field confine the charge particles inside the bulk plasma, it will also affect the sheath impedance which controls the rf current flowing through the discharge. Simulation studies have recently demonstrated the effect of magnetic field on the electron temperature and the sheath width in capacitive discharges. However the experimental measurements could not be performed due to the sheath dimensions being extremely small.

In this paper we discuss about a non-invasive method for determining the sheath width in a 13.56 MHz rf discharge in the presence of an external magnetic field. Further, the effect of magnetic field, discharge current and pressure on the capacitive sheaths is investigated. The experimental results report almost 55.5 % reduction in the sheath width for the argon discharge operating at 1.0 Pa background pressure and 7.0 mT of applied magnetic field compared with the unmagnetized case. The results suggest that the magnetic field can be used as a controlling knob to tune the sheath width and hence the ion bombarding energy in a single frequency capacitive discharge. This can enable the user to optimize the processing window in a desirable manner.

References [1] Passive inference of collision frequency in magnetized capacitive argon discharge. Physics of Plasmas 25.3 (2018)

13 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL1-7

Does the fate of 2D incompressible high Reynolds number turbulence depend on initial conditions? : A revisit!

Shishir Biswas1, Rajaraman Ganesh1 1Institute for Plasma Research, Bhat, Gandhinagar, Gujarat 382428, HBNI, India.

e-mail: [email protected]

In two dimensional (2D) incompressible, nearly inviscid fluid turbulence, inverse cascade of vorticity is enforced as total energy and total circulation are nearly conserved, along with several weakly conserved higher order Casimirs [1]. In the past, several competing “extremization” ideas have been looked into, to “predict” the final or late-time fate of this inverse cascade process, such as, a fluid entropy extremization model [1] and a fluid enstrophy extremization model [2,3]. In the past, these models have also been looked into using numerical simulations. In this work, using a newly developed, 2D high precision, very large scale GPU solver which can handle grid sizes easily, we revisit the above discussed idea: does one always obtain the same final state of vorticity at large scales or are there pockets of initial conditions which would lead toth very different late time large scale vorticity profiles? We consider initial conditions with various values of initial total positive circulation = and initial total negative circulation as = control+ parameters+ [1], where = is Ct ωt x,y,t = t dx dy fluid vorticity and investigate− − numerically, the fate of long time states. Several interesting t t observations obtained willC be presented.ω x,y,t = t dx dy ωz ∇ × v

References [1] Studies in Statistical Mechanics of Magnetised Plasmas: A Thesis [1998]: Rajaraman Ganesh [IPR]. [2] Montgomery D, Matthaeus WH, Stribling WT, Martinez D, Oughton S. Relaxation in two dimensions and the ‘‘sinh Poisson’’equation. Physics of Fluids A: Fluid Dynamics. 1992 Jan; 4(1):3-6. [3] Matthaeus WH, Stribling WT,‐ Martinez D, Oughton S, Montgomery D. Selective decay and coherent vortices in two-dimensional incompressible turbulence. Physical review letters. 1991 May 27; 66(21):2731.

14 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL1-8

Study on ion re-circulation and potential well structure in an inertial electrostatic confinement fusion device using 2D-3V PIC simulation

D. Bhattacharjee1, S. Adhikari2, N. Buzarbaruah1 & S. R. Mohanty1, 3 1Center of Plasma Physics-Institute for Plasma Research, Sonapur, Kamrup(M), Assam, 780402, India. 2Department of Physics, University of Oslo, PO Box 1048 Blindern, Oslo, Norway. 3Homi Bhabha National Institute, Anushaktinagar, Mumbai, Maharashtra, 400094, India.

e-mail: [email protected]

Kinetic simulations are performed using PIC (Particle-in-Cell) method to study the ion behavior inside a table-top neutron source, Inertial Electrostatic Confinement Fusion (IECF) device. In this device, lighter ions are accelerated, re-circulated and concentrated at the center by using an electrostatic field. These ions are capable of producing fusion at the central region of the cathode during high voltage operations [1, 2]. An open source PIC code, XOOPIC [3] is used to simulate the ion dynamics for different experimental conditions. The potential structure from the simulation indicates the formation of multiple potential well inside the cathode depending upon the applied cathode voltage (ranging from -1kV to -5kV) and the number of cathode grid wires. The ion density at the core region of this device has been observed to be of the order of 1016 m-3, which closely resembles the exact experimentally obtained results. The ion energy distribution function (IEDF) has been measured from the phase space at different locations to identify the patterns of ion dynamics for different grid assembly and experimental conditions. Finally, the simulated results are compared with the experimental results, measured using different Langmuir probes.

References

[1] R. Hirsch, J. Appl. Phys., 38, 4522 (1967). [2] N. Buzarbaruah, S.R. Mohanty and E. Hotta, Nucl. Instrum. Methods Phys. Res. Sec. A, 911, 66 (2018). [3] J.P. Verboncoeur, A.B. Langdon and N.T. Gladd, "An Object-Oriented Electromagnetic PIC Code", Comp. Phys. Comm., 87, 199 (1995).

15 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL1-9

Molecular dynamics simulation of collisional cooling of He and its binary mixtures with Ne, Ar, Kr and Xe for creating strongly coupled cryoplasmas

S. S. Mishra and S. Bhattacharjee Department of Physics, IIT Kanpur, India

e-mail: [email protected]

Cryoplasmas are microplasmas created at extremely low temperatures (below room temperature to 4K) and usually at atmospheric pressure. They are expected to provide a firm base to understand the physics of strongly coupled plasma systems, where the coupling parameter (gamma) (the ratio of mean Coulomb interaction energy of the particles to their mean kinetic energy) would be greater than or equal to 1. The relatively simpler production mechanism and large plasma lifetimes as compared to conventional laser-based techniques, makes them attractive. In these weakly ionized plasmas, the neutral gas acts as a controlling agent for manipulating the plasma parameters (electron/ion temperature and density), which in turn, allows to control the gamma values of the plasma. To this effect, the gas temperature dependence of plasma parameters in Helium cryoplasma has been investigated earlier [1]. However, the exact influence of neutral gas interactions at low temperatures on the plasma properties, remains an open question. In order to answer this question, two studies are vital: (i) proper knowledge of the correct interaction potential acting between the gaseous atoms, and (ii) the efficiency of collisional cooling of gaseous atoms and eventually the cooling of plasma species through the interactions with the neutral atoms in such low temperatures (~10K). Conventionally, the Lennard-Jones (LJ) potential is employed to model the gases, however, at low temperatures often discrepancies arise as the gas properties significantly deviate from their ideal behavior. Therefore, the applicability of the LJ potential must be scrutinized in the aforementioned temperature range. In order to investigate the cooling process of He gas and the effect of gas mixing of He with other noble gases such as Ne, Ar, Kr and Xe, on the process, a molecular dynamics simulation has been set up using LAMMPS [2]. To replicate the cooling mechanism used in cryoplasma experiments, the working gas, which is initially at 300K, is put in contact with the cold metallic walls, maintained at 10K. This will help in elucidating the collisional cooling process involved. Initially, the interactions among the gases are to be guided by LJ potential. To model the interactions of unlike gas atoms, two types of mixing rules are employed: Lorentz–Berthelot and Fender–Halsey [3]. In the colloquium, the cooling rate of pure He system and the mixtures will be presented. The effect of mass and interaction strength of secondary gas on the cooling rate of He are to be discussed. The performance of the LJ potential, and both the mixing rules, will be ascertained by comparing the transport properties with the available experimental results [4].

References [1] Y. Noma et al., J. Appl. Phys., 109, 053303 (2011). [2] S. Plimpton, J. Comp. Phys 117, 1(1995). [3] A. Frijns et. al., Micromachines, 11, 319 (2020). [4] A. Rahaman, Phys. Rev. A., 2, 136 (1964).

16 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL1-10

Effects of flow Velocity and Density of Dust Layers on the Kelvin-Helmholtz Instability in Strongly Coupled Dusty Plasma: Molecular Dynamic Study

Bivash Dolai and R. P. Prajapati Department of Pure and Applied Physics, Guru Ghasidas Vishwavidyalaya, Bilaspur-495009 (C.G.), India

e-mail: [email protected]

The effect of different velocities and density of flowing dusty plasma layers are investigated on hydrodynamic Kelvin-Helmholtz (K-H) instability. The dust particles are too massive as compared to the electrons and ions. Therefore, the electron and ion fluids are taken to be light Boltzmann fluid and they only contributes as the neutralizing background to the charged dust grains. The dust particles are interacting through the Yukawa potential. Thus, the system can be termed as Yukawa one component fluid. The problem has been simulated using the MD simulation technique through open source LAMMPS code. We consider the two layers of such Yukawa one component fluids with same and different dust density, and different velocity profiles. The effect of different flow velocities, flow direction and different density are studied on the K-H instability. We have calculated the growth rate of the K-H instability for such configurations. For excitation of K-H instability, the magnitude of the equilibrium velocity of fluid must be greater than the dust thermal velocity. It is found that the dust flow velocity and density gradient enhance the growth rate of the K-H instability.

References [1] J. Ashwin and R. Ganesh, Phys. Rev. Lett. 104, 215003 (2010). [2] S. K. Tiwari, A. Das, D. Angom, B. G. Patel and P. Kaw, Phys. Plasmas 19, 073703 (2012). [3] V. S. Dharodi, S. K. Tiwari, and A. Das, Phys. Plasmas 21, 073705 (2014).

17 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL1-11

Simulation Study of Planar Anode Micro Hollow Cathode Discharge Using Dielectric Layer

Khushboo Meena1, R P Lamba1 1CSIR-Central Electronics Engineering Research Institute (CSIR-CEERI), Pilani-333031, Rajasthan, India.

email: [email protected]

Microdischarges are very popular for a long time and they have many advantages due to their small size [1]. Micro Hollow Cathode Discharge(MHCD) is one of the micro discharge which is formed in the cylindrical shaped hollow cathode and responsible for the generation of high electron density discharge, but it has a very short period of a lifetime due to the sputtering effect on the cathode walls and moving of the discharge from glow to arc region [2]. There is another type of discharge called Dielectric Barrier Discharge(DBD)which is also known as silent discharge as well as Ozone production discharge. In this discharge single or double dielectric barrier layers are used between electrodes so, it has the advantage of low electrode erosion. So for benefitting the effect of both the discharges DBD and MHCD in a single model we combined both the discharge for the generation of high electron density without moving from glow to arc discharge and for increasing the life span of the discharge by overcoming the sputtering effect a hollow cathode structure. In this paper, a 2D-axis symmetric model is designed and simulated using the Plasma Module of COMSOL 5.4 Software [3]. This model includes the MHCD as well as DBD discharge. In this model, a dielectric layer of 40µm is placed on the inside wall of the anode. In this model, a planar anode is used which is covering one side of the hollow cathode. The diameter of the hollow cathode is 500µm and a height of 500µm is used. Argon gas is used for the discharge at atmospheric pressure. Pulsed voltage is applied to have the 1000ns period cycle. In this model for the ignition of the discharge takes place at the minimum distance between anode and cathode. After that discharge gets sustained in the hollow cathode cavity and attains the stable abnormal glow discharge having high electron density in the order of 1018 m-3.

References [1] A.D. White, “New hollow cathode glow discharge”, J. Appl. Phys. 30 711–719(1959). [2] C. Meyer, Daniel Demecz, E. L. Gurevich, U. Marggraf, G. Jestel, J. Franzke, J. Anal. At. Spectrom., 27, 677, (2012). [3] COMSOL Multiphysics Documentation, 2019, [online] Available: http://www.comsol.co.in.

18 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Fusion Science & Technology

19 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL2-1

Impact of Energetic Particles in the First-Wall Erosion in Fusion Power Reactors

P. N. Maya and S.P. Deshpande 1Institute for Plasma Research, Bhat, Gandhinagar, 382428, Gujarat, India

e-mail: [email protected]

Plasma-wall interactions in a fusion power reactor are significantly more complex than the present-day tokamaks due to the presence of highly energetic fusion products (14 MeV neutrons, 3.5 MeV alpha-particles), externally injected impurities along with charge-exchange neutrals. The non-linear interaction of these particles along with the hydrogen isotope plasma with the plasma-facing components can alter the fundamental processes of erosion, redeposition and consequently the impurity generation and transport in a tokamak. The energetic ion distribution on the first-wall is rather asymmetric and this results in additional erosion and redeposition zones on the first-wall. In this article we discuss the erosion of the first-wall material due to fast-alpha particles and charge-exchange H-isotope neutrals on the first-wall of fusion power reactors. For alpha particles, we will show the influence of different poloidal distributions of fast-ions in the erosion. We also discuss the effect of different first-wall materials in the impurity generation such as carbon, tungsten, lithium etc. An extrapolation of these results for different geometry and aspect ratio of the tokamak will be presented.

20 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL2-2

Disruptions study in Aditya-U Tokamak

Suman Dolui1,2, Kaushlender Singh1,2, Tanmay Macwan1,2, Harshita Raj1,2, Suman Aich1, Rohit Kumar1, K A Jadeja1, K M Patel1, V K Panchal1,S.Purohit, M.B Chowdhuri, R L Tanna1, J. Ghosh1,2 and ADITYA-U Team1 1 Institute for Plasma Research, Bhat, Gandhinagar, India, 382428 2Homi Bhabha National Institute, Mumbai, India, 400094

e-mail: [email protected]

Disruptions in tokamak, is a sudden loss of magnetic confinement of plasma. A huge amount of plasma current abruptly terminate in a few ms. As a consequence, plasma facing components and the vessel are encountered by huge amount of heat loads and electromagnetic force. Hence, due to disruption there is a chance of severe damage to the system. Avoidance of disruption [1] and real time mitigation is a very important field of work in tokamak. There are many possible causes for disruption. Disruption is a multidimensional catastrophic phenomena. Many number of disrupted plasma discharges have been studied in Aditya-U tokamak. Behavior of plasma parameters during disruption has been noticed carefully. It has been noticed that how some parameters like ‘rise rate of current’ in ramp-up phase , edge-q value[2] play a role in plasma disruptions and how they are incorporated with other parameters like amount of impurity , vertical magnetic field , error filed , plasma density and temperature. Overall it is being tried to create a plasma parameter space where the plasma production may be operated safely. Underlying physics of such phenomena also has been explored.

References

[1] ‘Novel approaches for mitigating runaway electrons and plasma disruptions in ADITYA tokamak’, R.L. Tanna et al 2015 Nucl. Fusion 55 063010. [2] Characterization of the plasma current quench during disruptions in ADITYA Tokamak’, Shishir Purohit et al 2020 Nucl. Fusion

21 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL2-3

Simulation of runaway electron generation in fusion grade tokamak and suppression by impurity injection

Ansh Patel1, Santosh P. Pandya2 1School of Liberal Studies, Pandit Deendayal Petroleum University, Gandhinagar, India 2Institute for Plasma Research, Bhat, Gandhinagar, India.

e-mail: [email protected]

During disruptions in fusion-grade tokamaks like ITER, large electric fields are induced following the thermal quench period which can generate a substantial amount of Runaway Electrons (RE) that can carry up to 10 MA current with energies as high as several tens of MeV [1-3]. These runaway electrons can cause significant damage to the Plasma Facing Components due to their localized energy deposition. To mitigate these effects, impurity injections of high-Z atoms have been proposed [1-3]. In our talk, we use a self-consistent 0D tokamak disruption model as implemented in PREDICT code [6] which has been upgraded to take into account the effect of impurity injections on RE dynamics as suggested in [4-5]. Dominant RE generation mechanisms such as the secondary avalanche mechanism as well as primary RE-generation mechanisms namely Dreicer, hot-tail, tritium decay and Compton scattering (from γ-rays emitted from activated walls) have been taken into account. These different RE-generation mechanisms provides seed RE-electrons of different amount and corresponding maximum amplitude of RE-current (Left plot below). In these simulations, the effect of impurities is taken into account considering collisions of REs with free and bound electrons as well as scattering from full and partially-shielded nuclear charge. These corrections were also implemented in the relativistic test particle model to simulate RE-dynamics in momentum space. We show that the presence of impurities has a non-uniform effect on the Runaway Electron Distribution function (Right plot below). Low energy RE (a few MeV) lose their energy due to collisional dissipation while the high energy RE are scattered in momentum space and dissipate their energy due to higher synchrotron backreaction due to its dependence on total energy and pitch-angle. We show that the combined effect of pitch-angle scattering induced by the collisions with impurity ions and synchrotron emission loss results in the faster dissipation of RE-energy distribution function [7]. The variation of different RE generation mechanisms during different phases of the disruption, mainly before and after impurity injections is reported.

Dissipation of High RE-energy energy distribution RE function

Average RE-energy Impurity injection at t=30 ms Ar = 1e+20 m-3

Low energy RE References:

22 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

[1] M. Lehnen, et.al., Journal of Nuclear Materials, 463, pp39-48, (2015) [2] E. M. Hollmann, et. al., Physics of Plasmas, 22, 021802, (2015) [3] M. Lehnen, et.al., ITER Disruption mitigation workshop, Report:ITR-18-002, (2018) [4] J. R. Martín-Solís, et.al., Physics of Plasmas, 22, 092512, (2015) [5] J. R. Martín-Solís, et.al., Nucl. Fusion , 57, 066025 (2017) [6] Santosh P. Pandya, PhD thesis, AIXM0036, Aix-Marseille University, France, (2019) [7] Ansh Patel, et.al., PTS-2020, MF-02, Abstract#45, (2020)

23 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL2-4

Simultaneous measurement of thermal conductivity and thermal diffusivity of ceramic pebble bed using transient hot-wire technique

Harsh Patel1, 2,*, Maulik Panchal1, Abhishek Saraswat1, Paritosh Chaudhuri1, 2 1Institute for Plasma Research, Bhat, Gandhinagar – 382428, India 2Homi Bhabha National Institute, Anushaktinagar, Mumbai – 400094, India

*E-mail address: [email protected]

Lithium-based ceramics in the form of pebble beds have been considered as tritium breeder material in the breeder blanket of the fusion reactor. It is very essential to study thermal characteristics of these ceramic pebble beds subjected to fusion relevant conditions. Thermal conductivity ( ), thermal diffusivity ( ) and specific heat ( ) of a packed bed are some of the important parameters for the design of breeder blanket module. In the present study, the transient hot-wire technique based experimental setup has been designed and fabricated to measure , and of Indian made lithium metatitanate (Li2TiO3) pebble bed. Thermal properties of Li2TiO3 pebble bed (1 ± 0.15 mm pebble diameter and 63% packing fraction) are measured within the temperature range of 45°C to 800°C in stagnant helium gas environment. In addition to this, the effect of gas pressure variation for the range of 0.105 MPa to 0.4 MPa has also been studied. Empirical equations are suggested for and of Li2TiO3 pebble bed as a function of temperature at different pressure in helium environment.

References

[1] S. Pupeschi, R. Knitter, and M. Kamlah, “Effective thermal conductivity of advanced ceramic breeder pebble beds,” Fusion Eng. Des., vol. 116, pp. 73–80, 2017.

[2] M. Panchal, C. Kang, A. Ying, and P. Chaudhuri, “Experimental measurement and numerical modeling of the effective thermal conductivity of lithium meta-titanate pebble bed,” Fusion Eng. Des., vol. 127, no. October 2017, pp. 34–39, 2018, doi: 10.1016/j.fusengdes.2017.12.003.

[3] M. Panchal, A. Saraswat, S. Verma, and P. Chaudhuri, “Measurement of effective thermal conductivity of lithium metatitanate pebble bed by transient hot-wire technique,” Fusion Eng. Des., vol. 158, no. April, p. 111718, 2020, doi: 10.1016/j.fusengdes.2020.111718.

24 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL2-5

A DDPM-DEM-CFD flow characteristic analysis of pebble bed for fusion blanket

Chirag Sedania,b*, Paritosh Chaudhuria,b a Institute For Plasma Research, Bhat, Gandhinagar, Gujarat, 382428, India. b Homi Bhabha National Institute, Anushaktinagar, Mumbai, 400094, India.

*Corresponding E-mail id: [email protected]

In a solid breeder blanket the functional material, lithium ceramics are kept in the form of pebble bed. Helium is used as purge gas which flows through the pebble bed. The flow characteristics are important in consideration of design and run the breeding blanket efficiently which depends on the arrangement of the pebble bed. In the present study, a computational model of unitary pebble bed was conducted using DDPM-DEM-CFD to study the purge gas flow characteristics of the gas in the pebble bed. The parameters which affect the flow characteristics are porosity, pressure distribution, and pressure drop and wall effect. The velocity distribution near the wall region was observed to have many fluctuations. The results show that the DDPM-DEM-CFD simulation model has an error with about 6% for estimating pressure drop when compared with the empirical equation (Ergun Equation). Also, an Artificial Neural Network (ANN) is used to predict the pressure drop. ANN is a machine learning technique which predicts the outcome based on the training given using the data set. Here, the data set is generated using the Ergun equation and then it is trained for the prediction. The results of the simulation are found to be in good agreement with the Ergun equation and ANN prediction.

References:

[1] P.J. Gierszewski, J.D. Sullivan, Ceramic sphere-pac breeder design for fusion blankets, Fusion Engineering Design 17 (1991) 95-104.

[2] A. Ying, A. Akiba, L.V. Boccaccini, S. Casadio, G. Dellórco, M. Enoeda, K. Hayashi, J.B. Hegeman, R. Knitter, J. van der Laan , J.D. Lulewicz, Z.Y. Wen, Status and perspective of the R&D on ceramic materials for testing in ITER, Journal Nuclear Materials 367-370 (2007) 1281-1286.

[3] A. Abou-Sena, f. Arbeiter, L.V. Boccaccini, J. Rey, G. Schlindwein, Experimental study and analysis of the purge gas pressure drop ccross the pebble bed for the fusion HCPB blanket, Fusion Engineering and Design, 88 (2013) 243-247.

[4] F. Augier, f.Idoux, J.Y. Delenne, Numerical Simulations of transfer and transport properties inside packed beds of spherical particles, Chem. Eng. Sci. 65 (2010) 1055-1064.

25 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

[5] T. Eppinger, K. Seidler, M. Kraume, DEM-CFD simulations of fixed bed reactors with small tube diameter ratios, Chem. Eng. J. 166 (2011) 324-331.

[6] G.D. Wehinger, T. Eppinger, M. Kraume, detailed numerical simulations of catalytic fixed-bed reactors: heterogeneous dry reforming of methane, Chem. Eng. Sci. 122 (2015) 197-209.

[7] Y. Seki, K. Ezato, K. Yokoyama, et al., A Study on Flow Field of Purge Gas for Tritium Transfer Though Breeder Pebble Bed in Fusion Blanket, NTHAS8,Beppu, Japan, 2012, pp. 9–12, December.

[8] A. Ali, A. Frederik, V.B. Lorenzo, et al., Experimental study and analysis of thepurge gas pressure drop across the pebble beds for the fusion HCPB blanket, Fusion Eng. Des. 88 (4) (2013) 243–247.

[9] Youhua Chen, Lei Chen, Songlin Liu, Guangnan Luo, Flow characteristic analysis of purge gas in unitary pebble bed by CFD simulation coupled with DEM geometry model for fusion blanket, Fusion Engineering and Design, 114 (2017) 84-90.

[10] https://www.itascacg.com

[11] https://www.ansys.com/products/fluids/ansys-fluent

[12] https://www.ansys.com/en-in

[13] P. A. Cundall and O. D. L. Strack. "A Discrete Numerical Model for Granular Assemblies". Geotechnique. 29. 47–65. 1979.

[14] H. Hertz. “Über die Berührung fester elastischer Körper”. Journal für die reine und angewandte Mathematik. 92. 156-171. 1881.

[15] Reimann, J., Vicente, J., Ferrero, C. Rack, A., Gan, Y. (2020) 3d tomography analysis of the packing structure of spherical particles in slender prismatic containers. International Journal of Materials Research. 111(1): 65-77.

[16] Reimann, J., Vicente, J., Brun, E., Ferrero, C., Gan, Y., Rack, A. (2017) X-ray tomography investigations of mono-sized sphere packing structures in cylindrical containers. Powder Technology, 318: 471-483.

[17] Moscardini, M., Gan, Y., Pupeschi, S., Kamlah, M. (2018) Discrete element method for effective thermal conductivity of packed pebbles accounting for the Smoluchowski effect. Fusion Engineering and Design, 127: 192-201.

[18] H. Calis, J. Nijenhuis, B. Paikert, F. Dutzenberg, C. van Den Bleek, CFD modeling and experimental validation of pressure drop and flow profile in a novel structured catalytic reactor packing, Chem. Eng. Sci. 56 (2001) 1713-1720.

[19] R.K. Reddy, J.B. Joshi, CFD modeling of pressure drop and drag coefficient in fixed and expanded beds, Chem. Eng. Res. Des. 86 (2008) 444-453.

26 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

[20] A. G. Dixon, M. Nijemeisland, E.H. Stitt, Packed tubular reactor modeling and catalyst design using computational fluid dynamics, Advance in Chemical Engineering 31 (2006) 307-389. [21] Gupta AK, Guntuku SC, Desu RK, Balu A (2015) Optimisation of turning parameters by integrating genetic algorithm with support vector regression and artificial neural networks. Int J Adv Manuf Technol 77(1–4):331–339.

[22] Prasad KS, Desu RK, Lade J, Singh SK, Gupta AK (2013) Finite element modeling and prediction of thickness strains of deep drawing using ANN and LS-Dyna for ASS304. AIP Conf Proc 1567(1):402–405.

[23] Gupta AK (2010) Predictive modelling of turning operations using response surface methodology, artificial neural networks and support vector regression. Int J Prod Res 48(3):763–778.

[24] Desu, R. K., Peeketi, A. R., & Annabattula, R. K. (2019). Artificial neural network-based prediction of effective thermal conductivity of a granular bed in a gaseous environment. Computational Particle Mechanics, 6(3), 503-514.

[25] S. Ergun, Fluid flow through packed bed columns, J. Mater. Sci. Chem. Eng. 48 (1952) 89-94.

27 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL2-6

Initial results of Laser Heated Emissive Probes operated in cold condition in Aditya-U Tokamak

A. Kanik1, A. Sarma1,2, J. Ghosh3, R. L. Tanna3, M. Shah3, T. Macwan3,4, S. Aich3, S. Patel3,5, K. Singh3,4, S. Duloi3,4, R. Kumar3, K. Jadeja3, K. Patel3 and ADITYA-U team 1Vellore Institute of Technology (Chennai) 2North East Centre for Training and Research (Shillong) 3Institute for Plasma Research (Gandhinagar) 4Homi Bhabha National Institute 5Birla Institute of Technology and Science (Jaipur)

e-mail: [email protected]

Measurement of a plasma potential spatial, azimuthal and radial profiles is a challenging task since ages and not many diagnostics can perform the task with accuracy. Langmuir probes have been used for indirect measurements of the plasma potential and other plasma parameters in almost every plasma devices. Despite of the fact of existence of many theories and experimental techniques, the percentage of error in observations is significant that becomes more intense with high magnetic fields. Emissive probe are efficient tools and excellent substitutes to Langmuir probes for direct measurement of plasma potential and it’s fluctuations with comparably more accuracy and have been an active diagnostics in many devices. Despite of the fact of the existence of many theories and experimental techniques, the percentage of error in observations is significant. In this paper, we report the measurement of floating potential and its fluctuations in edge region of ADITYA-U tokamak. An assembly for measurement of potential in the edge region of ADITYA-U tokamak plasma was designed, fabricated and installed for the first time. A novel experimental arrangement for the said measurements has been developed and installed on the ADITYA-U tokamak making use of an actuator which enables measurements up to 50 mm inside the limiter.

References [1] Vara Parasad Kella et al, Review of Scientific Instruments, 87, 043508 (2016) [2] J P Sheehan and N Hershkowitz, Plasma Sources Sci. Technol., 20 063001 (2011)

28 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL2-7

Evidence Of Non-local Transport in ADITYA-U Tokamak

T. Macwan1,2, H. Raj1,2, S. Dolui1,2, K. Singh1,2, S. Patel1,3, P Gautam1, N. Yadava1,4, J Ghosh1,2, R L Tanna1,2, K A Jadeja1, K M Patel1, R. Kumar1, S. Aich1,VK Panchal1, U. Nagora1,2, J. Raval1, D. Kumawat1, M B Chowdhuri1, R Manchanda1, P. K. Chattopadhyay1,2, A Sen1,2, R Pal1,5 and ADITYA-U Team1

1Institute for Plasma Research, Gandhinagar 382 428 2Homi Bhabha National Institute, Mumbai, 400 085 3Pandit Deendayal Petroleum University, Gandhinagar 382 007 4 The National Institute of Engineering, Mysuru 570 008 5 Saha Institute for Nuclear Physics, Kolkata 700 064

e-mail: [email protected]

One of the main challenges for the successful operation of future devices like ITER is the predictive capability of various transport models. The energy and particle transport in a tokamak is dominated by microscopic instabilities, which are assumed to be local. The locality here refers to the local gradients in density and temperature which gives rise to fluctuating fields, which are responsible for the diffusive transport across the magnetic field lines. However, recent experiments have revealed a non-locality in the heat and momentum transport [2]. Particularly, a phenomena known as ‘cold pulse propagation’ is considered a prime example of non-local transport. It is marked by an increase in the core temperature when the edge plasma is cooled, on a time scale faster than the diffusive time scales. It is triggered by injecting a trace amount of impurities in the plasma edge or with supersonic molecular beam injection (SMBI). In ADITYA-U tokamak, the cold pulse propagation is triggered by multiple puffs of H2 gas, which are usually used for plasma fuelling. Here, the dynamics of cold pulse in ADITYA-U is studied with the variation of the gas puff amount.

References [1] W. Horton, Rev. Mod. Phys., 71, 735 (1999) [2] K. Ida, Nucl Fusion, 55, 19 (2015)

29 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL2-8

Parametric Study of SMBI CD Nozzle for ADITYA-U Tokamak

Kaushlender Singh1,2, Suman Dolui1,2, Tanmay Macwan1,2, B Arambhadiya1,KA Jadeja1, K M Patel1, Siju George1,Sharvil Patel1,3 , Harshita Raj1,2, Ankit Kumar1,2, Suman Aich1, Rohit Kumar1, Y Pravastu1, D C Raval1, V K Panchal1, R L Tanna1,J Ghosh1,2 and ADITYA-U Team1

1 Institute for Plasma Research, Bhat, Gandhinagar, India, 382428 2Homi Bhabha National Institute, Mumbai, India, 400094 3 Pandit DeenDayal Petroleum University, Gandhinagar, India, 382007

e-mail: [email protected]

Converging diverging (CD) nozzle is one of the most important and fundamental inventions in the course of science. Several engineering and scientific advancements utilize the concept of compressible flows through CD nozzle [1]. Among its important uses, CD nozzles are also being used for Supersonic Molecular Beam Injection (SMBI) as a fueling technique for tokamaks [2]. While designing the SMBI system, we need to study various properties related to the geometrical design of the nozzle. Many important operational parameters such as Mach disk location [3], cluster formation [4], number of injected molecules, and variation of Mach number depend on the design of the CD nozzle [1] [5]. These can be optimized by simulation and analytic study of the CD nozzle’s geometry [1]. In this paper details of the recent upgrades in the installed SMBI system and parametric study of SMBI CD nozzle for ADITYA-U tokamak will be presented.

References [1] Jagmit Singh, Luis E. Zerpa, Benjamin Partington and Jose Gamboa, Heliyon 5 e01273 (2019) [2] Wang En-yao et al Sci. Technol. 3 673 (2001). [3] Wen S. Young, The Physics of Fluids 18, 1421 (1975). [4] O.F. Hagena and W. Obert, J. Chem. Phys. 56 (1972) 1793. [5] He, X., Feng, X., Zhong, M. et al. J. Mod. Transport. 22, 118–121 (2014).

30 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL2-9

Study of Sawtooth Induced Heat Pulse Propagation in the ADITYA Tokamak

S. Patel1, J. Ghosh2,3, M. B. Chowdhury2, K. B. K. Mayya1, T. Macwan2,3, R. Manchanda2, S. Aich2, S. Dolui2,3, K. Singh2,3, R. Kumar2, R. L. Tanna2, T. K. A. Jadeja2, K. Patel2, J. Raval2, V. Kumar2, S. Joisa2, P. K. Atrey2, U. C. V. S. Rao2, P. Vasu2, S. B. Bhatt2, Y. C. Saxena2, and ADITYA Team2

1Pandit Deendayal Petroleum University, Gandhinagar, Gujarat 382007 2Institute for Plasma Research, Gandhinagar, Gujarat 382428 3HBNI, Anushaktinagar, Mumbai, Maharashtra 400094

e-mail: [email protected]

Sawtooth instability is the commonly observed phenomena in all class of tokamak and have been widely used to understand and test the theoretical models for the transport of heat in tokamak device [1,2]. Sawtooth remains one of the active areas of research in thermonuclear fusion physics, considering removal of helium ash and impurity control in the plasma core [3]. In ADITYA tokamak, in many plasma discharges, sawtooth are observed for nearly entire duration providing original source of heat perturbation. In these plasma discharges, corresponding to sawtooth crash, inverted sawtooth are observed in spectral line emission emitting from the edge region of plasma. The time-lag analysis of soft X-ray and signal shows that sawtooth pulse propagates from core to edge region within 200 ec. To explain such fast propagation of sawtooth induced heat pulse, higher values of thermal diffusivity, about ten times that of thermal diffusivity estimated from power balance is required. To understand this phenomenon, present study investigates the effect of sawtooth crash in fast propagation of heat pulse in plasma discharges of ADITYA tokamak.

References [1] E. D. Fredrickson, M. E. Austin, R. Groebner et al., Phys. Plasmas, 7, No. 12, (2000). [2] M W Kissick et al Nucl. Fusion, 38, 821, (1998) [3] ITER Physics Expert Group on Disruptions, Plasma Control, and MHD et al Nucl. Fusion, 39, 2577 (1999).

31 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL2-10

Calculation Of Toroidal and Poloidal Rotation in Aditya-U Tokamak

Ankit Kumar1,2, G Shukla3, K Shah3 , Tanmay Macwan1,2 , Kaushlender Singh1,2 , Suman Dolui1,2 , M.B.Chawdhuri1, R Manchanda1, R.L.Tanna1, J.Ghosh1,2 , Aditya Team1 1Institute for Plasma Research, Bhat, Gandhinagar 382 428, India 2HBNI, Training School complex, Anushakti Nagar, Mumbai 400 085, India 3Department of Science, Pandit Deendayal Petroleum University, Gandhinagar 382 421, India

e-mail: [email protected]

Toroidal and poloidal rotation in a tokamak plasma is believed to play a significant role in reducing the turbulence in the edge region and thus improving the energy and particle confinement time [1,2]. Inside a tokamak, there are mainly two magnetic fields, toroidal field BT and poloidal field Bp. The presence of electric field along with the magnetic field gives rise to an

E×B drift. The Er -component of electric field along with BT give rise to an E×B drift in the poloidal direction which is termed as the poloidal rotation. Further, the E×B drift that arises in the toroidal direction due to Er &BP is known as the toroidal rotation. We have studied these rotations for Aditya-U tokamak and calculated the values for toroidal and poloidal rotation along the radial direction of the torus. Due to larger values of Er in the edge region as compared to the core region, the plasma rotation in the edge is found to be significantly larger than the core. We also studied the variation of the diamagnetic drift produced as the result of pressure gradient inside the tokamak.

References [1] Burrell, K.H. Phys. Plasmas 1997, 4, 1499–1518. [2] H. Biglari, P. H. Diamond, and P. W. Terry Physics of Fluids B: Plasma Physics 2, 1 (1990) [3] Pravesh Dhyani 2014 Nucl. Fusion 54 083023

32 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Basic Plasma

Theory

33 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL3-1

Electron-Acoustic Solitary waves in Fermi Plasma with Two-Temperature Electrons

Ankita Dey1, S. Pramanick2, S. Chakraborty3, M. Sarkar3, S. Chandra4 1Lady Brabourne College, Kolkata, West Bengal, India 2Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India 3Jadavpur University, Kolkata, West Bengal, India 4Physics Department Government General Degree College at Kushmandi, Dakshin Dinajpur, India

e-mail: [email protected]

Electron Acoustic waves in Fermi Plasma with two temperature electrons have various applications in space and laboratory-made plasmas. In some dense plasma systems like the inside of compact stars, Fermi plasma is important. We have studied Fermi plasma system with three components, two temperature electrons, and ions. The hot electrons are mobile and produce restoring force to the system while cold electrons are immobile and produce inertia to the system. We have studied the dispersion behavior of electron acoustic waves in Fermi plasma with two temperature electrons and investigated its dependence with various plasma parameters. we have investigated Korteweg-de Vries Burger’s equation for the solitary profile of Fermi plasmas with two temperature electrons and investigated its dependence with various plasma parameters.

References [1] Chandra, S.; Paul, S.N.; Ghosh, B.; “Electron-acoustic solitary waves in a relativisticallydegenerate quantum plasma with two-temperature electrons”, Astrophys Space Sci,343:213–219, (2013) [2] Ali, S., Shukla, P.K.: Phys. Plasmas 13, 022313 (2006) [3] Bains, A.S., Tribeche, M., Gill, T.S.: Phys. Lett. A 375, 2059 (2011)

34 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL3-2

Quantum Electro-static Shock Fronts in Two Component Plasma with Non-thermal Distributive Ion

Subhangi Chakraborty1, Jyotirmoy Goswami1,2* 1 JIS University, 81, Nilgunj Rd, Jagarata Pally, Deshpriya Nagar, Agarpara, Kolkata, West Bengal 700109 2 188, Raja Subodh Chandra Mallick Rd, Jadavpur, Kolkata, West Bengal 700032

e-mail: [email protected]

The theoretical investigation of shocks a dense quantum plasma containing electrons at finite temperature and non-thermal distributive ions has been administrated. The shock structures of small nonlinearity are studied by using the quality reductive perturbation method. we have got considered collisions to be absent, and the shocks arise out of viscous force. The KdV–Burger equation has been derived and analyzed numerically. The results are important in explaining the various phenomena of the laser-plasma interaction of dense plasma.

35 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL3-3

Thermal Instability of Two-Component Plasma with Radiative Heat-Loss Functions Frictional Effect of Neutrals and Hall Current

Sachin Kaothekar1 1Department of Physics, Mahakal Institute of Technology & Management, Ujjain-456664, M.P., India.

e-mail: [email protected], [email protected]

The effect of neutral frictions, Hall current and radiative heat-loss function on the thermal instability of viscous two-component plasma has been investigated incorporating the effects of finite electrical resistivity and thermal conductivity. A general dispersion relation is obtained using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem and a modified thermal condition of instability is obtained. We find that the thermal instability condition is modified due the presence of radiative heat-loss function, thermal conductivity and neutral particle. The Hall current parameter affects only the longitudinal mode of propagation. For the case of longitudinal propagation we find that the condition of thermal instability is independent of the finite electron inertia, Hall current, magnetic field strength, finite electrical resistivity and viscosity of two-components, but depends on the radiative heat-loss function, thermal conductivity and neutral particle. From the curves we find that the temperature dependent heat-loss function, thermal conductivity and viscosity of two-components shows stabilizing effect, while density dependent heat-loss function and finite electrical resistivity shows destabilizing effect. The effect of neutral collision frequency is destabilizing in longitudinal mode. These results are helpful in understanding the structure formation in HI region.

References [1] G. B. Field,. Astrophys. J. 142, 531-567, (1965). [2] S. Kaothekar, J. Porous Media, 21, 679-699, (2018). [3]P. Kempski, and E. Quataert, Mon. Not. Royal Astron. Soc., 493, 1801-1817, (2020).

36 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL3-4

Target Shape Effects on the Energy of Ions Accelerated in Radiation Pressure Dominant (RPD) Regime

S. Jain, K. K. Soni, N. K. Jaiman, K. P. Maheshwari Department of Pure & Applied Physics, University of Kota, Kota-324005 (Rajasthan)

e-mail: [email protected]

The study of the interaction of an ultra-intense laser pulse with a thin dense plasma foil is of fundamental importance for different research fields such as efficient ion acceleration, high frequency intense radiation sources, medical applications, investigation of high energy collective phenomena in relativistic astrophysics [1]. We consider the interaction of an ultrashort, ultra-intense laser with ultrathin plasma layer leading in the generation of ion beam [2]. In this reference, we evaluate the energy and luminosity of the ion beam and their dependence on the laser and target parameters. Numerical results are presented for the Gaussian shaped foil target and Flat target. The effect of plasma foil thickness on the accelerated ion energy and the luminosity has also been studied.

References [1] S. V. Bulanov, T. Zh. Esirkepov, M. Kando, A. S. Pirozhkov, and N. N. Rosanov, Phys. Uspekhi, 56, 429-464 (2013). [2] T. Zh. Esirpekov, M. Borghesi, S. V. Bulanov, G. Mourou, and T. Tajima, Phy. Rev. Lett., 92, 175003 (2004).

37 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL3-5

Study of slow mode solitons in a negative ion plasma with superthermal electrons

X. Mushinzimana1, F. Nsengiyumva2, L. L. Yadav3 1Department of Physics, University of Rwanda- College of Science and Technology, P. O. B. 3900 Kigali, Rwanda 2Department of Civil Engineering, Institut d'Enseignement Superieur de Ruhengeri, P. O. B. 155 Musanze, Rwanda 3Department of Mathematics, Science and Physical Education, University of Rwanda-College of Education, P.O. B. 55 Rwamagana, Rwanda

e-mail: [email protected]

Slow mode nonlinear structures are investigated in a negative ion plasma comprising heavy positive ions, light negative ions and kappa distributed electrons. After finding the linear dispersion relation, the reductive perturbation method is used to derive the Korteweg de Vries equation and to find the solitary wave solution. The effects of the positive and negative ion temperatures as well as the spectral index  on the soliton amplitude and width are studied in detail. These effects are also studied using the arbitrary large amplitude Sagdeev pseudopotential method. With this method, it is shown that as the ion temperatures increase, the soliton existence domain narrows.

References [1] T. S. Gill, P. Bala, H. Kaur, N. S. Saini, S. Bansal and J. Kaur, The European Physical Journal D, 31, 91-100 (2004). [2] K. Jilani, A. M. Mirza and T. A. Khan, Astrophys Space Sci, 344, 135-143 (2013). [3] X. Mushinzimana and F. Nsengiyumva, AIP Advances, 10, 065305 (2020).

38 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL3-6

Effect of the nonthermal electrons on ion-acoustic cnoidal wave in unmagnetized plasmas

P. C. Singhadiya1, J. K. Chawla2 and S. K. Jain 1Seth RLS Govt. College, Kaladera, Rajasthan, India-303801 2Department of Physics, Govt. College Tonk, Rajasthan, India-304001 Govt. College, Dholpur, Rajasthan, India-328001

e-mail: [email protected]

Using reductive perturbation method, Korteweg de Vries (KdV) and modified KdV (mKdV) equation is derived for a unmagnetized plasma having warm ions and nonthermal electrons. The cnoidal wave solution of the KdV and mKdV equation is discussed in detail. The effect of nonthermal electron on the characteristics of the cnoidal wave and soliton are also discussed. It is found that nonthermal electron has a significant effect on the amplitude and width of the cnoidal waves, while it also affects the width and amplitude of the soliton in plasmas. The numerical results are plotted within the plasma parameters for laboratory and space plasmas for illustration.

References [1] H. Schamel, Plasma Phys. 14, 905 (1972). [2] Yashvir, T. N. Bhatnagar and S. R. Sharma, Plasma Phys. Controlled Fusion 26, 1303 (1984). [3] L. L. Yadav, R. S. Tiwari, K. P. Maheshawari and S. R. Sharma, Phys. Rev. E 52,304 (1995). [4] R. S. Tiwari, S. L. Jain and J. K. Chawla, Phys. Plasmas 14, 022106 (2007). [5] R. Sabry, W. M. Moslem and P. K. Shukla, Plasma Phys. 16, 032302 (2009). [6] S. K. El-Labany, R. Sabry, W. F. El-Taibany and E. A. Elghmaz, Plasma Phys. 17, 042301 (2010). [7] O. R. Rufai, Plasma Phys. 22, 052309 (2015). [8] J. K. Chawla, P. C. Singhadiya and R, S. K. Tiwari, Pramana J. Phys., 94, 13 (2020).

39 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL3-7

Formation of shock fronts in inner magnetospheric plasma

J. Sarkar1, S. Chandra2, J. Goswami1, B. Ghosh1 1Department of Physics, Jadavpur University, Kolkata - 700 032, India 2Department of Physics, Government General Degree College at Kushmandi, Dakshin Dinajpur-733121, India

e-mail: [email protected]

Nonlinear analysis for the finite amplitude electron-acoustic-wave is considered in a magnetized viscous plasma. The quantum hydrodynamic model (QHD) is used to describe the thickly and thinly populated electron species with the Kappa distributive ion. Viscous effects have been considered for the thickly populated electron. By employing the standard reductive perturbation technique (RPT), the KdV-Burger equation has been derived, which exhibits shock waves. KdV-B equation transforms into the KdV equation when there is no viscous term. The form of the effective magnetic field is the Earth-like magnetospheric magnetic field. The shock fronts and the solitary structures have been studied with a variety of different plasma parameters. The results are essential in explaining the various phenomena in the inner magnetosphere.

40 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL3-8

Slow and fast modulation instability and envelope soliton of ion acoustic waves in fully relativistic plasma having nonthermal electrons

Indrani Paul1, Arkojyothi Chatterjee2 and Sailendra Nath Paul1,2 1 Department of Physics, Jadavpur University, Kolkata-700032, India. 2 East Kolkata Centre for Science Education and Research P-1, B.P.Township, Kolkata-700 094, India.

e-mail: [email protected];[email protected]

Modulation instability and envelope soliton of slow and fast ion acoustic waves have been theoretically studied in unmagnetized fully relativistic plasma consisting of cold positive ions having constant stream velocity and nonthermal electrons using Fried and Ichikawa method. The expression of nonlinear Schrodinger equation in fully relativistic plasma has been derived for slow- and fast- mode of the wave and the conditions for the existence of modulation instabilities are obtained. From the nonlinear Schrodinger equation, the solution for envelope solitons for slow- and fast- modes of the wave are also obtained. The profiles of bright- and dark-envelope solitons are drawn and discussed taking different values of ion-stream velocity and nonthermal electrons. It is observed that relativistic ion stream velocity and nonthermal electrons have significant roles on slow and fast modulation instability and envelope solitons in relativistic plasma. The results are new and would be applicable in astrophysical plasma.

References

[1] B D Fried and Y H Ichikawa, Journal of Physical Society of Japan, 34, 1073 (1973). [2] S N Paul and A Roychowdhury, Chaos Fractals and Solitons, 91, 406 (2016). [3] S N Paul, A Roychowdhury and Indrani Paul, Plasma Physics Reports, 45, 1011 (2019).

41 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL3-9

To Study the Growth Rates of Waves between Piezoelectric and Ferroelectric Semiconductor Using QHD Model In Quantum Plasma

Manisha Raghuvanshi1, Sanjay Dixit2 Department of physics, Govt. M.V.M college shivaji nagar, Bhopal, Barkatullah University Bhopal MP

e-mail: * [email protected]; ** [email protected]

Using QHD model, the parametric instability of piezoelectric and ferroelectric materials of semiconductor quantum plasma has been studied. We present a analytical investigation on compare the piezoelectric and ferroelectric properties of materials in semiconductor plasma .It is found that what’s effects in low and high temperature, dielectric constant, growth rate and frequency of the materials. Detailed analysis of the dielectric, ferroelectric and piezoelectric properties of BaTiO3 and InSb. In this article explained the various types of application in piezoelectric and ferroelectric materials in quantum plasma. The results obtained in this work are discussed and compare the properties of similar and distinct materials of the semiconductor quantum plasma. Key words: parametric instability, piezoelectric and ferroelectric materials, QHD model.

References

1. Haas, F. "A magnetohydrodynamic model for quantum plasmas."Physics of Plasmas,12.6(2005) 062117 2. Manfredi, Giovanni. "How to model quantum plasmas." Fields Inst. Commun 46 (2005)263-287. 3. Mattias Marklund and Padma K. Shukla “Nonlinear collective effects in photon–photonAnd Photon plasma interactions” Department of Physics, Umea University SE–901 87 Umea,Sweden, (2006). Phys.78 4. Cai-Xia, He, and Xue Ju-Kui. "Parametric instabilities in quantum plasmas with Electron exchange—correlation effects." Chinese Physics B 22.2 (2013): 025202. 5. Chen, Francis F. "Plasma Applications." Introduction to Plasma Physics and Controlled Fusion. Springer International Publishing, 2016. 355-411. 6. Ghosh, S., and S. Dixit. "Modulational instability of a laser beam in a piezoelectric Material with strain dependent dielectric constant." Physics Letters A 118.7 (1986), 354-356. 7. Guha, S., P. K. Sen, and S. Ghosh. "Parametric instability of acoustic waves in Transversely magnetised piezoelectric semiconductors." physica status solidi (a) 52.2 (1979): 407-414. 8. Haas, F., et al. "Quantum ion-acoustic waves." physics of plasmas 10.10 (2003).

42 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

9. Kaw, Predhiman K. "Parametric excitaiton of ultrasonic waves in piezoelectric"Semiconductor Journal of Applied Physics 44.4 (1973): 1497-1498. 10. Khan, S. A., S. Mahmood, and H. Saleem. "Linear and nonlinear ion-acoustic waves in very dense magnetized plasmas." Physics of Plasmas 15.8 (2008): 082303. 11. Markowich, P. A., and C. A. Ringhofer. “C. Schmeiser, “Semiconductor Equations” 1990 12. Salimullah, M., T. Ferdousi, and F. Majid. "Stimulated Brillouin scattering of Electromagnetic waves in magnetized semiconductor plasmas." Physical Review B 50.19 (1994): 14104. 13. Sharma, R. R., and V. K. Tripathi. "Stimulated Brillouin scattering of laser radiation in a piezoelectric semiconductor." Physical Review B 20.2 (1979): 748. 14. Shukla, P. K. "A new dust mode in quantum plasmas." Physics Letters A 352.3 (2006): 242-243. 15. Singh, T., and M. Salimullah. "Nonlinear interaction of a Gaussian EM beam With an electrostatic upper hybrid wave: Stimulated Raman scattering." Il Nuovo Cimento D 9.8 (1987): 987-998. 16. Uzma, Ch, et al. "Stimulated Brillouin scattering of laser radiation in a Piezoelectric semiconductor: Quantum effect." Journal of Applied Physics 105.1(2009): 013307.

43 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL3-10

Diagnostics of Ar-CO2 mixture plasma using CR model

N. Shukla1, R.K. Gangwar2, and R. Srivastava1 1Department of Physics, Indian Institute of Roorkee, Roorkee-247667 India 2Department of Physics, Indian Institute of Tirupati, Tirupati-517506 India

e-mail: [email protected]

We develop a reliable collisional radiative (CR) model for the Ar-CO2 mixture plasma. This model utilizes the complete set of electron impact excitation cross-sections of various fine structure levels of Ar by relativistic distorted wave (RDW) theory calculated by our group [1]. This model incorporated several important processes such as excitation and de-excitation of Ar due to its collision with electrons in the plasma, radiative absorption and decay, ionization as well as recombination. The model uses the OES measurements of recently reported low-pressure DC generated Ar-CO2 plasma by Rodriguez et al. [2]. The plasma parameters viz. electron density (ne) and electron temperature (Te) are obtained as a function of different pressures (0.2, 0.3, and 0.6 mbars) and discharge powers at 25 and 50% concentrations of CO2 in Ar. These results are determined using measured intensities of seven intense emission lines out of 3p54p (2p) → 3p54s (1s) fine-structure transitions. It is observed that both the electron density and electron temperature increase with the increase of CO 2 concentration, which is in confirmation with experimental predictions.

References [1] R. K. Gangwar et al. J. Appl. Phys. 111 053307(2012). [2] J. Rodriguez et al. Phys. Plasmas 25, 053512 (2018).

44 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL3-11

Large amplitude ion-acoustic compressive solitons in plasmas with positrons and superthermal electrons

S. K. Jain1, P. C. Singhadiya2 and J. K. Chawla 1Govt. College, Dholpur, Rajasthan, India-328001 2Seth RLS Govt. College, Kaladera, Rajasthan, India-303801 Department of Physics, Govt. College Tonk, Rajasthan, India-304001

e-mail: [email protected]

The large amplitude ion-acoustic solitons in plasma consisting of ions, positrons along with cold and hot superthermal electrons have been studied. An energy integral equation for the system has been derived with the help of SPM(Pseudo potential method). It is found that compressive solitons exist in the plasma system for the selected set of plasma parameters. The effect of the spectral indexes of hot electrons (kh), spectral indexes of cold electrons (kc), temperature ratio of two species of electron 1),( positron concentration ),( ionic temperature ratio ),( positron temperature ratio  )( and Mach number (M) on the characteristics of the large amplitude ion-acoustic solitons are discussed in detail. The amplitude of the solitons increases with an increase in positron concentration ),( ionic temperature ratio ),( positron temperature ratio  )( and Mach number (M), however any decrease in spectral indexes (kh, kc) increases the amplitude of the solitons. The present study of the paper may be helpful in space and astrophysical plasma system where positrons and superthermal eelectrons coexist.

References [1] F. B. Rizzato, Plasma Phys. Control. Fusion 40, 289 (1988). [2] F. C. Michel, Rev. Mod. Phys. 54, 1 (1982). [3] S. I. Popel, S. V. Vladimirov, P. K. Shukla, Phys. Plasmas 2, 716 (1995). [4] R. Bharuthram and P. K. Shukla, Phys. Fluids 29, 3214 (1996). [5] E. F. El-Shamy, Phys. Plasmas 21, 082110 (2014). [6] N. S. Saini, B. S. Chahal, A. S. Bains and C. Bedi, Phys. Plasmas 21, 022114 (2014). [7] K. Kumar and M. K. Mishra, AIP Advances 7, 115114 (2017). [8] P. C. Singhadiya, J. K. Chawla, and S. K. Jain, Pramana J. Phys., 94, 90 (2020).

45 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Dusty Plasma, Laser Plasma, Plasma Applications

46 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL4-1

Study of Arc Fluctuations of a DC Transferred Arc Plasma

S P Sethi1, D P Das2, S K Behera2 1CSIR-Institute of Minerals and Materials Technology, Bhubaneswar 751013, India 2CSIR-Institute of Minerals and Materials Technology, Bhubaneswar 751013, India

e-mail: [email protected]

Arc fluctuations, a vital issue in an DC Transferred Arc Plasma, DC transferred arc plasma is a sophisticated technique, widely used in pyro-metallurgy process, extraction of minerals from its ores, fine powder smelting. But to maintain a stable arcing is a crucial challenge for obtaining higher productivity and safe operation. Stability and instability of arc can be derived from arc fluctuation characteristics for a given current, gas flowrate, cathode electrode positions. The acquired arc fluctuation characteristics in terms of volts helps in identifying the stability and instability characteristics. The presented work justifies the parameters that contribute to the arc fluctuations in a smelting performance, and what precautions and techniques need to be initiated during the progress of smelting process, so that extraction process can be carried out by increasing the overall productivity of the process.

47 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL4-2

Inductive Energy Storage System with Plasma opening Switch: A review

Kanchi Sunil1, Rohit Shukla1,2, Archana Sharma1,2 1Homi Bhabha National Institute Mumbai-400094, 2Pulsed Power & Electro-Magnetics Division, Bhabha Atomic Research Centre Facility, Atchutapuram, Visakhapatnam, Andhra Pradesh, India-531011,

e-mail: [email protected]

Pulse compression technique is used to generate high powers in the range of Terawatt with secondary energy storage device as inductive energy store (IES) with plasma opening switch (POS) having charging time is in the range of microseconds and output pulse duration in nanoseconds. The inductive energy store is more advantage compared to most widely used capacitive energy storage devices with respect to energy density which is 10 -100 times high [1]. The parameters that define the performance of IES system are peak output voltage, peak output current, rise times and pulse widths of current and voltage. Employing of POS results in multiplication of voltage and power with good energy coupling between the source and load. The use of POS improves the load current rise times as well [1]. The IES with POS technology is used in different applications include generation of particle beams, radiation sources, fusion research and defense applications. Some of the facilities of plasma opening switch for mega-ampere are GIT-16 [2], MAGPIE [3], COBRA [4], DECADE [5], ACE-4 [6]. The experimental results of these facilities gives details of current conduction phase and opening phase of micro second POS. This paper provides details of different facilities of POS technology and simulation of ideal model of inductive energy system with different functions of variation of POS switch resistance connected to resistive load.

References [1] R. A. Meger., et. al., Appl. Phys. Lett., 42, 943 (1983). [2] S. P. Bugaev., et.al., Russian Physics Journal, 40, 1154-1161(1997). [3] Hall, G. N., et al., Review of Scientific Instruments, 85, 943-945 (2014). [4] Shelkovenko, Tatiana A., et al., IEEE transactions on plasma science, 34, 2336-2341 (2006). [5] P. Sincerny et al., Tenth IEEE International Pulsed Power Conference, 3-6 July 1995, Albuquerque, NM, USA, 405-416(1995). [6] R. Crumley, D. Husovsky and J. Thompson, 12th IEEE International Pulsed Power Conference, 27-30 June 1999, Monterey, CA, USA, 1118-1121(1999).

48 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL4-3

Role of plasma sheath in the energy management during plasma surface modification of polymer

Bivek Pradhan and Utpal Deka Department of Physics, Sikkim Manipal Institute of Technology, Sikkim Manipal University Majitar, Rangpo, Sikkim-737136

e-mail: [email protected]

The ubiquitous use plasma for surface treatment of polymers for various applications like automobile, biomedical, textile, etc is a well-established technique. The optimization of the plasma parameters for maximum efficiency after plasma treatment is of utmost importance. In this work we have presented the role of plasma sheath in managing the energy deposition on the surface of PTFE (poly(tetra-fluoro-ethylene) polymer. The amount of energy required for breaking of the polymer bonds in presence of secondary electron emission has been theoretically estimated. A multicomponent O2-N2 plasma is considered. The sheath potential in presence of secondary electron emission from the polymer surface has been evaluated as a function of varying density ratio of oxygen to nitrogen and also for different temperature ratio of electron to ion for cold and hot plasma is evaluated. The potential structure for different ratios remains similar and almost same but the magnitude of the potential changes for cold and hot plasma. The heat transmission coefficient through the sheath in presence of secondary emission from the polymer is evaluated. It is seen that the heat transmission coefficient varies linearly with w.r.t. electron to ion temperature ratio for the hot plasma and it is more in hot plasma than that of cold plasma. The time required for the bond breaking of C-C with bond energy of 348kJ/mol or 5.78eV for PTFE polymer is estimated and shown that it will take more time to break in case of cold plasma compared to that of hot plasma.

49 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL4-4

Dynamics of dust ion acoustic waves in the Low Earth Orbital (LEO) plasma region

Siba Prasad Acharya1, a, Abhik Mukherjee2, b, and M. S. Janaki1, c 1Saha Institute of Nuclear Physics, Kolkata, India 2National University of Science and Technology, “MISiS”, Moscow, Russia e-mail: a [email protected], b [email protected], c [email protected]

We consider the system consisting of the plasma environment in the Low Earth Orbital (LEO) region in presence of charged space debris objects. This system is modelled for the first time as a weakly coupled dusty plasma; where the charged space debris objects are treated as weakly coupled dust particles with two dimensional space and time dependences. The dynamics of the ion acoustic waves in the system is found to be governed by a forced Kadomtsev-Petviashvili (KP) type model equation, where the forcing term depends on the distribution of debris objects. Exact accelerated planar solitary wave solutions are obtained from the forced KP equation upon transferring the frame of reference, and applying a specific non holonomic constraint condition. For a different constraint condition, the forced KP equation also admits lump wave solutions. The dynamics of exact accelerated lump wave solutions, which are happened to be pinned, is also explored. Approximate dust ion acoustic wave solutions with time dependent amplitudes and velocities for different types of localized space debris functions are analyzed. Our work provides a much clearer insight of the debris dynamics in the plasma medium in the LEO region, revealing some novel results that are immensely helpful for various space missions. Different perspectives for practical applications of our theoretical results are discussed in detail.

References [1] A. Sen, S. Tiwari, S. Mishra, and P. Kaw, Advances in Space Research, Vol. 56, 429-435 (2015). [2] A. R. Seadawy, and K. El-Rashidy, Results in Physics, Vol. 8, 1216-1222 (2018). [3] M. Lin, and W. Duan, Chaos, Solitons and Fractals, Vol. 23, 929-937 (2005). [4] M. S. Janaki, B. K. Som, B. Dasgupta, and M. R. Gupta, Journal of the Physical Society of Japan, Vol. 60, 2977-2984 (1995). [5] S. Reyad, M. M. Selim, A. EL-Depsy, and S. K. El-Labany, Physics of Plasmas, Vol. 25, 083701 (2018). [6] X. Yong, W. X. Ma, Y. Huang, and Y. Liu, Computers and Mathematics with Applications, Vol. 75, 3414-3419 (2018). [7] J. Yu, F. Wang, W. Ma, Y. Sun, and C. M. Khaliue, Nonlinear Dynamics, Vol. 95, 1687-1692 (2019).

50 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL4-5

Effect of negative charge dust on ion-acoustic dressed solitons in unmagnetized plasmas

J. K. Chawla, P. C. Singhadiya1, A. K. Sain and S. K. Jain2 Department of Physics, Govt. College Tonk, Rajasthan, India-304001 1Seth RLS Govt. College, Kaladera, Rajasthan, India-303801 2Govt. College, Dholpur, Rajasthan, India-328001

e-mail: [email protected]

Propagation of an ion-acoustic soliton in a plasma consisting of negative charge dust is considered the reductive perturbation method (RPM). The well known RPM has been used to derive the KdV equation. This exact solution reduce to the dressed soliton solution when mach number is expanded in terms of soliton velocity. Variation of amplitude and width for the KdV soliton, core structure, dressed soliton and exact soliton are graphically represented to different values of negative ions and mach number. The present study of this paper may be helpful in space and astrophysical plasma system where negative charge dust ions are present.

References [1] Y. H. Ichikawa, T. Mitsu-Hashi and K. Konno, J. Phys. Soc. Jpn., 41, 1382 (1976). [2] N. Sugimoto and T. Kakutani, J. Phys. Soc. Jpn., 43, 1469 (1977). [3] R. S. Tiwari, A. Kaushik, M. K. Mishra, Physics Letters A, 365, 335 (2007). [4] R. S. Tiwari, Physics Letters A, 372, 3461 (2008). [5] Yashvir, R. S. Tiwari and S. R. Sharma, Canadian Journal of Physics, 66, 824 (1988). [6] R. S. Tiwari and M. K. Mishra, Physics of Plasmas, 13, 062112 (2006). [7] P. Chatterjee, K. Roy, G. Mondal, S. V. Muniandy, S. L. Yap and C. S. Wong, Physics of Plasmas, 16, 122112 (2009). [8] P. Chatterjee, K. Roy, S. V. Muniandy and C. S. Wong , Physics of Plasmas, 16, 112106 (2009). [9] K. Roy and P. Chatterjee, Indian Journal of Physics, 85, 1653 (2011).

51 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL4-6

Effect of collision on dust–ion acoustic shock wave in dusty plasma with negative ions

Jyotirmoy Goswami1*, Jit Sarkar1, Swarniv Chandra1,2 and Basudev Ghosh1 1 Department of Physics, Jadavpur University, Kolkata – 700 032, India 2 Department of Physics, Government College Kushmandi, W.B. – 733121, India

e-mail: [email protected]

In this paper we have investigated the properties of dust–ion acoustic (DIA) shock wave in a dusty plasma containing two types of ions. We have used the reductive perturbation technique (RPT) to derive the Korteweg–de Vries–Burgers (KdVB) equation for dust acoustic shock waves in a homogeneous, unmagnetized and collisional plasma containing Boltzmann distributed electrons, singly charged positive ions, singly charged negative ions and dust particles in the background. The KdVB equation is derived and its stationary analytical solution is numerically analyzed where the effect of collision is taken into account. It is found that the collision in the dusty plasma plays as a key role in dissipation for the propagation of DIA shock.

52 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL4-7

Equilibrium configuration of self gravitating dusty plasmas

Manish K Shukla Jawaharlal Nehru College, Pasighat, Arunachal Pradesh, India

Email: [email protected]

Using three dimensional molecular dynamics simulation, different equilibrium structures are obtained for self gravitating charged dust clouds. These equilibrium structures are spherically symmetric in nature which can be characterized by three parameters (i) number of particles in the cloud (ii) Temperature of the cloud, and (iii) a dimensionless parameter . The simulation results are explained using the mean field theory where gravitational force density is balanced by the sum of kinetic and electrostatic pressure of charged dust cloud. The significanceΓ of obtained results is also discussed in the context of structure formation in the astrophysical conditions.

References [1] M. K. Shukla and K Avinash, Phys. Plasmas 26, 013701 (2019). [2] K. Avinash, B. Eliasson, and P. Shukla, Phys. Lett. A 353, 105-108 (2006). [3] K. Avinash and P. K. Shukla, New J. Phys. 8, 2 (2006). [4] M. K. Shukla, K. Avinash, R. Mukherjee, and R. Ganesh, Phys. Plasmas 24, 113704 (2017).

53 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL4-8

Strong and collimated terahertz radiation by photo mixing of Hermite Cosh Gaussian lasers in collisional plasma

Sheetal Chaudhary, Manendra and Anil K. Malik Department of Physics, Ch. Charan Singh University, Meerut.

e-mail:[email protected]

THz spectral region has become a focus of active and thriving research because of its potential applications in remote sensing, topography, imaging, explosive detection, dentistry, chemical sciences, security identifications, terahertz time-domain spectroscopy (THz-TDS) [1-6]. An analytical model for terahertz (THz) wave emission by frequency difference of Hermite Cosh Gaussian lasers in collisional plasma with periodic density is developed. The effect of laser parameters (mode index , decentered parameter and initial phase difference ) and plasma parameters (plasma density structure, electron-neutral collisions) on emitted THz field profile is investigated. It is found that the highest THz field is obtained for and

(resonant excitation) at . The study also reveals that electron neutral collisions attenuate the field drastically. A very high THz field=v,=t,=t,, of G V m-1 and an efficiency = of 3% is obtained in our scheme = t for optimised laser and plasma parameters. References [1] B. Ferguson and X. C. Zhang, Nat. Mater. 1, 26(2002). [2] D. Dragoman, M. Dragoman, Prog. Quantum Electron. 28, 10(2010). [3] W. P. Leemans, C. G. R. Geddes, J. Faure, C. Tóth, J. V. Tilborg, C. B. Schroeder, E. Esarey, G. Fubiani, D. Auerbach, B. Marcelis, M. A. Carnahan, R. A. Kaindl, J. Byrd, and M. C. Martin, Phys. Rev. Lett. 91, 074802(2003). [4] S. Ebbinghaus, K. Schröck, J. C. Schauer, E. Bründermann, M. Heyden, G. Schwaab, M. Böke, J. Winter, M. Tani, M. Havenith, Plasma Sources Sci. Technol. 15, 72 (2006). [5] P. H. Siegel, IEEE Tran. Tera. Sci. Technol. 50, 910(2002). [6] F. Sizov, Opto Electron. Rev. 18, 10(2010).

54 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL4-9

Effect of laser pulse profile on controlling the growth of Rayleigh-Taylor instability in radiation pressure dominant regime

Krishna Kumar Soni, Shalu Jain, N. K. Jaiman, and K. P. Maheshwari Department of Pure & Applied Physics, University of Kota, Kota-324005 (Rajasthan)

e-mail: [email protected]

In the radiation pressure dominant (RPD) regime the interaction of an intense relativistic laser pulse with an ultrathin, dense solid foil converts it into overdense plasma instantaneously. This plasma foil is accelerated as a whole by incident laser pulse. It becomes unstable due to the onset of Rayleigh-Taylor instability (RTI). This RTI tears the foil into plasma clumps. It affects the ion acceleration process. The ion energy spectrum becomes broadened. In the comoving frame of the plasma foil the RTI makes it transparent for the incident radiation. The growth rate of RTI depends on the pulse profile of the incident laser. So, by suitably tailored laser pulse one can control the growth of RTI, and hence stabilize the ion acceleration. This paper presents a comparative study of energy and momentum transfer by the incident Gaussian and Lorentzian laser pulse to the plasma ions. Numerical results for the comparison of incident laser pulse profile for controlling the growth of RTI are presented.

55 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

OL4-10

Laser-driven radially polarized terahertz radiation generation in hot Plasma

Manendra and Anil K Malik Department of Physics, Chaudhary Charan Singh University Meerut, UP-250004, India

e-mail: [email protected]

Bright radially polarized Terahertz (THz) radiation have invited great interest from researchers due to various potential application in the field of medical imaging, chemical science, spectroscopic identifications of complex molecules, explosive detection, security identification, topography, remote sensing, outer space communication and submillimeter radars [1 - 6]. We report radially polarized terahertz (THz) wave generation based on nonlinear mixing of two radially polarized beams in density modulated plasma. We incorporate in our model the effect of plasma electron temperature (Te) on THz field intensity and efficiency. THz field intensity and efficiency of THz monotonically increase with plasma electron temperature (Te). We observe that the effect of plasma electron temperature is more prominent around the resonance excitation i.e. . The profile of THz depends only on the laser parameters and it is independentv of plasma electron temperature. In our numerical investigation under the optimized − parameters, radially polarized THz radiation with the high electric field and the efficiency can be obtained to meet the demands of the above mentioned potential application. Radially polarized THz field is more suitable to penetrate deeply without any risk of collateral damage inside the skin layers thereby improved the safety and efficacy of treatment [7].

Key words: Terahertz radiation, Electron temperature, Plasma, Efficiency, Radially [1]polarized D Dragoman, M Dragoman, Prog. Quant. Elect. 28 10 (2010). [2] W P Leemans, C G R Geddes, J. Faure, Tóth Cs, Tilborg J V, Schroeder C B, Esarey E, Fubiani G, Auerbach D, Marcelis B, Carnahan M A, Kaindl R A, Byrd J, and Martin M C, Phys. Rev. Lett. 91 074802 (2003). [3] Schroeder C B, Esarey E , Tilborg J Van, Leemans W P, Phys. Rev. E 69 016501 (2004). [4] Ebbinghaus S , Schröck K, Schauer J C , Bründermann E, Heyden M, Schwaab G , Böke M, Winter J, Tani M, Havenith M, Plasma Sourc. Sci. Technol, 15 72 (2006). [5] P H Siegel, IEEE , 50 910 (2002). [6] F Sizov ,Opt. Electron. Rev. 18 10 (2010). [7] B Varghese, S Turco, V Bonito, and R Verhagen, Opt. Express 21 18304 (2013).

56 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Full Manuscript PSC-1 to PSC-13

57 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

PSC -1

Simulation of runaway electron generation in fusion grade tokamak and suppression by impurity injection

Ansh Patel1, Santosh P. Pandya2 1School of Liberal Studies, PanditDeendayal Petroleum University, Gandhinagar, India 2Institute for Plasma Research, Bhat, Gandhinagar, India.

e-mail: [email protected]

Abstract

During disruptions in fusion-grade tokamaks like ITER, large electric fields are induced following the thermal quench (TQ) period which can generate a substantial amount of Runaway Electrons (REs) that can carry up to 10 MA current with energies as high as several tens of MeV [1-3] in current quench phase (CQ). These runaway electrons can cause significant damage to the plasma-facing-components due to their localized energy deposition. To mitigate these effects, impurity injections of high-Z atoms have been proposed [1-3]. In this paper, we use a self-consistent 0D tokamak disruption model as implemented in PREDICT code [6] which has been upgraded to take into account the effect of impurity injections on RE dynamics as suggested in [4-5]. Dominant RE generation mechanisms such as the secondary avalanche mechanism as well as primary RE-generation mechanisms namely Dreicer, hot-tail, tritium decay and Compton scattering (from γ-rays emitted from activated walls) have been taken into account. These different RE-generation mechanisms provides seed REs of different amount and corresponding maximum amplitude of RE-current. In these simulations, the effect of impurities is taken into account considering collisions of REs with free and bound electrons as well as scattering from full and partially-shielded nuclear charge. These corrections were also implemented in the relativistic test particle model to simulate RE-dynamics in momentum space. We show that the presence of impurities has a non-uniform effect on the Runaway Electron Distribution function. Low energy RE lose their energy due to collisional dissipation while the high energy RE are scattered in momentum space and dissipate their energy due to higher synchrotron backreaction due to its dependence on total energy and pitch-angle. We also show that the combined effect of pitch-angle scattering induced by the collisions with impurity ions and synchrotron emission loss results in the faster dissipation of RE-energy distribution function [7]. The variation of different RE generation mechanisms during different phases of the disruption, mainly before and after impurity injections is reported.

Key words: Runaway electrons, collisional dissipation, impurity injection, avalanche mechanism

Introduction: Electrons in plasma are said to ‘run-away’ when the Coulomb collisional drag force acting on them becomes smaller than the accelerating force due to an external electric field. While Runaway electrons (REs) are an interesting phenomenon, they can be very problematic for fusion-grade tokamaks like ITER, where large electric fields induced during the disruption phase can multiply a RE seed population enormously by the avalanche effect [1]. These REs can carry

58 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India substantial amounts of the pre-disruption plasma current and have energies as high as few tens of MeV. The uncontrolled loss of such REs should be avoided since they deposit their energies in a highly localized manner on the plasma-facing-components and can damage them.

Massive material injection (MMI) is a possible solution to mitigate the detrimental effects of RE energy deposition [2]. Impurities such as He, Ne, Ar can be injected either in the form of solid pellets (SPI) or direct gas injection (MGI) which increases collisionality in the plasma leading to re-thermalization of low energy (~few MeV) REs and energy loss of high energy (~tens of MeV) REs.

The generation and suppression of RE during the CQ phase is the subject of this paper. The generation of runaway electrons is considered by taking into account all significant primary generation mechanisms as well as avalanching. We utilize a self-consistent calculation of electric field taking into account collisional and synchrotron drag force in the presence of impurities. The rest of the paper is structured as follows: the second section describes the model utilized for the numerical study, and the results are presented in the third section.

Model: A 0-D model taking into account the evolution of plasma and runaway electron (RE) current along with runway energy has been implemented in the PREDICT code [6] for disruption scenarios. The electric field is modelled taking into account replacement of ohmic current into RE current as: where are the total and runaway plasma current densities and is the plasma = − resistivity. The total current Ip is evolved using: , = ,

t The RE density is calculated independently=− through the discharge due to various generation mechanisms [5]:

㏨ꘐ伸 −쳌 −䂺䂺 䂺−ꘐ ꘐ䂺 from which= the runaway+ current is calculated+ as + + . No radial runaway− losses are considered which corresponds to the most pessimistic case with regards to RE generation in disruption scenarios. However re-thermalization of REs= due to energy loss is considered by using the critical energy for RE generation as a cut-off point below which the test electrons are not considered as runaways.

The relativistic test particle equations that govern RE energy dynamics in momentum space including collisional and synchrotron-radiation induced losses are given as:

h h 䂺ꘐꘐ + v + gc + gy h = − t − h h h = − − gc + gy h t where and are correctionalh factors that take into account the presence of impurities as calculated in [5]. 䂺ꘐꘐ Formation of runaway beam We start our numerical study at the beginning of the current quench (CQ) phase and assume a RE seed of 0.1kA generated due to incomplete thermalization of the electron energy distribution

59 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India function, also known as the hot-tail mechanism, with plasma temperature = 5 eV and deuterium 20 -3 plasma density nD= 10 m .REs are then generated by other primary generation mechanisms: Dreicer generation, tritium decay, and Compton scattering sources taking into account corrections [5] due to the presence of impurities. The avalanching of thermal electrons (both free and bound) into the RE region occurs due to induced high electric fields. The contribution due to all primary generation mechanisms during different phases of the current quench phase in fig.1(a) can be seen in fig.2(a). The high electric field causes avalanching of the runaway electrons which suppresses the electric field in return. The critical energy for RE generation increases gradually

with the drop in the electric field which suppresses further RE generation in the later part of the CQ phase. Fig.1(b) shows a temporal evolution of RE-beam energy considering different generation mechanisms.

Fig. 1(a) RE generation due to various generation mechanisms. 1(b) RE beam energy due to various generation mechanisms (D: Dreicer, A: Avalanche, T:Tritium decay, C:Compton, H: Hot tail)

In the baseline scenario with impurity, the MMI occurs at 30 ms and we assume that the impurity Argon atoms are assimilated completely and evenly inside the plasma. The RE current and 20 -3 distribution function for the two baseline cases: without MMI and with nAr = 10 m injected at 30 ms can be seen in fig. 2(c) and fig. 2(d).

60 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Fig. 2(a) Contribution of various generation mechanisms in the beginning of the disruption and CQ phase. 2(b) RE beam energy in absence and presence of impurity. 2(c) Runaway electron distribution function in absence of impurity. 2(d) Runaway electron distribution function in presence of impurity injection.

The amount of hot-tail seed used here is a moderate estimation. The hot-tail seed is a strong function of the thermal quench (TQ) time and pre-disruption temperature [8] and can carry up to a few MeV of RE current for the most pessimistic scenario. However radial losses associated with the break-up of magnetic surfaces during the thermal quench phase also have to be taken into account. Accurate estimates of the hot-tail seed would require 3D MHD simulations however it is reasonable to assume that some of the seed survives. Varying amounts of hot-tail seed due to varying discharge parameters have been shown in fig.3 (a) as calculated using an analytical approximation derived in [8] assuming an exponential drop of temperature during the thermal quench.

Contour level in Ampere

Fig. 3(a) Hot tail seed RE due to varying pre-disruption temperature and Thermal Quench time (TQ).

Suppression of runaway beam The RE beam starts dissipating its energy after the MMI due to collisional energy losses with the impurity ions as well as synchrotron radiation losses. The RE current also decays due to re-thermalization of the REs. A higher amount of injected impurities causes faster decay of RE current and energy due to the higher amount of energy losses as can be seen in fig. 4(a). Low energy REs (~up to a few MeV) lose their energy mainly due to collisions with free, bound electrons as well as with shielded, unshielded nuclear charge. High energy REs (~tens of MeV) are pitch angle scattered in momentum space due to interactions with partially ionized impurities leading to strong synchrotron radiation losses. As shown in fig. 4(b), the perpendicular momentum of REs increases drastically on impurity injections which enhances synchrotron radiation losses and consequently thermalizes the REs. In fig.4 (c), the ratio of synchrotron backreaction force to the collisional drag force is shown for two different RE fractions born at different times during the discharge. For the early-born, high energy fraction (blue), the increase in perpendicular momentum enhances synchrotron losses significantly as compared to collisional losses. In contrast, for the late-born, low-energy fraction (red), collisional and synchrotron losses play almost an equal role. Hence, the presence of impurities has a two-fold effect on RE energy dissipation: the higher number of collisions decrease the RE energy and pitch-angle scattering of REs in presence of impurities also enhances synchrotron losses, especially for high energy REs.

61 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Fig.4(a) Effect of impurity amount on RE current. 4(b) 2D momentum space plot of RE showing pitch-angle scattering. 4(c) Ratio of synchrotron and collisional drag force for two different REs. 4(d) Effect of impurity amount on RE average energy

Conclusions: A numerical study of RE dynamics in the presence of impurities is performed using a 0D disruption model considering significant sources RE sources that would be present in a fusion grade tokamak. The contribution of primary sources is shown to be considerable in the initial part of the CQ phase after which fast avalanching of RE current suppresses the electric field and consequently primary generation mechanisms. The presence of impurities is shown to cause decay of RE current and energy with a higher amount of impurities leading to faster decay of both parameters (RE-current and beam energy). Pitch angle scattering caused by collisions with impurity ions enhance synchrotron emissions drastically and is very significant especially for high energy REs.

References [1] M. Lehnen, et.al.,Journal of Nuclear Materials, 463, pp39-48, (2015) [2] E. M. Hollmann, et. al., Physics of Plasmas, 22, 021802, (2015) [3] M. Lehnen, et.al., ITER Disruption mitigation workshop, Report:ITR-18-002, (2018) [4] J. R. Martín-Solís, et.al.,Physics of Plasmas, 22, 092512, (2015) [5] J. R. Martín-Solís, et.al.,Nucl. Fusion ,57, 066025 (2017) [6] Santosh P. Pandya, PhD thesis, AIXM0036, Aix-Marseille University, France, (2019) [7] Ansh Patel, et.al., PTS-2020, MF-02, Abstract#45, (2020)

62 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

[8] H. M. Smith and E. Verwichte, Physics of Plasmas 15, 072502 (2008)

PSC-2

Effects of flow Velocity and Density of Dust Layers on the Kelvin-Helmholtz Instability in Strongly Coupled Dusty Plasma: Molecular Dynamic Study

Bivash Dolai and R. P. Prajapati Department of Pure and Applied Physics, Guru Ghasidas Vishwavidyalaya, Bilaspur-495009 (C.G.), India

e-mail: [email protected]

Abstract

The effect of different velocities and density of flowing dusty plasma layers are investigated on hydrodynamic Kelvin-Helmholtz (K-H) instability. The dust particles are too massive as compared to the electrons and ions. Therefore, the electron and ion fluids are taken to be light Boltzmann fluid and they only contributes as the neutralizing background to the charged dust grains. The dust particles are interacting through the Yukawa potential. Thus, the system can be termed as Yukawa one component fluid. The problem has been simulated using the MD simulation technique through open source LAMMPS code. We consider the two layers of such Yukawa one component fluids with same and different dust density, and different velocity profiles. The effect of different flow velocities, flow direction and different density are studied on the K-H instability. We have calculated the growth rate of the K-H instability for such configurations. For excitation of K-H instability, the magnitude of the equilibrium velocity of fluid must be greater than the dust thermal velocity. It is found that the dust flow velocity and density gradient enhance the growth rate of the K-H instability.

Key words: Dusty plasma, Strongly coupled plasma, Kelvin-Helmholtz instability, Molecular dynamics simulation.

Introduction: The major examples of plasma in nature are high temperature weakly coupled plasma i.e., the average kinetic energy of the particles is larger than the average kinetic energy of the particles due to their thermal motions. Such type of plasma is generally called the ideal plasma. Also, there exist examples of non-ideal plasma where the average potential energy dominates over the average kinetic energy of the particles [1]. The dusty or complex plasma is one of the good examples of such category. The dust grains may exist easily in the strongly coupled state due to their high charges or in other words due to their extremely low charge to mass ratio [2]. The coupling between the particles is mathematically quantified through a dimensionless Coulomb coupling parameter ( ) which is defined as the ratio of average potential energy to the average kinetic energy of the particles,

63 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

……… (1) In case of Yukawa systems where screening parameter κ > 0, the plasma does not show the actual long range crystalline behaviour at finite temperature (Td > 0) [3]. There exists an intermediate state where the Yukawa system shows consequence of both liquid and solid like behaviour. In the case of two-dimensional dusty plasma system with κ = 0.5 this state is limited to 140. In this regime, the medium behaves like a viscoelastic system. The fluid model is not adequate to describe such Yukawa systems. There is phenomenological GHD model to describe = such Yukawa dusty plasma systems [4]. Though GHD model is accepted and used widely [5] [6] to study such viscoelastic dusty plasma medium, the simulation studies [7] [8] [9] are also very important to describe the phenomena in this regime. The hydrodynamic Kelvin-Helmholtz (K-H) instability occurs when there exists relative velocity between the different layers of the fluids. The dusty plasma has often encounter sheared flow in several situations viz. protoplanetory disks, Saturn ring and cometary tails. In these objects and also in several experimental situations, the sheared flow excites the K-H instability in the dusty plasma medium. Theoretically, the state is described by the GHD model, but the implication of this model for wide range of coupling parameter and screening parameter is an interesting and open problem. Hence, the simulation studies are necessary to understand several important phenomena in this regime, and in recent these studies also prevail great interests [7] [8]. Several theoretical and experimental investigations are done in this regime to understand the collective dynamics of this state. The investigation of K-H instability close and beyond to the regime where crystallization of the dusty plasma medium occurs is of great interest. In the MD simulation study of K-H instability, Ashwin and Ganesh (2010) have investigated the effect of coupling strength well below the crystallization limit. In the present chapter, we investigate the K-H instability in the regime close and beyond the liquid-solid regime. We investigate the effect of different flow velocity and flow direction, and also the effect of density gradient on the growth of the K-H instability using MD simulation.

Molecular Dynamics (MD) Model: The electrons and ions are considered to be light Boltzmann fluids and the dynamics of the charged dust grains are considered in the simulation. The background plasma provides the screening to the Coulomb interaction of the dust grains. Thus, the dust grains are interacting through the screened Coulomb potential or Yukawa potential, given by

………………… (2) where Qd is the constant charge on the dust grain, and λD are inter-grain distance and Debye length of the background plasma. The ratio is an important plasma characteristic, and called as screening parameter (κ). The acting force on the dust grains corresponding to the Yukawa potential is given by λ

…………………………. (3) The equation of motion for the dust particle following Newton’s second law of motion is given by,

……………………………. (4)

64 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

The excitation of the K-H instability is produced by the external flow velocity in the x direction. In the above equation the term is the force due to the external flow. We consider only two-dimensional (X-Y) case in this simulation study. ㏨ Simulation Details: We have used the open source LAMMPS code to carry out the MD simulation of the strongly correlated dust grains in the liquid-solid regime. We have considered a 2D simulation system as square box along X and Y directions. with LX = LY = 400 (-200 to 200 ). Here is the Wigner-Seitz radius in the 2D dusty plasma layer and is the 2D density of the single dusty plasma layer. The particles are entered in the simulation box through the basis of hexagonal = v unit cells. A monolayer with 159803 number of particles are created. The boundaries are considered as periodic. We use the typical simulation parameters as follows: dust grain charge Qd = 11940, grain mass md = 6.99× kg, = 4.18× m. The Debye length of the background plasma is taken as 8.36× −vm and hence the screening−h parameter κ remains 0.5 throughout the simulations. The forcevt cutoff−h distance is chosenvt to be 20 in our simulation. The characteristic λdust plasma frequencyvt for these considered parameter is 35.86 s-1 and corresponding response time scale ( ) of the dust particles is 0.175 s. The simulation is performed in dimensionless unit (LJ in LAMMPS) and the Verlet algorithm is= used to update the positions and velocities of each particle. The time step is chosen critically so that the phenomena occurring in the response time scale of the dust particles are easily observable and it is not high enough for moving a particle too much distance in a single step (to a nonphysical position).

Fig 1-3: variation in (1) Kinetic energy, (2) potential energy, and (3) Total energy in equilibration process for ᴦ =140 and κ = 0.5.

Now our aim is to simulate the configured system for intermediate coupling parameters. The coupling parameter can be set to different values by changing or dust temperature ( ). Here we fix the intergrain distance and change the dust temperature to acquire the desired coupling parameter. Since the dust particles are arranged initially in the simulation box through the basis of hexagonal unit cells. The initial intergrain distance of the charged dust particle and hence the initial coupling parameter of the system is determined by the lattice parameter of the unit cell. To establish the thermal equilibrium for a particular ᴦ, we evolve the system in canonical (NVT) ensemble using Noose-Hoover thermostat for 40 s. Then the canonical thermostat is disconnected and the system is evolved for another 20 s in micro-canonical (NVE) thermostat. The energy plots for canonical and micro canonical equilibration run are shown in the figures 1-3. The total energy is the sum of the Yukawa potential energy and the thermal kinetic energy of the particles. Here, the energies represent the total energies of the particles in the ensembles. The energy of any particle ensemble is minimum when they are arranged in any regular lattice structure, hence in the starting of the canonical run the energies of the ensemble start to increase initially, then after sufficient run energies show a little variation. From the figures 1-3, it is clear that canonical run of 40 s is sufficient. Another 20 s of microcanonical run ensure the stable system for a desired . The system is now ready for simulation. The simulation is performed finally in the canonical thermostat. Results and Discussion: The initial state for the simulation is prepared by canonical and then microcanonical equilibration respectively. Thus, after achieving the thermal equilibrium the system is evolved with time step t = 0.01 to observe the excitation of K-H instability. The screening parameter κ is kept constant

65 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India at 0.5 throughout the simulation process. We consider an equilibrium sheared flow velocity in the direction. The velocity profile of the charged dust fluid layers is expressed as,

…………………….. (5) where is the equilibrium shear velocity, is the amplitude of the perturbation, and is the perturbation wavenumber with be the mode number of the perturbation. t v The growth of the perturbed velocity㏨ field from the equilibrium shear velocity = will demonstrate the instability in any simulation process. The amplitude of the sinusoidal v perturbation is kept small ( ) in comparison㏨ of equilibrium shear velocity. The considered shear flow speed is subsonic and the initial velocity profile satisfies the incompressibility condition ( ㏨v = thv). The sinusoidal perturbation grows as time passed. The perturbed velocity grows exponentially as time elapse. Tracking the power associated with the growing perturbed mode serves∇h a = good t measure of the growth rate of the instability and the saturation in the nonlinear㏨v stage. Here, we track the time evolution of the perturbed kinetic energy in the direction to find the growth rate of a particular mode m. The perturbed kinetic energy is normalized to its initial value and expressed as, 쳌

…………………………… (6) The figure 4 shows the growth of the K-H instability as the time evolution of kinetic energy in the y direction in log-linear scale. In the left subplot (a) of figure 4, the time evolution of kinetic energy is shown using log-linear scale for 140, and . In the right subplot (b), the time evolution of kinetic energy is shown using log-linear scale for 140, and t . = = th = = t = vht =

Fig:4 Time evolution of perturbed kinetic energy in log-linear scale for = 140, , and (a) , (b) = ㏨t = th ㏨t = vht In both figures initially the perturbed kinetic energy is growing exponentially as indicated by the linear portion of the curves. As time passes the perturbed kinetic energy or velocity field achieve high amplitude, which are comparable to the equilibrium values. As a result, the perturbed energy finally saturates after initial exponential growth. The slope of the linear portion of the time evolution curve of kinetic energy in the direction gives value which is approximately twice of the growth rate of the linear K-H instability. The red lines in both subplots (a) and (b) of the figure 4 show a linear fit to the initial linear쳌 growth rate regime of the K-H instability. In subplot (b), the black circle indicates the evolution of nonlinear stage of the unstable K-H mode, the growth later saturates in nonlinear stage.

66 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Fig:5 The atomistic view Fig:6 The atomistic view of the growth of of the growth of perturbation with time perturbation with time for . for .

t ㏨ = vht = vht

The excitation of K-H instability for dispersive and compressible charged dust fluid has been studied. The K-H vorticity contours are shown in figures 5 and 6. The time evolution of perturbed kinetic energies in the y direction are studied for different mode m for several combinations of physical parameters. In the figure 5, the growth of K-H instability is shown for different values of coupling parameters. Three layers of charged dust fluids are presented. The upper and lower red colored layers of particles are moving in the negative direction and middle blue particle layer is moving in the positive direction with equilibrium flow velocity. The vorticity contours are shown in figure 5 for 140 and 150 with different normalized times. =

(8) (7)

Fig: The numerical normalized growth rate w of the K-H instability is determined through MD simulation and plotted against wavenumber k, (7) for and (8) for . ㏨t = th = vht The initial equilibrium velocity is taken to be 1.0. The numerical growth rates of the linear K-H instability are determined from the slopes as described in figure 4. The normalized growth rate of the linear K-H instability is plotted against wavenumber k in the figure 7. This figure shows that, the growth rate of the linear K-H instability is increasing with increase in ᴦ. Thus, the coupling parameter ᴦ shows the destabilizing effect on the linear K-H instability in the regime near and above dust crystallization. In the figure 6 growth of K-H instability is shown for different values of equilibrium velocities. The vorticity contours are shown in the figure 6 for V0 = 0.5 and 1.0 with different normalized times. The coupling parameter is taken constant as 140. The relative velocity between the layers are 1.0 and 2.0 respectively. The normalized growth rate of the linear

67 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

K-H instability is plotted against wavenumber k in the figure 8. This figure shows that, the growth rate of the linear K-H instability increases with the magnitude of equilibrium flow velocity of the dust layers. Hence, the equilibrium shear flow have destabilizing influence on the linear K-H instability in the regime near and above dust crystallization. The figure shows very slow excitation of instability when V0 = 0.5. To obtain the significant value of the growth rate of instability, the ratio of equilibrium flow velocity to the dust thermal velocity must be larger than unity. The velocity shear between fluid layers excites K-H instability. In real the fluid layers may be of different densities. The initial equilibrium density of all the three layers of the charged dust fluids are kept constant in the earlier discussions. Now we are interested to investigate the effect of density gradients on the growth rate of the K-H instability. We consider the sharp density gradient between the layers of the charged dust fluids. The density of the upper and lower fluid (colored as red) is kept equal and higher than the middle fluid layer (colored as blue). The temperature of the charged dust grain is kept constant throughout the whole simulation box. The initial coupling parameter will be different for upper and lower dust layers than the middle dust layer, as their density and hence the interparticle distances are different. The three layers of the dust particles are equilibrated separately with 40 s of canonical and then 20 s of microcanonical run. The equilibrated positions of all the particles are added in the main simulation box. The sinusoidal perturbations are imposed then similarly as stated in equation (8.4). The positions and velocities of each particle are recorded as time evolved. The time step is taken as 0.0036 MD unit. The growth of the K-H instability in the interface for different time is shown in figure 9. It is found that the sharp density gradient enhances the growth of the K-H instability. The density gradient excites DAW which propagates from the interface to the lower dense fluid. A compression and elongation of the lower dense middle blue marked region can be seen in the figure 9. Owing to the consideration of periodic boundary condition the DAW excitation come back in the fluid through both upper and lower boundary of the simulation box. But this is nonphysical, to inhibit this come back and to perform detail investigation of the combined excitation of DAW and K-H instability we need to extend the simulation box in the y direction sufficiently. This is Fig:9 The atomistic view of the beyond scope of the current work and will be investigated growth of the K-H instability with in future. The influence of the direction of the equilibrium time is shown for equilibrium flow flow velocity has also been investigated. It is found that if velocity . both fluid layers flow in the same direction with relative

t velocity then, the growth of the K-H vortex in y direction is low and the㏨ vortexes= vht propagate in the direction of flow velocity rapidly. Conclusions: The molecular dynamics (MD) simulation is performed to study the problem of Kelvin-Helmholtz (K-H) instability in dusty plasma. The effects of different flow velocities and density gradients have been investigated on the hydrodynamic K-H instability. The electron and ion fluids are considered as light Boltzmann fluids and they are only providing the neutralizing background of plasma to the charged dust grains. Due to the high charges the dust particles are strongly correlated. The dust particles are interacting through the Yukawa potential. Thus, the system can be termed as Yukawa one component fluid. The problem has been simulated in particle level using the MD simulation through open source LAMMPS code. The SCDP with screening parameter k = 0.5 shows long range orders around 140. In this work, we investigate the excitation of K-H instability close and beyond 140. We consider two layers of such Yukawa one component fluids with similar dust densities and = different velocity profiles in the first case. The effects of different flow velocities and = flow direction are studied on the K-H instability. We have calculated the growth rate of the K-H instability for such configurations. In the second configuration, we consider the density gradient in the two fluid

68 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India layers and estimate the growth of K-H instability for different velocity profiles. The destabilization influence of coupling parameter is confirmed as reported by Ashwin and Ganesh [7]. The time evolution of small sinusoidal perturbation for different coupling parameters, equilibrium flow velocity and densities of fluid layers are analyzed. The time evolution of the K-H instability is observed in the present simulation study. It is found that, the different dust flow velocities and density gradients enhance the growth rate of the K-H instability. For excitation of K-H instability, the magnitude of the equilibrium velocity of fluid must be greater than the dust thermal velocity. Here we find that, the normalized equilibrium velocity V0 = 0.5, the growth of the K-H instability is very slow and the growth is linear. But, for V0 = 1.0, the growth is faster and linear for very short duration, and the nonlinear development of K-H instability and mixing occurs rapidly. References [1] S. Ichimaru, Rev. Mod. Phys. 54, 1017 (1982). [2] R. L. Merlino, and A. J. Goree, Phys. Today 57, 32 (2004). [3] Donkó, Z, Hartmann, P, and Kalman, G (2009). J. Phys. Conf. Ser. 162, p. 012016. [4] Frenkel, Y I (1946). Kinetic Theory of Liquids. Oxford: Clarendon Press. [5] Kaw, P K and Sen, A (1998). Phys. Plasmas 5, p. 3552. [6] Dolai, B and Prajapati, R P (2018). Phys. Plasmas 23, p. 083708. [7] Ashwin, J and Ganesh, R (2010). Phys. Rev. Lett. 104, p. 215003. [8] Tiwari, S K, Das, A, Angom, D, Patel, B G, and Kaw, P (2012). Phys. Plasmas 19, p. 073703. [9] Dharodi, V S, Tiwari, S K, and Das, A (2014). Phys. Plasmas 21, p. 073705. [10] Bonitz, M, Moldabekov, Zh A, and Ramazanov, T S (2019). Phys. Plasmas 26, p. 090601.

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PSC-3

Study on ion re-circulation and potential well structure in an inertial electrostatic confinement fusion device using PIC simulation

D. Bhattacharjee1, S. Adhikari2 and S. R. Mohanty1, 3 1Center of Plasma Physics-Institute for Plasma Research, Sonapur, Kamrup(m), Assam-782402, India 2Department of Physics, University of Oslo, PO Box 1048 Blindern, NO-0316 Oslo, Norway 3Homi Bhabha National Institute, Anushaktinagar, Mumbai, Maharashtra, 400094, India

e-mail: [email protected]

Abstract

PIC (Particle-in-Cell) simulations are performed to study the ion behavior inside a table-top neutron source, Inertial Electrostatic Confinement Fusion (IECF) device. In this device, lighter ions are accelerated, re-circulated and concentrated at the center by using an electrostatic field. These ions are capable of producing fusion at the central region of the cathode during high voltage operations. An open source PIC code, XOOPIC is used to simulate the ion dynamics for different experimental conditions. Ion re-circulation is visualized during run time and the phase space of ions depicts the same, which resembles the star mode of discharge. Potential profiles have been studied in the voltage ranging from -1 to -5 kV and clear formation of double potential well is observed inside the cathode grids. Finally, the simulated results are compared with the experimental results, measured using a cylindrical Langmuir probe.

Key words: IECF, PIC, Potential well, Neutrons.

Introduction: Magnetic or laser based devices are familiar for plasma confinement and to produce fusion. However, inertial electrostatic confinement fusion (IECF) is an alternate approach for producing fusion which is less complicated, easily realized and cost effective. The IECF is a portable, table-top device in which lighter ions are accelerated towards the center of the chamber due to the application of a purely electrostatic field. The cathode consists of cylindrical wire grids kept vertically at the center and is highly transparent through which the energetic ions generate to and fro motion or re-circulation. In this re-circulation process, the ions get confined inside the cathode, where, they collide with each other or with the neutrals (beam-beam or beam-background collision) and finally produce fusion at the central region of the device. Although, the IECF device cannot be used for the purpose of thermonuclear energy production due to its small Q-value, it has very wide range of near term applications. The neutrons, which are the basic products of the device, can be used in cancer treatment (BNCT), radiography, for explosive material detection, in ion thrusters, etc. [1]. Moreover, x-ray production and radiography, ion irradiation, foil activation etc. are some other applications of the device. The pioneer behind the development of the IEDF device is P. Farnsworth [2], and later, R. Hirsch [3] worked with him to upgrade the device as a fusion source. They have developed the ion gun spherical IECF device to confine the ions at the center of the device. Over the years, the device has been improved and promoted by many other researchers across the globe by introducing single, double and triple gridded system in both the cylindrical and spherical geometries [1].

70 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

The re-circulation of ions across the cathode openings is the basic process through which the ions get confined at the center and finally produce fusion (at more than about -30 kV applied voltage). Also, formation of multiple potential well structure inside the cathode is another important phenomena of the device to continue the ion re-circulation [1,3]. In this present work, we have focused our study on ion re-circulation across the cathode grids and the formation of potential wells inside the cathode during relatively lower cathode voltage operations (up to -5 kV). We have designed and simulated the cylindrical IECF device using particle-in-cell (PIC) method to study the ion dynamics and to obtain the potential profiles as well as the ion phase space to visualize the ion re-circulation process. Lastly, we have compared the simulated profiles with the available experimental results, in this work.

Modeling: To visualize the ion behavior inside the cylindrical IECF device we have performed the electrostatic PIC method using XOOPIC code [4] which is a 2D-3V object oriented PIC code with an in-built Poisson solver. The code includes Monte Carlo Collision (MCC) algorithms to model the collisions of the particles. Multigrid Poisson’s solver is used which describes the boundary conditions of the simulation. The simulated domain and the parameters are designed to recreate the exact experimental environment with a cross section of the cylindrical device including the cross section of the cathode grids (having 8 numbers of grid wires), as shown in the figure 1(b). We have also modeled the electron emitters to emit equal flux of electrons continuously into the simulation domain. Deuterium is used as the background gas and the emitted electrons interacts with

(a) (b)

Fig. 1: (a) Schematic of the cylindrical IECF device, (b) Cross-section of the simulation domain with the cathode grids. them to produce ions due to ionization. A high negative voltage is applied across the cathode as a result of which the ions accelerated towards it. The time step (Δt) of the simulation is so chosen to satisfy the Courant condition [5] and the spatial step (Δx) is considered such that it is always less than or equal to the Debye length of the system. The drift velocity of the fastest particle present in the system decides the time step size [6]. Performing adequate calculations, the simulation parameters are determined. The time step is found to be ~10-11 s, and the specific weight taken, is of the order of 109 in this simulation. The primary electron and ion temperatures are assumed to be 3 and 0.1 eV, respectively. The input file of the XOOPIC is prepared considering all the parameters and conditions mentioned here. A typical period to achieve the steady state is about 2 – 3 days in our computer. Few scripts are also developed in MATLAB® in order to visualize the simulation data.

71 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

(a) (b)

Fig. 2: (a) Ion phase space, (b) Bottom view during experiment, showing ion channels coming out of the central highly dense region.

Results and Discussion: As mentioned earlier, ion re-circulation is the primary(b) process in such IECF devices. We can visualize the re-circulation during run-time and the phase space of ions during -1 kV operation also depicts it, as shown in figure 2(a). During the acceleration of the ions towards the highly transparent cathode, some of the ions passed through the grid opening to the other side of the chamber. Again, some other ions collide at the center and get scattered to different directions through the grid spacing, and some of them collide with the cathode grids and produce secondary electrons. The ions which pass through the cathode grid openings either directly or via scattering, re-circulates across it along some particular channels which can be observed in the simulated profile as well as in the actual experiment, as shown in figure (2). The experimental photograph (figure 2(b)) is taken from the bottom side of the chamber in which the channels (spokes) of ions are vividly visible. This mode of discharge is popularly known as the star mode [1] in the IECF device.

Fig. 3: Surface plot of potential during -1kV cathode voltage.

(a) (b)

Fig. 4: (a) Simulated, (b) experimental potential profiles from -1 to -5 kV cathode voltage operations. At -5 kV voltage, formation of multiple (double) potential wells is observed.

72 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

On the other hand, observation of the potential profiles shows some interesting phenomena. The structure of the potential profile, specially, inside the cathode grids become very important due to the formation of space charge of both ions and electrons and multiple potential wells can be observed during high voltage operations. Figure (3) shows the surface plot of the potential profile during -1 kV cathode voltage operation. We have tried to study the structural changes in the potential profiles from -1 to -5 kV cathode voltages. After reaching the steady state in the simulation, we have plotted the equatorial profiles of potential for different applied voltages and are compared with the experimentally obtained profiles [7], as shown in figure (4). As we increase the cathode voltage, acceleration of the ions towards the cathode grids will be increased, they will fall into the potential well made by the applied negative voltage to the cathode and their concentration inside the cathode will also increase. Due to the increased concentration of ions inside the cathode, they will form a space charge of ions at some point of time. This space charge of ions can be termed as the virtual anode inside the real cathode. Moreover, the virtual anode so formed will not allow further ions to accelerate towards it, rather the outside ions will be repelled and the secondary electrons will be attracted this time. These electrons will move into the virtual anode and their density may be increased if we further increase the cathode voltage. If the electron density increases, they may form a space charge of electrons which may be termed as the virtual cathode inside the real cathode. In the simulated profiles clear formation of the virtual anode (space charge of ions) is observed up to -4 kV cathode voltage operation. The depth of the potential well and the height of the virtual anode increases with the increase in applied voltage. At -5 kV voltage, we have observed an indication of formation of another virtual electrode, i.e., a virtual cathode due to electron space charge at the center. In the experimental results using a Langmuir probe, we have observed similar kind of profiles. In fact, the formation multiple potential well in -5 kV operation is more prominent in the experiment, as shown in figure 4(b). However, the maximum potential drop in the experimental results are less than that observed in the simulation. For example, in case of -4 kV operation, the maximum negative potential observed during experiment is ~-2600V while it is around -3300V in case of simulation. This is due to the presence of the probe inside the chamber which forms a sheath around it so that exact measurement of potential is a difficult task. On the other hand, due to the absence of any foreign body during simulation, we don’t have such issues.

Conclusion: Continuous ion re-circulation and formation of multiple potential well inside the cathode are the basis for the fusion reaction to occur in such IECF devices, during high voltage operations. Ion re-circulation can be visualized during run time of the XOOPIC simulation and from the ion phase space ion channels can be easily observed. Experimental photograph also shows the same. In the potential profiles, depth of the potential well is found to be increased with the increase in applied negative voltage. During -5 kV, formation of double well is observed. Langmuir probe measurements also supports the simulated results when observed experimentally. In future, we are planning to study other parameters like ion density, ion energy distribution function, etc. using XOOPIC simulation and will also try to improve the simulation further in order to visualize the data during fusion relevant (more than -30 kV) energies.

Acknowledgment: I acknowledge my supervisor, Director of IPR, Center director of CPP-IPR, and my lab-mates for their support. I am also thankful to Department of Atomic Energy (DAE) for their financial support to carried out my work.

References [1] G. H. Miley and S. K. Murali, Inertial electrostatic confinement (iec) fusion, Fundamentals and Applications, Springer (2014).

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[2] P. T. Farnsworth, Electric discharge device for producing interactions between nuclei (1966), US Patent 3,258,402. [3] R. Hirsch, Inertial-electrostatic confinement of ionized fusion gases, Journal of Applied Physics 38, 4522 (1967). [4] J. P. Verboncoeur, A. B. Langdon, and N. Gladd, An object-oriented electromagnetic pic code, Computer Physics Communications 87, 199 (1995). [5] C. De Moura, C. Kubrusly, and S. Carlos, The courant-friedrichs-lewy (c) condition, Appl Math Comput 10, 12 (2013). [6] C. Birdsall and A. Langdon, Plasma physics via computer simulation (CRC press, 2004). [7] D. Bhattacharjee, D. Jigdung, N. Buzarbaruah, S. R. Mohanty, and H. Bailung, Studies on virtual electrode and ion sheath characteristics in a cylindrical inertial electrostatic confinement fusion device, Physics of Plasmas 26, 073514 (2019).

74 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

PSC-4

Slow and fast modulation instability and envelope soliton of ion acoustic waves in fully relativistic plasma having nonthermal electrons

Indrani Paul1, Arkojyothi Chatterjee2 and Sailendra Nath Paul1,2 1 Department of Physics, Jadavpur University, Kolkata-700032, India 2East Kolkata Centre for Science Education and Research P-1, B.P.Township, Kolkata-700 094, India.

e-mail: [email protected]

Abstract

Slow and fast modulation instability, envelope soliton of ion acoustic wave have been theoretically studied in cold unmagnetized fully relativistic plasma consisting of cold positive ions having constant stream velocity and nonthermal electrons using Fried and Ichikawa method. The expression of nonlinear Schrodinger equation in fully relativistic plasma has been derived for slow- and fast- mode of the wave and the conditions for the existence of modulation instabilities are obtained. From the nonlinear Schrodinger equation, the solution for envelope solitons for slow- and fast- modes of the wave are also obtained. The profiles of bright- and dark-envelope solitons are drawn and discussed taking different values of ion-stream velocity and nonthermal electrons. The results are new and would be applicable in astrophysical plasma. Keywords: Relativistic plasma, Ion acoustic wave, Two temperature electrons, Modulation instability, Envelope solitons, Nonlinear Schrodinger equation , Fried and Ichikawa method.

1. Introduction

In weakly relativistic plasma, Das and Paul [1,2] have first derived the Korteweg-deVries (K-dV) equation using reductive perturbation method of Washimi and Taniuti [3 ] to study ion acoustic solitary waves (IASWs) considering a collision less and unmagnetized weakly relativistic plasma consisting of cold ions and isothermal electrons. It was first shown that relativistic effect gives significant contribution to IASWs only in presence of streaming of ions. Later, various authors have considered different parameters in weakly relativistic plasma , e.g. ion-temperature, negative ions beam ions two-temperature electrons , nonisothermal electrons etc. for the studies of ion-acoustic solitary waves. However, solitary waves in relativistic plasma in presence of nonthermal electrons gives rise to some interesting results. But, few authors have studied the modulation instability of ion acoustic waves in fully relativistic plasma. Ghosh and Banerjee [4] have theoretically studied nonlinear amplitude modulation of ion-acoustic waves (IAWs) in fully relativistic unmagnetized two-fluid plasma by using complete set of fully relativistic dynamic equations. The growth rate is shown to decrease with increase in the relativistic effect. We are interested here to study modulation instability and envelope solitons in a fully relativistic plasma composed of cold relativistic ions

75 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India andnonthermal electrons. We have derived the nonlinear Schrodinger equation by using the Fried and Ichikawa method [5] instead of multiple scale perturbation technique. 2.Formulation The plasma is assumed to be fully relativistic unmagnetized collision less having nonthermal electrons . So, the basic equations describing the plasma dynamics in non-dimensional form can be written as: n     2 i (n u )  0 - - - (1), ()u u   - - - (2), n  n - - - (3) t  x i i ti  x ir  x x2 e i

1 u 2  2    i where, u ui / , 1- 2  , ir c 

ϕ is the electrostatic potential, ni and ui are the density and velocity of ions, uir is the relativistic velocity of ions, c is the velocity of light; ne is the density of electrons, In the above Eqs. (1)-(3) the densities of electrons are normalized with respect to the equilibrium density of ions n0 , the distances are normalized by the Debye length, time by the ion plasma period, velocity by ion-acoustic speed and potential  by  BT e / e .

The boundary conditions are : ui  u0 , ni  1 and   0 as x   .

Since we assume the electrons to be nonthermally distributed, the electron density ne in Eq. (3) is given by 2 ne (1    )exp(  ) (4) where,  4p / (1  3 p ) ,  measures the deviation from thermalized state p determines the number of nonthermal electrons in the plasma. Using Fried and Ichikawa [5] we have derived the Nonlinear Schrodinger (NLS) equation given by 2      2 i() Cg  P2  Q    0 t  x  x (5) where, P is the dispersive coefficient P and Q is the nonlinear coefficient Q .

The nonlinear coefficient Q of NLS equation (5 ) for slow and fast wave are obtained as

4 3 6 5/2 10 (22  2f  3  1  3 f ) Qf 6 (23  1   1  4 f )  6 2 3/2 21 31 (  1  2f   1 )

(6a)

3 10 (2 4  3   )  6   5/2   2 2s 1 3s Qs 6 (2 3 1 1 4s ) 6 2 3/2 21 31 (  1  2s   1 )

(6b)

76 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Vf u o  Vs u o   2 fV f  u o , 2 s  V s  u o , 3 f  1 2  , 3s  1  2  , c  c  Where,  5V2 u 2 8 V uu2 V 2   5V2 u 2 8 V u u2 V 2   f o  f o o f 5 , s o  s o  o  s  5 4 f  4 2 2 2  4s  4 2 2 2   c c c c   c c c c  The dispersive coefficient P for fast and slow mode of the wave is obtained as 1 k 3/2 1 k 3/2   1   1 PFast 2 5/2 , PSlow 2 5/2 (7) 2 (k 1 ) 2 (k 1 )

1 (1 3 ) u2         io In (6) and (7), the parameters 1 (1 ),2 , 3 ,1 1  2  2 6 c 

3. Results and discussions A) The modulation instability The amplitude modulation of ion acoustic waves (IAW) in fully relativistic plasma consisting of inertial cold ions and isothermal two- temperature can be studied by using the NLS equation (6). The maximum growth rate of modulation instability of ion acoustic wave is 2 m  Q  0 . (8) 2 α0 is a real constant and   Q  0 is the amplitude dependent frequency shift. The sign of the product PQ determines the stability / instability of the ion-acoustic wave. If the product PQ is negative (i.e. PQ < 0) the ion acoustic wave will be unstable relatively modulation. But, the wave will be stable relatively modulation if PQ ( i.e. PQ > 0) is positive.

Growth rate of unstable waves The growth rates of unstable IAW wave given by Eq.(12 ) are numerically estimated and graphically shown in Fig.1(a) and Fig.1(b) for different values of ion stream velocity and nonthermal parameter of electrons in fully relativistic plasma.

77 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

7 3 10

X2  j 3 7 2 10 X2 j 4

X2 j 5 GrothRate

X2 j 6 7 1 10

0 4 6 8 10

k j Wave Number

60

40 Xsj 1

Xsj 3

Xsj 5

Xsj 6 20

0 0.2 0.4 0.6 0.8 1

kj

Fig.1(a). Growth rate for slow mode ion acoustic wave different relativistic stream velocity. The red, blue, green and magenta graphs represent u0/c=0.4, 0.533,0.667 and 0.8 respectively,  =0.3,c=1.5; Fig.1(b) -Growth Rate of slow mode for different values of  . The red, blue, green and magenta curves represent  =0.1. 0.3, 0.5 and 0.6; u0/c=0.6, c=2.

B) Envelope Soliton

The solitary wave solutions of ion acoustic wave (IAW ) may be obtained from the NLS equation (5). The product PQ may be positive or negative which give two types localized solitary wave solutions. For PQ < 0 , the wave is modulationally unstable and the bright- envelope-soliton (or bright soliton) is excited. But, when PQ > 0 the wave is modulationally stable and gives a dark-envelope-soliton (or dark soliton). In fact, bright solitons are localized large-amplitude excitations on the envelope of certain carrier waves. Their formation requires an attractive or focusing nonlinearity. The dark solitons are dips or holes in a large-amplitude wave background. Their formation requires a repulsive or defocusing nonlinearity. The profiles of bright-envelope solitons and dark envelope solitons for different values of ion stream velocity nonthermal parameter of electrons are shown in Figs.2(a) and 2(b) for bright solitons.

78 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

0.08

0.1

0.06

 j 2  bs j 1

 j 4 0.04  bs j 2

 j 5  bs j 4 0.05 Bright Soliton Profile Soliton Bright Bright Soliton Profile Soliton Bright

0.02

0 0 5 0 5 5 0 5

 j  j Fig.2 (a) Profiles of bright soliton for slow mode of the wave different values relativistic ion stream velocity (u0/c).The red, blue, green and magenta lines correspond to u0/c =0.267, 0.533, 0.667 ; Other parameters are and  =0.3,c=1.5; Fig.2(b) Profiles of bright soliton for slow mode of the wave for different values  .The red, blue and green lines correspond to  =0.1, 0.2 and 0.6; Other parameters are .c=2, u0/c=0.6

4. Conclusion

In this paper we have theoretically studied modulation instability of slow and fast mode of ion acoustic waves along with the possible generation of both dark- and bright- envelope soliton in a fully relativistic plasma consisting of cold ions and nonthermal electrons using Fried and Ichikawa method.In our analysis, the form of envelope soliton is derived from the NLS equation and structures of bright and dark envelope solitons for slow and fast mode are graphically shown and discussed. i) Growth Rate: The growth rates of unstable slow- mode slowly increases with ion stream velocity u0 / c and wave number k .The growth rate of slow- mode increases with the increase of  and wave number k. ii) Bright Solitons: The bright solitons of slow- mode for different values of u0 / c with fixed values of k ( k =1) are compressive in nature the amplitude decreases with the increase of ion stream velocity. The bright soliton of slow- mode for different values of  and fixed values of k are compressive in nature and its amplitude increases with the increase of  .

The relativistic plasmas occur in a variety of situations, such as, space-plasmas, laser- plasma interaction , plasma sheet boundary layer of earth’s magnetosphere . The relativistic motion in plasmas is assumed to exist during the early evolution of the Universe . In astrophysical observations it has been found that particles are ejected with high velocities during solar bursts or the explosion of stars huge amounts of matter in the form of ionized gases are ejected from these astrophysical objects at very high velocities .

References

[1] G C Das and S N Paul (1983) , XVI International Conf. Phenomena in Ionized Gases, August 29-September 2, 1983. [2] G C Das and S N Paul ,. The Physics of Fluids 28, 823( 1985). [3] H Washimi and T Taniuti, Physical Review Letters 17, 996 (1966). [4] B Ghosh and S Banerjee , Journal of Plasma Physics 81, 905810308 (2015). [5] B D Fried and Y H Ichikawa, Journal of Physical Society of Japan 34, 1073(1973).

79 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

PSC -5

Effect of negative charge dust on ion-acoustic dressed solitons in unmagnetized plasmas

J. K. Chawla, P. C. Singhadiya1, A. K. Sain and S. K. Jain2 Department of Physics, Govt. College Tonk, Rajasthan, India-304001 1Seth RLS Govt. College, Kaladera, Rajasthan, India-303801 2Govt. College, Dholpur, Rajasthan, India-328001

e-mail: [email protected]

Abstract

Propagation of an ion-acoustic soliton in a plasma consisting of negative charge dust is considered the reductive perturbation method (RPM). The well known RPM has been used to derive the KdV equation. This exact solution reduce to the dressed soliton solution when mach number is expanded in terms of soliton velocity. Variation of amplitude and width for the KdV soliton, core structure, dressed soliton and exact soliton are graphically represented to different values of negative ions and mach number. The present study of this paper may be helpful in space and astrophysical plasma system where negative charge dust ions are present.

Key words: Soliton, RPM , Dusty Plasma, soliton

Introduction: In recent years, interest in study of dusty plasmas has arisen because of its occurrence in space and astrophysics. Vladimirov et al. [1] studied the ion acoustic waves in complex laboratory plasmas containing dust grains and negative ions, where effects of relevant processes were considered. Mamun and Shukla [2] used two models for negative ion distributions, i.e., Boltzmannian and the streaming, and found that the negative ion number density and streaming velocity could greatly affect the dust surface potential, and therefore the dust charge. Baluku et al. [3] investigated dust ion acoustic solitons in an unmagnetized dusty plasma comprising cold dust particles, adiabatic fluid ions, and electrons satisfying a kappa distribution using both small amplitude and arbitrary amplitude techniques. A theoretical investigation of dusty plasma consisting of ion fluid, non-thermal electrons and fluctuating immobile dust particles has been made by Alinejad [4]. Ichikawa et al. [6] and Sugimoto and Kakutani [7] have been studied the dressed soliton in plasmas. Ion acoustic dressed soliton in EPI [8-9], ion beam [10] and dusty [11] plasmas have been studied using sagdeev potential technique and RPM. They discuss the characteristics of the soliton such as amplitude, width and velocity. Chatterjee et al. [12] and Roy and Chatterjee [13] have been studied the dressed soliton in quantum plasmas and dusty pair-ion plasma. Effect of the quantum parameters and characteristics of soliton such as amplitude and width. Tiwari [9] studied only the effect of fractional concentration on amplitude and width the soliton. The aim of this research paper have been studied the propagation of ion-acoustic dressed soliton in nonthermal electrons in plasmas by considering the RBM, the first and second coupled

80 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India evolution equation, namely the KdV equations is derived. Through elimination of the secular terms, the KdV soliton, core structure, dressed soliton and exact soliton are determined.

Basic equations: We consider a collisionless unmagnetized plasma consisting of ions and dust. The dynamics of the plasma is given by following set of normalized fluid equation: N VN  i  ii  0 (1) t x V V  i V i  (2) t i  xx N VN  d  dd  0 (3) t x V V  d V d   (4) t d  xx  2 1     NNe (5) x2 id Here N and V are the normalized density and fluid velocity of the plasma ions respectively.  is the electric potential.   MZ dd ,/  mmM idd ,/   nn id 00 ,/ and  Z d . These quantities have been rendered dimensionless in terms of equilibrium plasma density n0 ),( ion 2/1 sound speed mT ie )/( and characteristic potential e eT ),/( respectively. The space coordinate 2/12 speed x)( has been normalized in terms of Debye length speed D   e 00 enT )/( and time coordinates by the inverse of ion plasma frequency.

Stationary solitons solution : We introduce the usual transformation in equation (1) – (5) and obtain stationary soliton solution   Mtx (6) Where M is the Mach number of soliton. Integrating Eqs. (1) - (5) and using the necessary boundary conditions (Ni,d → 1, and Vi,d → 0 as   ) for a soliton structure, gives M N i  2 M  2  (7) M N d  2 M  2  (8) Integrating the value of Ni in (7) and Nd in (8), multiplying both side by dd  ,/ integrating once and using the necessary boundary conditions (Ni,d → 1, and Vi,d → 0 as   ) we get the following relation 1 2 Vd   0)()( (9) 2  where the Sagdeev potential V  is given by 2  M  2   2       2    V 11)( e   11 2  M  11 2    M   M  (10)

81 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

 32 I expand the value of e 1   ... and using this Taylor series expansion in (9) and 62 include also the effect of fourth-order nonlinearities of electric potential ).( The equation (9) reduces to 2 2 3 4 d  1 2  3 (11) Where   1  1    (12) 1  MM 22   1 2 1    2  4 4  (13)  MM 3  1  5 3 5     3  6 6  (14)  12 4 4MM  Integrating of eq. (11) with respect to  and using the boundary conditions ( dd   ,0/   0 as   ) gives stationary exact soliton solution as /2     21 (15) 2/1  4     31  2   1 2   A  11)(cosh2   2  Where 2/1    A   1  (16)  4  The exact soliton solution (15) is the same results to (9a) earlier investigation [9]. We denote (15) as small amplitude as compared with the KdV soliton, because its expansion in small amplitude limit can give rises to the KdV soliton and dressed soliton solution when the RPM is used for the analysis. We expand the Mach number (M) of soliton velocity   as M 1  in (12) – (14), and 2 retaining terms up to  in  1 , and terms up to  in  2 , and keeping  3 , independent of  such that each terms on R.H.S. of (11) is of fourth order in combined nonlinearities of  and . we find out 2 1     3211   (17)

2 R  4  (18) 1      15   3  (19) 3  12  where 2  113    R  (20) 13  2  We using (17) – (19) and retain terms up to the order of 2 in (15)

 1 2   kkk 21   (21)  2   4  3  k3 1  (22)  2  R 

82 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

2/1       6k     31  6       41  1 k k1  ...   2   4 4  4   (23) where   11    k  (24) R   R 12414    k  (25) 1 R 2 and     2 RR  16831116  k  (26) 2 R 3 Substituting (17) - (19) in (15) and retain terms up to the order of 2 in the expansion, we can write the dressed soliton solution as 2 ~ 2 ~ 2 ~  1 sec Ah  2 sec tanh AAh  (27) where  2 kk 2 kk   kkk   2  2 3  3  2 2  31 1 2 3   1 131 kkkkkkkkk 3 81624   2 132 kkkkkk 3 842   R R   R 

 2 kk   kkk  (28)  2    3   2 2  31 2 2 3   kkkkk 31 84   132 kkkkk 3 822   R   R  (29) ~ Including the contribution of 2 term in (15), we can expressed A as 2/1 2/1 ~   1  1   A       (30)  4   2  Keeping terms of order  only soliton solution (27) reduces to the KdV soliton 3   sec 2 Ah  (31) 2 where 2/1    A    (32)  4  Equation (27) is following first (core structure) and second terms (cloud structure) 2 ~ core  1 sec Ah  (33) 2 ~ 2 ~ cloud  2 sec tanh AAh  (34) Results and Discussion: We present the variations of amplitude, width and product of amplitude and square of width (P = 2 amplitude × Width ) of the KdV soliton k , core structure c , cloud structure cl , dressed soliton  d , and the small amplitude exact soliton solution s .

Figure (1) shows the variation of  S (solid blue color line),  KdV (dashed red color line), core

(dotted black color line),  dS (dotted green color line) andcloud (solid yellow color line) versus  for different value of  = 0.006, 0.007 and 0.008 at the Md = 10000, Zd= -100, and M = 1.2.

83 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Here we find that as finite  increases, the small amplitude of  S ,  KdV , core ,  dS and cloud corresponding to  also increases but the potential of the KdV soliton  KdV )( is constant.

Fig. Cap.

Fig. 1. Variation of  S (solid blue color line),  KdV (dashed red color line), core (dotted black color line),  dS (dotted green color line) andcloud (solid yellow color line) vs  for different value of  = 0.006,0.007 and 0.008 at the Md = 10000, Zd= -100, and M = 1.2.

Conclusions: The small amplitude exact soliton solution, KdV soliton, core and cloud structure and dressed soliton solution which described the ion-acoustic dressed soliton in unmagnetized plasma with nonthermal electron is derived. The main conclusion of this paper are the following For a given value of soliton velocity, the amplitude of exact soliton and core structure (KdV soliton and dressed soliton) decreases (constant) as nonthermal increases but for a given value of  , the amplitude of exact soliton, core structure, KdV soliton and dressed soliton increases as soliton velocity increases.

References [1] S V Vladimirov, K Ostrikov, M Y Yu, and G E Morfill, Phys. Rev. E 67, 036406 (2003). [2] A A Mamun and P K Shukla, Phys. Plasmas 10, 1518 (2003). [3] H Alinejad, Astrophys Space Sci, Volume 327, Issue 1, pp 131-137 (2010). [4] T K Baluku, M A Hellberg, I Kourakis and N S Saini, Phys. Plasmas 17, 053702 (2010). [5] S L Jain, R S Tiwari and M K Mishra, Astrophysics and Space Science 357 (1), 57 (2015). [6] Y H Ichikawa, T Mitsu-Hashi and K Konno J. Phys. Soc. Jpn. 41, 1382 (1976). [7] N Sugimoto and T Kakutani J. Phys. Soc. Jpn. 43, 1469 (1977). [8] R S Tiwari, AKaushik, M K Mishra Physics Letters A 365, 335 (2007). [9] R S Tiwari Physics Letters A 372, 3461 (2008). [10] Yashvir, R S Tiwari and S R Sharma Canadian Journal of Physics 66, 824 (1988). [11] R S Tiwari and M K Mishra Physics of Plasmas 13, 062112 (2006). [12] P Chatterjee, K Roy, G Mondal, S V Muniandy, S L Yap and C S Wong Physics of Plasmas 16, 122112 (2009). P Chatterjee, K Roy, S V Muniandy and C S Wong Physics of Plasmas 16, 112106 (2009). [13] K Roy and P Chatterjee Indian Journal of Physics 85, 1653 (2011).

84 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

PSC-6

Inductive Energy Storage System with Plasma Opening Switch: A review

Kanchi Sunil1, Rohit Shukla1,2, Archana Sharma1,2 1Homi Bhabha National Institute, Mumbai-400094, 2Pulsed Power & Electro-Magnetics Division, Bhabha Atomic Research Centre Facility, Atchutapuram, Visakhapatnam, Andhra Pradesh, India-531011,

e-mail: [email protected]

Abstract

Pulse compression technique is used to generate high powers in the range of Terawatt with secondary energy storage device as inductive energy store (IES) with plasma opening switch (POS) having charging time is in the range of microseconds and output pulse duration in nanoseconds. The inductive energy store is more advantage compared to most widely used capacitive energy storage devices with respect to energy density which is 10 -100 times high [1]. The parameters that define the performance of IES system are peak output voltage, peak output current, rise times and pulse widths of current and voltage. Employing of POS results in multiplication of voltage and power with good energy coupling between the source and load. The use of POS improves the load current rise times as well [1]. The IES with POS technology is used in different applications include generation of particle beams, radiation sources, fusion research and defense applications. Some of the facilities of plasma opening switch for mega-ampere are GIT-16 [2], MAGPIE [3], COBRA [4], DECADE [5], ACE-4 [6]. The experimental results of these facilities gives details of current conduction phase and opening phase of micro second POS. This paper provides details of different facilities of POS technology and simulation of ideal model of inductive energy system with different functions of variation of POS switch resistance connected to resistive load.

Key words: Inductive Energy Storage, Plasma Opening Switch, mega-ampere

Introduction: In pulsed power engineering, the applications of inductive energy storage systems have good interest. The IES with POS is a solution for many problems which includes power enhancement, output pulse width and rise time reduction, prepulse elimination and design of pulse generators with low cost for different applications. The Fig-1 shows the IES with plasma opening switch.

85 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Fig.1: Schematic view of POS operation The working of POS is as follows: a plasma path is formed between the high voltage electrode and grounded electrode parallel to load. On conduction of the path due to plasma puffing, the energy stored in capacitor is transferred to inductive store. Due to changes of plasma parameters, the path becomes non-conducting suddenly (POS opens), which generates high voltage across the switch and load. Under these conditions, the total energy stored in inductor is transferred to load [7]. This paper provides the review on different POS technologies available in literature in Section-I and simulation of ideal IES system in section II. The section-III gives the conclusion of paper.

I. Facilities of POS Technology

1. GIT-16 (S. P. Bugaev et.al) The GIT technology was developed by High Current Electronics Institute, Russia for the experiments on high-temperature plasmas generated by gas puff and wire array implosions. The GIT-16 is a 6.8 mega-joule pulsed power generator in which the technology of direct pumping of an IES from Marx capacitor bank [8] and delivery of energy to a Z-pinch [9] load with microsecond POS employed. Each module consists of a primary energy store (set of Marx generators), a vacuum bushing insulator and a vacuum transmission line. The primary energy store consists of two sections connected in parallel in which each sections contains 12-stage Marx generator. The GIT-16 pulse generator has negative output voltage generation of 2MV with current as 7.6MA [10]. The currents in this is monitored by Rogowski coils.

2. MAGPIE MAGPIE is pulsed power facility in Imperial College London. MAGPIE consists of four Marx capacitor banks which is discharged in to four independent pulse forming lines (PFLs) [11]. These are combined into single vertical transmission line which delivers maximum of 1.4MA of current within 250ns to load as vacuum chamber [12]. The peak electron density measured through interferometry technique is 2.5×1018 per cm3 [13].

3. DECADE The DECADE pulsed power generator is developed by US based Physics International Company. This generator is multi-module system working in X-ray explosive emission diodes. The main parts of module are Marx generator (570kJ of energy) [5], the intermediate storage capacitor, the triggered closing switches, a water line, the vacuum insulator, the inductive store is designed using magnetically insulated transmission line, the POS and the diode load. When POS in full conduction state, the maximum current reached up to 1.8 MA within 300 ns. The primary energy store Marx generator consists of six modules, each containing twelve stages 85 kV per stage. The output voltage of the Marx generator reached to 1MV. The intermediate energy storage capacitor is discharged through six simultaneously operated triggered gas switches. The plasma sources are coaxial cable guns that produce a plasma density of approximately 1015 cm-3 [14].

86 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

4. ACE-4 The ACE-4 pulsed power facility is Mega joule system capable of delivering 4MJ [6] developed by Maxwell Company, USA. Power Conditioning is performed using IES with POS. The flashboards are used as plasma sources for the ACE-4. The Marx module consist of 24 generators. In conduction phase, the maximum current in the POS builds up to 5 MA in 1.6 µs. During conduction phase current front propagates down the plasma in a snowplow mode, pushing the plasma ahead and to the sides, until the current channel reaches the end of the POS region. The existing plasma in the regions of POS eventually thins such that it will not allow the current to flow, and a gap is formed, transferring the current to the load. The current is typically transferred to the electron diode load in 100 ns. The electron density measured using the laser based interference technique is approximately ~1015/cm3 to maximum of 1018/cm3 according to literature [14, 15].

5. COBRA The COBRA pulsed power facility is designed at Cornell University for wire array X pinch studies. The two applications for which the COBRA designed is to study X pinch as loads and to develop X pinches in return current path as source of point-projection radiography of wire arrays. The primary source consists of storage capacitor charged to 70kV. The output of primary source charges the four coaxial water pulse forming lines having resistance of 1.8 ohm with line delay as 30ns. The intermediate capacitive store charged from two pairs of water PFLs is discharged through two self-breaking gas switch. The four charged output PFLs from intermediate source discharged independently using laser triggered spark gap switches. The discharge current of 1MA has rise time of 230ns with full width and half maximum of 350ns [16].

II. Simulation of Ideal Model of OS with IES

The Opening Switches play important role in the IES system. The Fig-6 shows the inductive energy storage system. The main circuit of IES contains a primary storage device, a triggered closing switch, storage inductor (secondary storage device), an OS and a load. The design and development of opening switch is the challenge in the present scenario. The OS should have less resistance while conducting, high resistance while in open state, capability of interrupting high currents in short duration, high dielectric strength and fast recovery response. The rise of the resistance increase of OS should be less such that it can interrupt the high amplitudes of currents in short time i.e., the pulse width is in the order of micro or nano seconds. The rate of change of resistance in OS is the parameter that describes its performance.

Fig. 2: IES with Primary storage device as capacitors Operation Principle: The basic operation of the IESS, in which the energy is be stored in the form of magnetic field during the current flowing through inductor. The inductor is charged through the sources like capacitors, battery, magnetic flux compression generators, etc. As the OS is closed, primary current flows in the circuit which charges the inductor and a practical inductor contains on ESR (R) depends purely on the design of inductor. We have to design the inductor such that it has less

87 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

losses in primary loop and the time constant of the circuit (L/R) must be greater than time (t) to trigger the switches from the charging of the source. The charging time of inductor is based on thet time constant of primary loop. The current in the OS is interrupted such that the total current will be transferred to the load generating high voltages across the load terminals.

Circuit Analysis: The circuit shown in the Fig-6 is the simplest and ideal IES which was considered here for analysis reported by Pai. S.T. The voltage source in series with the inductor is considered as the current source in the primary loop to charge the storage inductor. Here the OS is considered equivalent to time dependent resistor R(t). The different cases of variation of OS resistance is discussed in detail.䂺 Case(i): The OS is considered as the linearly rising resistance switch with time. The switch resistance is defined as . Where k is the slope which is constant. The circuit voltage and current equations =

䂺  (1) = +  The solution of the load current is obtained by applying+ the= t boundary conditions i.e., at t=0, =  , = 䂺 䂺 (2) the time at which the maximum current can be obtained is calculated by equating the derivative of L = 䂺 + exp ln + − the to zero and given by

L (3) =

Fig. 3: Switch current profile and Load current profile for case (i) with different switching speeds

Case(ii): In this case the resistance of the OS is considered as the step function, with conditions as, at t=0, R=0 and as t > 0, constant value of R=Rf. This variation of resistance is represented be (4) By applying the boundary conditions and considering− the load as inductive load (LL) the load current is expressed as = v − (5) − Where constants, , L 䂺 = v − From the above equation if the initial value of the current and Rf is made high then the power at = + = the load terminals will be high.

88 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Case(iii): Now, if the resistance variation of the OS is considered as step rise i.e., in step. If the load is inductive load then from the law of conservation of the magnetic flux, the load current is expressed as t 䂺 (6) Where, constant ‘a’ is already defined above. L = 䂺

Fig. 4: Switch current profile and Load current profile for (a) case (ii) (b) case(iii)

Conclusions

In this paper, the plasma opening switch based inductive energy storage pulse generator technologies developed by various laboratories and researches are reviewed and there current and voltage ratings were reported. The simulations of ideal model of opening switch based IES system with variation of switch resistance is carried out and results were reported. We aim to design a nanosecond plasma opening switch based inductive energy system which can deliver current in the range of mega amperes, output voltage in the range of mega volts and energy of 40kJ.

References [7] R. A. Meger et. al., Appl. Phys. Lett., 42, 943(1983). [8] S. P. Bugaev et.al., Russian Physics Journal, 40, 1154-1161(1997). [9] G. N.Hall et al., Review of Scientific Instruments, 85, 943-945(2014). [10] Shelkovenko, Tatiana A et al., IEEE transactions on plasma science, 34, 2336-2341(2006). [11] P. Sincerny et al., Tenth IEEE International Pulsed Power Conference, 3-6 July 1995, Albuquerque, NM, USA, 405-416(1995). [12] R. Crumley, D. Husovsky and J. Thompson, 12th IEEE International Pulsed Power Conference, 27-30 June 1999, Monterey, CA, USA, 1118-1121(1999). [13] B. V. Weber et al., IEEE Transactions on Plasma Science, 19(5), 757-766(1991). [14] W. J. Carey and J. R. Mayes, Conference Record of the Twenty-Fifth International Power Modulator Symposium, 2002 and 2002 High-Voltage Workshop, 30 June-3 July 2002, CA, USA, 625-628(2002), [15] M G Haines, Plasma Physics and Controlled Fusion: IOP Science, 53(9), 093001(2011). [16] https://www.hcei.tsc.ru/en/cat/fields/fields.html for information on [17] Liansheng Xia et al., Review of Scientific Instruments, 79, 086113(2014).

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[18] https://www.imperial.ac.uk/plasma-physics/magpie/ [19] T. Clayson et al., IEEE Transactions on Plasma Science, 46(11), 3734-3740(2018). [20] Pulse Generators with Plasma Opening Switches. In: Pulsed Power. Springer, Boston, MA, 2005. [21] Niansheng Qi et. al., IEEE transactions on plasma science, 30(1), 227-238(2002). [22] https://www.lps.cornell.edu/project/cobra/

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PSC-7

Simulation Study of Planar Anode Micro Hollow Cathode Discharge Using Dielectric Layer

Khushboo Meena1, R P Lamba1 1CSIR-Central Electronics Engineering Research Institute (CSIR-CEERI), Pilani-333031, Rajasthan, India.

e-mail: [email protected]

Abstract

Microdischarges are very popular for a long time and they have many advantages. Micro Hollow Cathode Discharge is one of the micro discharges which is formed in the cylindrical shaped hollow cathode and responsible for the generation of high electron density discharge, but it has a very short period of a lifetime due to the sputtering effect on the cathode walls and moving of the discharge from glow to arc region. There is another type of discharge called Dielectric Barrier Discharge; it has the advantage of low electrode erosion. In this paper, a 2D-axis symmetric model is designed and simulated using the Plasma Module of COMSOL 5.4 Software. This model includes the MHCD as well as DBD discharge. In this model, a dielectric layer of 40µm is placed on the inside wall of the anode. In this model, a planar anode is used which is covering one side of the hollow cathode. The diameter of the hollow cathode is 500µm and a height of 500µm is used. Argon gas is used for the discharge at atmospheric pressure. Pulsed voltage is applied to have the 1000ns period cycle. In this model for the ignition of the discharge takes place at the minimum distance between anode and cathode. After that discharge gets sustained in the hollow cathode cavity and attains the stable abnormal glow discharge having high electron density in the order of 1018 m-3.

Key words: Microdischarges, Dielectric Barrier, Hollow cathode

Introduction: The microdischarges are very popular due to their small sizes and many other advantages over macro discharges. The Micro hollow cathode discharges (MHCD) are firstly introduced by the A.D. White in 1959[1]. From there it covers the long journey of many decades and evolved during this time. The MHCD is used in different technologies such as laser technology, UV generators, material processing, etc. They conduct the high discharge current as comparatively conventional discharge [4-5]. Two scaling laws are followed by the MHCD first is pd (pressure and distance between the electrodes) law which depends on Paschen’s curve for the breakdown voltage and another law is pD (pressure and Diameter of the hollow cathode) scaling law or Allis White law. The pendulum effect is responsible for the hollow cathode effect which is electrostatic trapping of the fast electrons which causes oscillating motion within the cathode hollow cavity. But it has the disadvantage of a short period of life-time due to the sputtering effect on the cathode walls caused by electrodes and glow to arc transition of discharge.

91 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

The Dielectric barrier discharge [DBD] which is also called the silent discharge is also very popular because of its capability of ozone generation. These discharges have less electron density as compared to the MHCD but it forms a steady uniform glow discharge and prevents the glow to arc transition. In this discharge dielectric layer is used between electrodes, it may be single dielectric or double dielectric as peruse.

In this paper, we have tried to coaxially use the MHCD and DBD [2]. We have used the single dielectric layer on the planar anode and placed it on the hollow cathode. For simulation we have used the COMSOL 5.4 software and the 2D- axis-symmetric model is designed in the plasma module it has been explained in First Section [3]. In Second section simulation studies and result has been shown with the help of spatial distribution discharge and other results. In the last section, the conclusion has been noted regarding the results.

Simulation studies and Results: In this paper COMSOL 5.4 software is used to simulate the designed model. A 2D-axis symmetric model is designed using the plasma module. In figure 1 schematic diagram of the designed model is shown. In this model Micro hollow cathode of diameter 500 µm is used having the height of the 500µm to maintain the aspect ratio as 1:1. In this model, a planar anode is used on the one window of the cathode cavity and a dielectric layer is placed between the anode and cathode of 40µm as shown in the figure. Simulation has been carried out at the atmospheric pressure in the presence of argon gas. We are using a square pulse with a rise time of 100ns and pulse width is 1000ns per cycle. This Nanosecond square pulse is used to provide the hollow cathode effect at higher pD values because according to the Allis white law pD range for hollow cathode discharge is 0.1-10 Torr cm. But because we are using a single dielectric layer in this model it opens up the higher range for pD value.

Fig. 1: Schematic diagram of the designed MHCD

 Spatial distribution of discharge: Spatial distribution of the discharge is shown by the Iso-surface plot of a given model in figure 2. In this design discharge ignites near the anode wall and after ignition discharge moves towards the cathode cavity where it gets sustained. This process repeats itself for every pulse. In given figure 2(a) ignition of the

92 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

discharge is shown at 1kV. After the ignition at around 100ns discharge gets collected inside the hollow cathode due to the pendulum effect with the high electron density order of 1018 m-3 as shown in figure 2(b).

(a) (b)

(c) (d)

Fig. 2: Iso-surface plot of the discharge in the given design at 1kV for 50kHz frequency.

During the deceiving pulse at around 900ns, it starts again confining the discharge and confined at 1000ns as seen in figure 2(c) and 2(d). It shows that for the nanosecond pulse cycle even for higher pD values discharge takes place in the hollow cathode. And due to the dielectric layer discharge did not move towards the glow to arc region and confined for higher electron density.

 VI- Characteristics: For each cycle, current peaks are observed during the rise time and fall time as in given figure 3 at rising pulse during 0-100ns current peak is coming of 2.5mA. After that during the plain pulse width from 100ns -900 ns current starts decreasing and becomes zero. Again for the fall time from 900ns-1000ns current is showing the peak value of range 3mA but in negative due to the fall cycle. There is also a second peak which is due to the hollow cathode effect.

93 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Fig. 3: IV- Characteristics of the designed model at 1kV for square wave nanosecond pulsed cycle.

 Mass Fraction: In MHCD mass fraction of metastable atoms are higher than the Argon ions which are due to the hollow cathode effect (HCE). The pendulum effect of fast electrons is responsible for this cause. As shown in figure 4 we are getting a higher value of metastable atoms than the Argon Ions which shows the presence of HCE.

Fig. 4: Mass fraction plot of Metastable and Argon Ions.

Conclusions: In this paper by simulating the Planar Anode design model it has been observed that by using the dielectric layer we can have the high electron density in hollow cathode without

94 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India moving from glow to arc discharge. It has been seen that due to the use of a dielectric layer pD value can be increased. The Ignition of the discharge dielectric barrier plays an important role and at 1kV breakdown occurs according to Paschen’s law. This value of higher breakdown voltage occurs due to the high thickness and low dielectric constant of the dielectric material.

It has been observed that due to the pulsed voltage-current peaks are occurring at the rise and fall times and after that, it moves towards the zero. With the help of the mass fraction plot, it was also being verified that this design is showing the hollow cathode effect which is responsible for the high electron density of the order of 1018 m-3.

References [1] A.D. White, “New hollow cathode glow discharge”, J. Appl. Phys. 30 711–719(1959). [2] C. Meyer, Daniel Demecz, E. L. Gurevich, U. Marggraf, G. Jestel, J. Franzke, J. Anal. At. Spectrom., 27, 677, (2012). [3] COMSOL Multiphysics Documentation, 2019, [online] Available: http://www.comsol.co.in. [4] K. H. Schoenbach, A. El-Habachi, W. Shi, and M. Ciocca, “High-pressure hollow cathode discharges,” PlasmaSources Science and Technology, vol. 6, no. 4, p. 468, 1997. [5] K. Becker, K. Schoenbach, and J. Eden, “Microplasmas and applications,” Journal of Physics D: Applied Physics, vol. 39, no. 3, p. R55, 2006.

95 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

PSC-8

Effect of laser pulse profile on controlling the growth of Rayleigh-Taylor instability in radiation pressure dominant regime

Krishna Kumar Soni, Shalu Jain, N.K. Jaiman, and K.P. Maheshwari Department of Pure & Applied Physics, University of Kota, Kota-324005 (Rajasthan)

e-mail: [email protected]

Abstract

In the radiation pressure dominant (RPD) regime the interaction of an intense relativistic laser pulse with an ultrathin, dense solid foil converts it into overdense plasma instantaneously. This plasma foil is accelerated as a whole by incident laser pulse. It becomes unstable due to the onset of Rayleigh-Taylor instability (RTI). This RTI tears the foil into plasma clumps. It affects the ion acceleration process. The ion energy spectrum becomes broadened. In the co-moving frame of the plasma foil the RTI makes it transparent for the incident radiation. The growth rate of RTI depends on the pulse profile of the incident laser. So, by suitably tailored laser pulse one can control the growth of RTI, and hence stabilize the ion acceleration. This paper presents a comparative study of energy and momentum transfer by the incident Gaussian and Lorentzian laser pulse to the plasma ions. Numerical results for the comparison of incident laser pulse profile for controlling the growth of RTI are presented.

Key words: Laser plasma interaction, Ion acceleration, Rayleigh-Taylor instability

Introduction: Laser driven ion acceleration mechanism is a very important mechanism of ion acceleration due to its smaller in size, cost effective, and compactness [1, 2]. Increasing the laser intensities ~ 19  22 /1010 cmW 2 by chirped pulse amplification technique the interaction of the laser pulse with ultrathin dense solid foil becomes nonlinear [3, 4]. Beyond this stage of laser intensity, i.e. at 23 /10~ cmWI 2 we meet a new regime of ion acceleration known as radiation pressure dominant regime [2, 5-6]. In the RPD regime an intense laser pulse interacts with an ultrathin, solid metal foil made of electrons and ions. As a result of this interaction the metal foil get converts into an overdense plasma foil instantly which reflects the incident laser pulse and acts as a relativistic plasma mirror [5-8]. The radiation pressure of the incident laser pulse pushes the electron layer in the forward direction and the intense electric field so created pulls the ions along with them with almost the same speed as that of electrons and thus have a kinetic energy above that of the electrons [5]. The plasma foil gains energy which is proportional to the incident laser pulse energy [5]. Due to extremely high radiation pressure (~ 30 tera-bar) associated with the incident intense laser pulse having intensity ~ 23 /10 cmW 2 plasma exhibits relativistic nonlinearities through the reflected and transmitted radiation from it and becomes unstable due to onset of Rayleigh-Taylor instability [1, 6, 9-10]. The RTI occurs when a lighter fluid accelerates a heavier fluid. This RTI can disrupt the acceleration process and tear the plasma foil into clumps of denser lower energy plasma [6, 9]. It follows that a controlled growth of the RTI can stabilize the foil opacity and acceleration process. The growth-rate of the RTI depends upon the phase profile of the incident

96 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India laser pulse. One can control the growth of the RTI by choosing an appropriate profile of the incident laser pulse. In this paper we give our analytical and numerical results of laser pulse profile for controlling the growth of the RTI. Numerical results for ion energy and momentum are also presented. We find that a Gaussian pulse profile is better than a Lorentzian pulse for controlling the growth of RTI. This paper is organized as follows. In section 2 of this paper we give the equation of motion of the thin plasma foil and its solution in terms of ion momentum in the RPD regime. Section 3 deals with the equations describing the Rayleigh-Taylor instability. Numerical results and discussion are given in section 4. Conclusions are drawn in the last section.

2. Equation of motion: The equation of motion of a surface element of a perfectly reflecting plasma mirror in the laboratory frame is [6, 9]:  dtpd   //  (1)  where p is the momentum of the ions in the plasma foil,  is the radiation pressure,  is the unit vector normal to the foil surface, and  is the surface density. Let the mirror velocity and the mirror normal vector remain in the  yx plane then the equation of motion (1) for the target element can therefore be written as [9]

 p P  y  p y P  x x  , and  . (2)  t  0  s  t  0  s

Here, p x and p y are the component of the ion momentum in the x and y direction, respectively,   ln 000 ,  0 is the initial plasma density, and l0 is the initial thickness of the foil. Let the electromagnetic (EM) wave propagate along the x - axis then the radiation pressure of the normally incident EM wave on the foil surface can be written in the lab frame as E 2 1  P  0 , where   /  pcmp 222 , (3) 2 1  ix x is the normalized velocity of the foil in the lab frame, E0 is the electric field of the laser pulse,

m i is the mass of the ion, and c is the speed of light in vacuum. Lagrangian coordinates,  and  are chosen such that   tyxyx ),,(,, and  ddds   2/122 . Let the unperturbed mirror moves along the x - axis so that d  0, and   dsd . Since the electric field of incident EM wave depends on time in the lab frame as 0 00   / ctxtEE  . So introducing the new variable  0   / ctxt  , which is the wave phase at the unperturbed mirror element position with  0 the laser pulse frequency in the lab 0 0 frame, we obtained dtd 0 1/   x . Here,  x is the unperturbed mirror velocity along the x - axis. Using the variable  we can write Eq. (2) as: dp 0 E 2      pcm  202 x  0 i x . (4) d 2  0202 00 i  x   ppcm x 0 Here, p x is the unperturbed x component of ion momentum. Introducing the average  R   E 2   normalized intensity of the EM wave w   d  , with R   0 , and 0 2 0 mi  00

2 c 0 0  , by using initial condition p x    00 the solution of Eq. (4) will be given by : 0  2  ww    0    cmp . (5) x i 12  w 

97 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

2022 2 Kinetic energy of the accelerated ions can be calculate as:  ,kini  i  x   i cmcpcm . By using Eq. (5) kinetic energy will be given by w2     cm 2 . (6) , ikini 12  w  3. Rayleigh-Taylor instability: The plasma foil accelerated by the radiation pressure of the laser pulse is unstable due to the onset of the Rayleigh-Taylor instability. To investigate the linear stability of the accelerated foil with 1 1 0 respect to perturbations x  ,t  , and y  ,t , we linearize Eq. (2) around the solution px   , we obtain [6, 9]  p 0    R   cm  R    x   1     1  , and   i   1     1  . (7)    x    y   0  y    x  i cm  2  p x    2 Here, we retain only the terms that are in the ultrarelativistic limit. One can obtain WKB solutions of Eq. (7) in the form [9]  1    i   exp,     ''  kid   . (8)  0  Substituting Eq. (8) in Eq. (7), we find (with growth-rate  >>1) 1 1 0   Rk   2/   , with x ~   / pcmi xiy . (9)

4. Results and Discussion: From Eq. (9) we see that the growth of the RTI depends on the phase profile of the incident laser pulse. By choosing an appropriate profile of the incident EM pulse we can control the growth of RTI and hence stabilize the foil acceleration. To obtain the analytical and numerical results for the effect of laser pulse profile on the growth of RTI, we choose the following pulse shapes 2 (A) Gaussian pulse 0  EE 0  67.1exp   , and 2 (B) Lorentzian pulse 0  EE 0   29.11/   . Using these expressions in Eq. (5) we obtain the momentum of the accelerated ions as 0 0 1 /ix   Rcmp 0 68.6/  0  erf 67.1   and /ix  Rcmp 0 0  29.1tan58.2/   for Gaussian and Lorentzian pulse, respectively which depend on the pulse profiles of the incident laser pulse. With the use of Eq. (9) the profile dependent exponential growth  Rk        d  of the RTI are 0 erf 1809.1   and 0  3618.22 Rk 1 0 1 29.1sinh   for Gaussian and Lorentzian pulse profiles, respectively. 2 29.1 Numerical results are obtained with the help of MATLAB software for the following set of laser pulse and plasma parameters: laser pulse intensity I  23 /1037.1~ cmW 2 (that is expected for 22 3 proposed superpower lasers such as HiPER and ELI [11]), plasma density n0  /105.5 cm , foil thickness l0  5.0 0 , 0 1 m , mm ei 1836/ . Fig: 1 depicts the variation of momentum of the accelerated ions with wave phase  for Gaussian and Lorentzian laser pulse profiles. From this figure we see that the ion momentum increases with increasing the wave phase for both the laser pulses. The momentum imparted to the ions are 0.32 GeV/ c and 0.16 GeV/ c for the value of  10 for Lorentzian and Gaussian laser pulse, respectively. In fig: 2 we shows the variation of energy of the accelerated ions with wave phase  of the incident laser pulse having Gaussian and Lorentzian pulse profiles. This curve show that the ion energy increases with increasing the wave phase for both the laser pulses. For  10 there are 0.05 GeV and 0.02 GeV energy of the accelerated ions for Lorentzian and Gaussian laser pulse, respectively. Fig: 3 shows the

98 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India exponential growth    of the RTI with wave phase in case of Gaussian and Lorentzian pulse profiles of the incident laser pulse. From this figure we see that for the value  10 the growth of RTI in case of Lorentzian pulse is 3.3 times higher than the case of Gaussian laser pulse. Since for the stability of the ion acceleration process against RTI we need a laser pulse for which the growth of instability must be minimal. So Gaussian laser pulse is better suited than the Lorentzian pulse in controlling the growth of RTI.

0.35

0.3

0.25 Gaussian laser pulse Lorentzian laser pulse 0.2

0.15

0.1 Normalized Momentum Normalized 0.05

0 0 2 4 6 8 10  0 Fig. 1: Shows the variation of normalized momentum / ix cmp of the ions with wave phase  for Gaussian and Lorentzian pulse.

0.06

0.05

0.04 Gaussian laser pulse Lorentzian laser pulse 0.03

0.02 Normalized Energy Normalized 0.01

0 0 2 4 6 8 10  2 Fig. 2: Shows the variation of normalized energy  , / ikini cm of the ions with wave phase  for Gaussian and Lorentzian pulse.

1.5

1 Gaussian pulse Lorentzian pulse

0.5

Growth of Rayleigh-Taylor instability Rayleigh-Taylor of Growth 0 0 2 4 6 8 10 

99 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Fig. 3: Shows the exponential growth-rate of the RTI with wave phase  for Gaussian and Lorentzian pulse. 5. Conclusions: In the RPD regime the momentum/energy transferred from laser pulse to the plasma ions depends on the pulse profile of the incident laser pulse. In this regime the momentum and energy transfer to the ions by the Lorentzian pulse is 1.54 times and 2.67 times that of the Gaussian pulse, respectively. We see that in case of Lorentzian laser pulse the instability grows much faster with the wave phase. So by comparing the numerical results for growth of RTI we find that the Gaussian laser pulse is better suited than the Lorentzian pulse for controlling the growth of RTI.

Acknowledgemets Financial support from the Department of Atomic Energy (DAE), Board of Research in Nuclear Sciences (BRNS) Mumbai, (Government of India) under the research project no. 39/14/07/2018-BRNS is thankfully acknowledged. Thanks are due to Professor Sudip Sengupta for several academic discussion and support.

References [1] F. Pegoraro, and S. V. Bulanov, Eur. Phys. J. D, 55, 399-405 (2009). [2] A. Macchi, M. Borghesi, and M. Passoni, Rev. Mod. Phys., 85, 751-793 (2013). [3] T. Brabec, and F. Krausz, Rev. Mod. Phys., 72, 545-591 (2000). [4] G. A. Mourou, T. Tajima, and S. V. Bulanov, Rev. Mod. Phys., 78, 309-371 (2006). [5] T. Zh. Esirkepov, M. Borghesi, S. V. Bulanov, G. Mourou, and T. Tajima, Phys. Rev. Lett., 92, 175003 (2004). [6] S. V. Bulanov, T. Zh. Esirkepov, M. Kando, A. S. Pirozhkov, and N. N. Rosanov, Phys. Usp., 56, 429-464 (2013). [7] Krishna Kumar Soni, and K. P. Maheshwari, Pramana J. Phys., 87, 1-6 (2016). [8] F. Mackenroth, and S. S. Bulanov, Phys. Plasmas, 26, 023103 (2019). [9] F. Pegoraro, and S. V. Bulanov, Phys. Rev. Lett., 99, 065002 (2007). [10] A. Sgattoni, S. Sinigardi, L. Fedeli, F. Pegoraro, and A. Macchi, Phys. Rev. E, 91, 013106 (2015). [11] M. Dunne, Nature Phys., 2, 2-5 (2006).

100 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

PSC-9

Effect of the nonthermal electrons on ion-acoustic cnoidal wave in unmagnetized plasmas

P. C. Singhadiya1, J. K. Chawla2, S. K. Jain 1Seth RLS Govt. College, Kaladera, Rajasthan, India-303801 2Department of Physics, Govt. College Tonk, Rajasthan, India-304001 Govt. College, Dholpur, Rajasthan, India-328001

e-mail: [email protected]

Abstract

Using reductive perturbation method, Korteweg de Vries (KdV) equation is derived for a unmagnetized plasma having warm ions and nonthermal electrons. The cnoidal wave solution of the KdV equation is discussed in detail. The effect of nonthermal electron on the characteristics of the cnoidal wave and soliton are also discussed. It is found that nonthermal electron has a significant effect on the amplitude and width of the cnoidal waves, while it also affects the width and amplitude of the soliton in plasmas. The numerical results are plotted within the plasma parameters for laboratory and space plasmas for illustration.

Key words: KdV equation, cnoidal wave, soliton Introduction: Many researcher studied the characteristics of nonlinear periodic waves in plasmas [1-24]. The cnoidal waves can be expected to play an important role in the nonlinear transport processes in plasma [1-3]. The nonlinear periodic waves (NPWs) expressed in terms of Jacobian elliptical-functions, like sn, cn and dn waves, are finding important applications in diverse areas of physics. One of them is the nonlinear transport phenomena. Yadav et al. [14] have been studied the ion acoustic cnoidal wave (IACW) in a magnetized plasma. They found that increase the angle of obliqueness then increase the amplitude of the IACW. Yadav et al. [16] studied the ion acoustic nonlinear periodic waves (IANPWs) in plasma with two-electron-temperature. Tiwari et al. [18] studied the IACW in a unmagnetized plasma. They found the averaged nonlinear ion flux, using the RPM. Yadav and Sayal [19] have been studied the obliquely propagating dust acoustic cnoidal waves in a magnetized dusty plasma. They discussed the characteristics of dust acoustic cnoidal waves and soliton. IACWs in unmagnetized plasma with hot isothermal electrons, cold ions and dust have been studied by Jain et al. [20]. The effect of dust concentration, charge on dust grains and mass ratio of dust grains on amplitude, phase velocity and averaged nonlinear ion flux of the dusty plasma discussed in details. Wang et al. [21] studied the IAW in a magnetized plasma with positrons, using the Painleve expansion method. The IACWs in a dense magnetoplasma have been studied by El-Shamy [22]. They have derived the KdV equation with using the pseudo potential approach and discussed its cnoidal wave solution for relativistic degenerate electrons in magnetized plasma. Kaur et al. [23-24] have been studied the cnoidal and solitary waves in magnetized and unmagnetized plasma. They discussed characteristics of dust magnetosonic periodic (cnoidal) and solitary waves in details. In the past years, several authors studied the ion-acoustic wave (IAW) in unmagnetized [25,27,29,34-35] and magnetized [27,28,30,33,36,37] plasma having non-thermal electrons.

101 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Sabry et al. [30] and El-labany et al. [31] examine the effect of nonthermal electrons on the properties of the ion-acoustic waves in magnetized plasma. The effect of the nonthermal electrons and positron concentrations on IAWs in a plasma have been studied by Pakzad and Tribeche [34]. They discuss the effect of nonthermal parameters on the characteristics on the IAWs. Rufai [36] studied the auroral electrostatic solitons and supersolitons in a magnetized nonthermal plasma. It is found that increase the value of the nonthermal parameters then amplitude of soliton decreases. Chawla et al. [37] studied the effect of nonthermal electron and positron on ion-acoustic solitary wave in magnetized plasmas. Basic equations: We consider collisionless unmagnetized plasma consisting of ions and nonthermal electrons. The nonlinear dynamics behavior of ion acoustic waves is governed by the following normalized usual equations:

xt nvn  0)( (1)

t x vvv x   x nn (2) 2  2  x ne 1    ne (3) Where , n and v are the electric potential, normalized density and fluid velocity of the plasma 2/12 respectively.  ,   /TT ei and D   e 00 enT )/( are nonthermal parameter, ionic temperature ratio and Debye length speed respectively. Derivation of the KdV equation using the RPM: In order to investigate the NLPWs in plasma, we employ the standard RPM to derive the KdV equation. The independent variables are stretched   and   as: 2/1   tx ),(   2/3 t where  is a small parameter and  is the phase velocity of the wave. The dependent variables are then expended as 1  nnn )2(2)1(  ...  vvv )2(2)1(  ...  )2(2)1(  ... (4) Substituting there expressions along with stretched coordinates into (1) - (3) and we obtain the first order quantities as n )1( 1   )1( (5) )1( )1( v 1   C1 (6) Here C1 is an integration constant which may depend on the variable . Thus, we obtain the following phase velocity (  ) of the cnoidal wave in the ion-acoustic wave frame 11    2  (7) 1   We get a relationship among the second order 2   1   2 1 v )2( 11   )2(  )1( 2  )1(2  C  )( (8) 4 2  2

Where C2  )( is the second integration constant which is independent of  but may depend on . In the derivation of (8), the periodic boundary condition implies that

t C1  0 (9) There C1 is independent of  and . We obtain the following KdV equation, using first and second order equation 3  1  1  yCx 1   0 (10) Where

102 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

 2  3 1113   3  1 x1  , y1  12   2 12   2 (11) In (10)  is used in place in  )1( . Cnoidal wave solution of the Kdv equation: In order to determine the steady state solution of the KdV equation (10), we consider

 u1 (12)

Where u1 is a constant velocity. Integrating equation (10) twice with respect to  , we obtain

1 2 d    0)( (13) 2  where the Sagdeev potential  )( is given by 2 u 2 x1 3  0 )( 0  (14) y1 62 y1 2

0 and  0 are respectively, the charge density and electric field when  vanishes. We find the ion acoustic soliton solution 2  m  Wh )/(sec , (15) 2/1 where the amplitude of the soliton m  /3 xu 11 and width of the soliton  uyW 11 )/4( . Results and Discussion: To investigate the existence regions and nature of the ion - acoustic cnoidal wave and soliton in nonthermal plasma, we have done numerical calculations for different set of plasma parameters (  , u, ,  0 and 0 ). The Sagdeev potential and phase plane plot with the change in nonthrmal parameter are shown in figure (1) - (4).The numerical results are displayed in figure (1) (Eqn. 13), where we have plotted the phase plane for the fixed values of the parameters as taken in figure (2). In the dotted line (i.e.,

0  002.0 and  0  007.0 ) nonthermal parameter   = 0 (blue color), 0.1 (black color), 0.15 (green color) and 0.2 (red color) of figure (1). On the other side, the solid phase curve (i.e., 0  0 and  0  0 ) nonthermal parameter   = 0 (blue color), 0.1 (black color), 0.15 (green color) and 0.2 (red color) in figure (1). It shows that if we increase the value of the nonthermal parameter  , the electric potential   of the cnoidal wave and soliton increases. In figure (2) (Eqn. 13), we have potted the phase curve for the fixed values of parameters (  , u,  0 and 0 ) as taken in figure (1) but having different value of ionic temperature ratio ( ) = 0.2. It shows that if we increase the value of the nonthermal parameter  , the electric potential   of the cnoidal wave and soliton decreases. A comparison of figure (1) and (2) shows that for the fixed values of parameters, if we increases the value of ionic temperature ratio  ),( the electric potential   slightly decreases. The change in the amplitude of the Sagdeev potential   with respect to potential  given by equation (14). For the different values of nonthermal parameter   is illustrated in figure (3) with the finite value of  0  007.0 and 0  ,002.0 the dotted line: nonthermal parameter   = 0 (blue color), 0.1 (black color), 0.15 (green color) and 0.2 (red color) curves represent the Sagdeev potential corresponding to cnoidal waves whereas the solid curve represents the soliton with

 0  0 and 0  ,0 and nonthermal parameter  = 0 (blue color), 0.1 (black color), 0.15

103 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

(green color) and 0.2 (red color). It shows that if we increase the value of nonthermal parameter  , the amplitude of the cnoidal wave and soliton increases. In figure (4), represents the variation in the Sagdeev potential  with respect to potential  for the fixed values of parameters ( , u,  0 and 0 ) as taken in figure (3), but having different value of nonthermal electron  )( at ionic temperature ratio   .2.0 A comparison of figures (3) and (4) shows that for the fixed value of parameters ( u,  0 and 0 ), if we increase the value of  , the amplitude of the cnoidal wave and soliton slightly decreases.

Fig. Cap.

Figure 1. Variation of d  with respect to potential  for different value of  0  007.0 and

0  002.0 (dotted line),  0  0 and 0  0 (solid line), at phase velocity u  ,015.0 ionic temperature ratio   ,1.0 and nonthermal electron  )( = 0 (blue color), 0.1(black color), 0.15 (green color) and 0.2 (blue color).

Figure 2. Variation of d  with respect to potential  for different value of  0  007.0 and

0  002.0 (dotted line),  0  0 and 0  0 (solid line), at phase velocity u  ,015.0 ionic temperature ratio   ,2.0 and nonthermal electron  )( = 0 (blue color), 0.1 (black color), 0.15 (green color) and 0.2 (blue color). Figure 3. Variation of Sagdeev potential   vs. potential  for different value of

 0  007.0 and 0  002.0 (dotted line),  0  0 and 0  0 (solid line), at phase velocity u  ,015.0 ionic temperature ratio   ,1.0 and nonthermal electron  )( = 0 (blue color), 0.1(black color), 0.15(green color) and 0.2 (red color). Figure 4. Variation of Sagdeev potential   vs. potential  for different value of

 0  007.0 and 0  002.0 (dotted line),  0  0 and 0  0 (solid line), at phase velocity u  ,015.0 ionic temperature ratio   ,2.0 and nonthermal electron  )( = 0 (blue color), 0.1(black color), 0.15 (green color) and 0.2 (red color). Conclusions: In summary, we have addressed the problem of the cnoidal wave and soliton in unmagnetized plasma with nonthermal electrons and ions. The KdV equation is derived using the reductive perturbation method. The effect of different ranges of nonthermal parameters on cnoidal wave and soliton is studied. The results obtained in this study may be useful to explain nonlinear periodic waves associated with ion-acoustic waves in the astrophysical environment where unmagnetized ions and nonthermal electrons are present. References [1] H. Schamel, Plasma Phys. 14, 905 (1972). [2] Y. H. Ichikawa, Phys. Scr. 20, 296 (1979). [3] K. Konno, T. Mitsuhashi and Y. H. Ichikawa, Soc. Jpn. 46, 1907 (1979). [4] L. C. Lee and J. R. Kan, Phys. Fluids 24, 430 (1981). [5] M. Temrin, K. Cerny, W. Lotko and F. S. Mozer, Phys. Rev. Lett. 48, 1175 (1982). [6] Yashvir, T. N. Bhatnagar and S. R. Sharma, Plasma Phys. Controlled Fusion 26, 1303 (1984). [7] R. Boström, G. Gustafsson, B. Holback, G. Holmgren, H. Kustem and P. Kinter, Phys. Rev.

104 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Lett. 61, 82 (1988). [8] A. V. Gurevich and L. Stenflo, Phys. Scr. 38, 855 (1988). [9] A. Roychowdhary, G. Pakira and S. N. Paul, J. Plasma Phys. 41, 447 (1989). [10] U. Kauschke and H. Schlüter, Plasma Phys. Controlled Fusion 33, 1309 (1990). [11] K. P. Das, F. W. Sluijter and F. Verheest, Phys. Scr. 45, 358 (1992). [12] W. J. Pierson, Jr., M. A. Donelan and W. H. Hui, J. Geophys. Res. 97, 5607 (1992,). [13] U. Kauschke and H. Schlüter, Plasma Phys. Controlled Fusion 34, 935 (1992). [14] L. L. Yadav, R. S. Tiwari and S. R. Sharma, J. Plasma Phys. 51, 355 (1994). [15]. L. L. Yadav, R. S. Tiwari and S. R. Sharma, Phys. Scr. 40, 245 (1994). [16] L. L. Yadav, R. S. Tiwari, K. P. Maheshawari and S. R. Sharma, Phys. Rev. E 52, 3045 (1995). [17] Y. V. Kartashov, Y. A. Vysloukh and L. Torner, Phys. Rev. E 67, 066612 (2003). [18] R. S. Tiwari, S. L. Jain and J. K. Chawla, Phys. Plasmas 14, 022106 (2007). [19] L. L. Yadav and V. K. Sayal, Phys. Plasmas 16, 113703 (2009). [20] S. L. Jain, R. S. Tiwari and M. K. Mishra, Phys. Plasmas 19, 103702 (2012). [21] J. Y. Wang, X. P. Cheng, X. Y. Tang, J. R. Yang and B. Ren, Phys. Plasmas 21, 032111 (2014). [22] E. F. El-Shamy, Phys. Rev. E 91, 03105 (2015). [23] N. Kaur, M. Singh, R. Kohli and N. S. Saini, IEEE Trans. Plasma Sci. PP, 1-7 (2017). [24] N. Kaur, M. Singh and N. S. Saini, Phys. Plasmas 25, 043704 (2018). [25] G. C. Das and S. G. Tagare, Plasma Phys. 17, 1025 (1975). [26] R. A. Crains, A. A. Mamun, R. Bingham and P. K. Shukla, Physica Scripta T 63, 80 (1996). [27] A. A. Mamun, Phys. Rev. E 55, 1852 (1997). [28] A. Bandyopadhayay and K. P. Das, Physica Scripta 61, 92 (2000). [29] T. S. Gill, P. Bala, H. Kaur, N. S. Saini, S. Bansal and J. Kaur, Eur. Phys. J. D 31, 91 (2004). [30] R. Sabry, W. M. Moslem and P. K. Shukla, Plasma Phys. 16, 032302 (2009). [31] S. K. El-Labany, R. Sabry, W. F. El-Taibany and E. A. Elghmaz, Plasma Phys. 17, 042301 (2010). [32] M. K. Mishra and S. K. Jain, J. Plasma Phys. 79, 893 (2012). [33] S. K. El-Labany, R. Sabry, W. F. El-Taibany and E. A. Elghmaz, Astro Phys Space Sci 340, 77 (2012). [34] H. R. Pakzad and M. Tribeche, J. Fusion Energy DOI: 10.1007/s/0894-.012-9503-9 (2012). [35] A. Mannan, A. A. Mamun and P. K. Shukla, Phys. Scr. 85, 065501 (2012). [36] O. R. Rufai, Plasma Phys. 22, 052309 (2015). [37] J. K. Chawla, P. C. Singhadiya and R. S. Tiwari, Pramana- J. Phys. 94, 13 (2020).

105 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

PSC -10

Target Shape Effects on the Energy of Ions Accelerated in the Radiation Pressure Dominated (RPD) Regime

S. Jain, K. K. Soni, N. K. Jaiman, K. P. Maheshwari Department of Pure & Applied Physics, University of Kota, Kota-324005 (Rajasthan)

e-mail: [email protected]

Abstract

The study of the interaction of an ultra-intense laser pulse with a thin dense plasma foil is of fundamental importance for different research fields such as efficient ion acceleration, high frequency intense radiation sources, medical applications, investigation of high energy collective phenomena in relativistic astrophysics [1]. We consider the interaction of an ultrashort, ultra-intense laser with ultrathin plasma layer leading in the generation of ion beam [2]. In this reference, we evaluate the energy and luminosity of the ion beam and their dependence on the laser and target parameters. Numerical results are presented for the Gaussian shaped foil target and flat target. The effect of plasma foil thickness on the accelerated ion energy and the luminosity has also been studied.

Key words: Radiation pressure acceleration (RPA), Gaussian shaped foil target, Flat target.

Introduction: High density ultra-short relativistic ion beam is generated when an ultra-short EM wave interacts with ultrathin foil. Higher laser intensities (  20 /10 cmWI 2 ) allow us to use laser induced particle acceleration for novel high-energy-physics applications [1, 2]. Various regimes have been discussed in the framework of this concept [1, 3]. Recently, a new mechanism for laser driven ion acceleration was proposed, where particles gain energy directly from the radiation pressure (RP) exerted onto the target by the laser beam [4]. The RPA mechanism predicts superior scaling in terms of ion energy and conversion efficiency [2]. In this RPA regime the electromagnetic (EM) wave is totally reflected by a plasma mirror prompted by an EM wave. This anticipates the energy conversion efficiency defined as the ratio of the mechanical energy of 2 the plasma foil to the electromagnetic energy given by   and   V . Here, V is 1    c the instantaneous foil velocity and c is the speed of light. In the limit  1 , this acceleration mechanism becomes more efficient i.e.   1. For RPA to become dominant, a thin foil is irradiated by a circularly polarized laser pulse at   normal incidence. Owing to the absence of an oscillating component in the  Bv force, electron heating is strongly suppressed. Instead, electrons are compressed to a highly dense electron layer gathering in front of the laser pulse which in turn accelerates ions [5]. By choosing the laser

106 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India intensity, target thickness, and density such that the radiation pressure equals the restoring force given by the charge separation field, the whole focal volume therefore propagates ballistically as a quasineutral plasma bunch and continually gaining energy from the laser field. In this scenario, all particle species are accelerated to the same velocity, which substantially results in a monochromatic spectrum [6]. Thus, RPA scheme has important fundamental features such as the dependence of ion energy on the laser pulse fluence, narrow energy spectrum, low divergence and high acceleration efficiency [7, 8]. In addition to the requirement of obtaining the maximum ion energy for high-energy physics application, we come to include an important parameter such as the luminosity of an ion beam characterizing the number of accelerated ions crossing a unit area of the beam in unit time. In particular, the generated ion beam should possess high luminosity. This can be achieved by focusing the particle beam into a focal spot or by irradiating the foil with an appropriately modulated laser pulse. Theoretical models have shown very optimistic results for quasi monoenergetic ion beams for adequately long driver laser pulses [6]. However, multidimensional simulations show the inevitable dispersion of charged particles, electrons and ions, when the target is deformed [9]. In this paper, we restudy the problem by considering the different shapes of target and give our analytical and numerical results depicting the effect of target shaping on ion-energy gain and luminosity of an ion beam. Numerical results are also obtained for different target thickness in respect of the wavelength of incident laser pulse. This paper is organized as follows: section 2 gives the equation of motion of thin plasma foil in RPD regime. Numerical results and discussion are given in section 3. Conclusions are drawn in the last section.

Equation of motion of thin plasma foil: At first, we study about the deformation of target under the interaction of a laser pulse. From the momentum conservation law between the laser and the target, the evolution of the target normalized velocity   can be described by the following equation of motion of the thin plasma foil under the RPA scheme as [10]: 2 d   E L   1    R   . (1) 2 ie cmlndt 1   2 Here,  11   , EL   is the electric field associated with the laser pulse, which depends on the variable   txt , ne is the plasma density, l is the foil thickness, m i is the ion mass, R  is the reflectivity of thin plasma foil in the rest frame of the foil,    11    ,  is the frequency of the incident laser pulse. In the simplest case, when the foil is initially at rest i.e.   0)0( and assuming total reflection i.e. R  1 , then one obtains the general solution for the ion velocity  as [1, 11]:  WW   2    (2) W 2  W   22 2 2F  E     L  L  Here, W  and FL  d represents the fluence of the laser beam. Thus e ln 0 4 W 2 the kinetic energy of the accelerated ions is given by the expression   cm 2 . ii W 1

If the areal density   e ln is shaped properly then the target can be kept flat. One can use a target with the Gaussian thickness distribution as follows [9]: m  2     r    lll exp,max    . (3)  01   2      T  

107 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Here, r is the transverse distance to the laser axis, l1 , l0 , T , m are the shape parameters. Parameter of fundamental importance such as the luminosity of the beam of ions accelerated in the RPD regime is mathematically expressed by [1]: 2 2 f  N  104 cm   34  tot     12 L 10 12   scm ][ (4) 10 kHz 10     

Here, N tot is the number of accelerated ions,   is the transverse size of the beam and f is the laser repetition rate.

Results and Discussion: We solve equation (1) by making use of MATLAB software and the numerical results are shown in below figures. For numerical calculation we have taken the typical set of parameters: peak 22 2 laser intensity 0  10 cmWI , laser pulse duration 50 fs , focal spot radius 10 m , laser repetition rate  10kHzf , transverse size of the laser beam   10 , laser wavelength 2 2 321  1 m , plasma density e  169 nn Cr , where Cr  e  emn  /101.14 cm is the critical density. Layout of both Flat target and Gaussian shaped foil target may be differentiated by taking different sets of l0 and l1 values. For the sake of simplicity, we present our results for a

Gaussian shaped foil target whose parameters arel0  3.0  , T  7 , l1  15.0  , m  1. For the flat target, we just set l1  3.0  , other parameters are the same.

1.2 Shaped Foil Target FLAT Target

0.8 Normalized Energy 0.4

0 0 200 400 600 Normalized Time Fig. 1: Normalized energy as a function of normalized time t  for different target shapes

36 x 10 2

Shaped Foil Target

FLAT Target

1 Luminosity

0 0 100 200 300 400 500 600 Normalized Time

Fig. 2: Luminosity of ion beam as a function of normalized time t  for different target shapes    Fig. 1 and 2 show the variation of normalized energy  i  of the accelerated ions and  2   i cm  luminosity with normalized time t  , respectively for 2 types of target, viz. Gaussian shaped

108 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India foil target and flat target. These curves indicate that for a fixed value of 300~ fst , the ion energy is ~ 1170.6 MeV and ~ 766.35 MeV corresponding to Gaussian shaped foil target and flat target (FT), respectively. The corresponding luminosity for both Gaussian shaped and Flat target is found to be 108.1 scm  1234 and 102.4 scm  1234 , respectively. 0.6

l <  l =  0.4 l > 

Normalized Energy 0.2

0 0 200 400 600 800 Normalized Time Fig. 3: Normalized energy as a function of normalized time for different values of foil thickness     i  Fig. 3 and 4 show the variation of normalized energy  2  of the accelerated ions and ion  i cm  beam luminosity with normalized time t , respectively for three different values of the target foil thickness, i.e., 800nml    , 1000nm    and 1200nm    . These curves indicate that for a fixed value of 300~ fst , the accelerated ion energy for l   , l   and l   is ~367.41 MeV, ~299.97 MeV and ~255.79 MeV, respectively. We also estimate the corresponding luminosity of 35 x 10 18

16 l <  14 l =  l >  12

10

8 Luminosity

6

4

2

0 100 200 300 400 500 600 700 800 900 Normalized Time Fig. 4: Luminosity as a function of normalized time for different values of foil thickness accelerated ions originating from the focal spot of the laser. It is found to be 1019 scm  1234 , 104.27 scm  1234 and 107.37 scm  1234 , respectively for l   , l   and l   .

Conclusions: Electron-ion layer moving at a relativistic speed almost fully reflects the incident laser pulse in the radiation pressure dominant regime. The reflection coefficient being dependent on the polarization of the incident laser pulse influences the energy transfer. Moreover, a properly shaped target can lead to an efficient transfer of energy and momentum to the ions as a result of the interaction between the incident laser pulse and thin plasma foil. From our results, we found an interesting fact that the energy of the accelerated ions is more (~ 1170.6 MeV) when the shaped foil target is irradiated by the incident laser pulse. From this finding, one can conclude that the total number of ions in the center part of the shaped foil target is originally less than that

109 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India in the case of the flat target and the luminosity is higher for Flat target which will be favorable for solving the problems of fundamental physics applications. Our result also depicts that the maximum energy corresponding to 133~ fst is estimated to be 0.75 GeV when the ions get acceleration by Gaussian shaped foil target, which is close to the Chen simulation result as illustrated in [13, Fig. 1(b)]. Having made a comparative study of plasma foil thickness we found that one of the plasma foils possess the minimum thickness accelerates the ions more efficiently in comparison to the thick foils. The increasing value of foil thickness makes the accelerated ion energy smaller. The maximum energy obtained by the ions is ~ 367.41 MeV corresponding to nml  )(800 . This energy value diminishes gradually when the thickness rises and reaches ~ 255.79 MeV for  nml  )(1000 .

Acknowledgement Financial support from the Department of Science & Technology, New Delhi, (Government of India) under the research project no. DST/INSPIRE Fellowship/ 2017/IF170835 is thankfully acknowledged.

References [1] S. V. Bulanov, T. Zh. Esirkepov, M. Kando, A. S. Pirozhkov, and N. N. Rosanov, Phys. Uspekhi, 56, 429-464 (2013). [2] T. Zh. Esirpekov, M. Borghesi, S. V. Bulanov, G. Mourou, and T. Tajima, Phy. Rev. Lett., 92, 175003 (2004). [3] A. Macchi, M. Borghesi, and M. Passoni, Rev. Mod. Phys., 85, 751 (2013). [4] A. Macchi, F. Cattani, T. V. Liseykina, and F. Cornolti, Phys. Rev. Lett., 94, 165003 (2005). [5] A. Henig et. al., Phy. Rev. Lett., 103, 245003 (2009). [6] O. Klimo, J. Psikal, and J. Limpouch, Phys. Rev. ST Accel. Beams, 11, 031301 (2008). [7] S. Kar et. al., Phys. Rev. Lett., 109, 185006 (2012). [8] A. Maachi, S. Veghini, T. V. Liseykina, and F. Pegoraro, New J. Phys., 12, 045013 (2010). [9] M. Chen , A. Pukhov, and T. P. Tu, Phy. Rev. Lett., 103, 024081 (2009). [10] S. S. Bulanov, E. Esarey, C. B. Schroeder, S. V. Bulanov, T. Zh. Esirkepov, M. Kando, F. Pegoraro, and W. P. Leemans, Phys. Plasmas, 23, 056703 (2016). [11] E. Yu. Echkina, I. N. Innovenkov, T. Zh. Esirkepov, F. Pegoraro, M. Borghesi, and S. V. Bulanov, Plasma Phys. Rep., 36, 15-29 (2010).

110 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

PSC-11

Effect of magnetic field on the sheath width of a 13.56 MHz radio frequency capacitive argon discharge

S Binwal1, S K Karkari2, L Nair1 1Jamia Millia Islamia (A Central University), Jamia Nagar, New Delhi, 110025, India 2Institute for Plasma Research, HBNI, Bhat Village, Gandhinagar, Gujarat, 382428, India

e-mail: [email protected]

Abstract

A 13.56 MHz, parallel plate capacitive discharge is investigated in the presence of magnetic field. A non-invasive method of estimating the sheath width has been demonstrated using the electrical impedance measurements. Further, the effect of magnetic field, discharge current and pressure on the capacitive sheaths is investigated. The experimental results report almost 55.5 % reduction in the sheath width for the argon discharge operating at 1.0 Pa background pressure and 7.0 mT of applied magnetic field compared with the unmagnetized case.

Key words: capacitive discharge, magnetic field, sheath width, non-intrusive technique, electrical measurements

Introduction: The sheath is a positive space charge region that separates the quasineutral plasma from the electrode surface. Almost the entire voltage applied to the discharge plates gets dropped across the sheath region. The positive ions on entering the sheath with an initial Bohm velocity are further accelerated inside the sheath and bombard the electrode surface with high kinetic energy. Therefore, sheath plays an important role in the surface modification on the substrate by ion bombardment. In case of a capacitive coupled radio frequency (CCRF) discharge, in the time scale , the electrons respond instantaneously to the time varying electric field whereas ions respond to the time averaged sheath potential. The parameters that control the ion dynamics in RF sheath are the mean free path of ions (pressure) and the ion transit time across the sheath (τion). These parameters depend on the sheath width which is a function of sheath voltage and plasma density [1]. For achieving high etch rates, mono-energetic ions are preferred. Therefore, low pressure and high plasma density is generally suitable. A transverse magnetic field can be introduced to achieve high density plasma at low operating pressure. The magnetic field influences the ion energy and ion angular distribution through the sheath width.

Although, both fluid [2] and PIC simulation [3- 5] studies have demonstrated the effect of magnetic field on the sheath. Fewer experimental works has been carried to investigate the role of applied magnetic field on the sheath width in a symmetric CCRF discharge [6-7]. In this paper we analyzed the effect of magnetic field on the capacitive RF sheaths. A non-invasive method of estimating the sheath width has also been demonstrated using the electrical impedance measurements.

111 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Experimental setup: The schematic of the experimental chamber is given in Ref-[8-10]. It consists of two rectangular parallel plate electrodes which are 40 cm long and 10 cm wide, separated by a distance of 8 cm housed inside a cylindrical glass chamber. The electrodes are driven by a 13.56 MHz RF generator via automatic impedance tuner having an L-type matching circuit. The output of the matching circuit is connected to the parallel plates through an isolation transformer in a push-pull configuration. The chamber is equipped with a set of turbo and rotary vacuum pumps to achieve a base pressure of 6 × 10−6 Pa. The system is placed between a pair of race-track shape electromagnetic coils providing uniform transverse magnetic field along the width of the plates. The potential between the plates is measured by a pair of high voltage Tektronics capacitive voltage probe. The discharge current is measured by IPC miniature current transformer. The experimental system is calibrated prior to the experiment to account for the inherent delays introduced because of the length of the cables of voltage /current probes and stray capacitances [8-10].

Model to estimate maximum sheath width: In the homogenous discharge model [11], the ion density can be simply treated uniform throughout the discharge and the electron density has a step like profile. If the potential on the wall ( ) is transiently large and negative such that electrons are repelled from the sheath. This leaves behind a matrix of positive ions. The potential in the sheath in 1-dimension can be expressed by Poisson’s equation as follows: − ,

(1) t Here, is the ion/electron density at the plasma- sheath boundary . =− t Equation (1) is integrated with wall potential with respect to the plasma. The mean t t sheath width can be expressed as [12]: = = − 伸 (2) 伸 v = t In equation (2), the information of plasma density and voltage drop across the sheath is required to estimate the sheath width. In capacitive discharge most of the applied voltage ( ) is dropped across the sheath. Therefore, it is reasonable to assume . The information of density is usually obtained from the probe measurements. To avoid using Langmuir probe which 伸 is an intrusive diagnostic, the value of n0 is estimated from the externally measured RF current. The RF current has three components namely the displacement current ( , which is due to variation in the sheath width with RF cycle, a constant ion current and the electron current ( ) which has an exponential dependence on the sheath voltage [12]. In one RF cycle, the 䂺 constant ion current needs to be balanced by the electron current. The sheath region is devoid of electrons. The electron can reach the electrodes only at an instant on RF cycle when the sheath collapses at the electrode. In this phase, the displacement current becomes zero and the small ion current contribution can be neglected in comparison to the electron thermal current. At this time, the sheath at the opposing electrode attains maximum sheath width ( ). This reduces the RF current to, and the expression can be rewritten in terms of as follows: t㏨伸 = h t (3) h Here is the electrode area and the thermal velocity of electrons given t = ㏨伸 as − . The RF current, can be replaced in (3) by the = htt × vt ㏨伸 experimentally measured current,−v which denotes the net RF current flowing through the 伸 plasma.㏨ = h × vt (4) = +

112 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

The values R and X can be estimated by following the procedure discussed in Ref:[8]. Thus, using equation (2), (3) and (4) the expression for maximum sheath width can be written as: (5) v vh = h × vt × 䂺 In this expression, the temperature dependence on sheath width is minimal against RF potential. Therefore, it is reasonable to approximate Te in the range of 2- 4 eV. In the subsequent section, maximum sheath width is estimated using equations (5) by assuming Te= 4 eV.

Results and Discussion: (a) Variation of sheath width with discharge current In Fig-1 it is seen that in the un-magnetized case, sm rises with a slow pace almost linearly on increasing Irms. However, an opposing trend is observed when the magnetic field is applied as shown in fig-2. In this case, sm decreases to reach a saturation value as Irms is increased. Fundamentally, the sheath width is inversely proportional to the electron density sm 1/ne and directly proportional to the sheath voltage sm Vsh [12]. In the low pressure unmagnetized capacitive discharge, increasing discharge current or power does not guaranty the increase∝ in plasma density. It is found in the literature that∝ in an unmagnetized CCRF discharge a large fraction of discharge power is dissipated in ion acceleration in the sheath. The power dissipation by ions in the sheath results in a higher Vsh value and a saturation in plasma density. Therefore, the sheath width slightly increases with increasing the discharge current. In case of B=7.0 mT, higher fraction of power is coupled to the electrons in the bulk. This results in an enhancement of electron density with the discharge current. Although, Vsh also linearly vary with discharge current but the rate of change of density is more dominant. Hence the sheath width monotonically decreases with the discharge current.

Fig-1: Plot of the sheath width vs discharge Fig-2: Plot of the sheath width vs discharge current for unmagnetized case at 1.0 Pa to 5.0 current for B=7.0 mT at 1.0 Pa to 5.0 Pa. Pa.

(b) Pressure effects on sheath width With increase in the background pressure, more ionizing neutrals are available in the discharge. This results in an increase in plasma density. Therefore, the sheath width is expected to fall with pressure. This is clearly observed for the unmagnetized case. However, in the magnetized case, the increase in plasma density with pressure is also associated with an enhancement in cross B-field diffusion losses. Therefore the variation in sheath width with pressure is relatively small as compared to the un-magnetized case.

(a) Effect of magnetic field on sheath width

113 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Fig-3 represents the sheath width vs magnetic field plots for two different discharge current values. It is seen that with increase in magnetic field there is a monotonic fall in the sheath width. The application of transverse magnetic field reduces the radial losses and therefore enhances the density of the discharge. The amplitude of the discharge voltage is also significantly reduced in presence of magnetic field. Accordingly, there will be a reduction in the amplitude of voltage drop across sheath. Both these effects will commutatively reduce the sheath width in the magnetized discharge.

Fig-3: Plot of the sheath width vs magnetic field for two discharge current values at 1.0 Pa.

Similar effect of magnetic field on the RF sheath in a symmetric discharge was reported in a particle in cell simulation study by Sharma et al [3]. They demonstrated that in a single frequency CCRF discharge, simultaneous control of the ion flux and ion energy bombarding on a surface is possible by a suitable choice of a transverse magnetic field. Their results showed that the sheath width was reduced by 60% of the value by applying a transverse static magnetic field of 3.5 mT in a Helium discharge. They also reported a 4-fold increment in the ion flux at the electrode. These results suggest that the application of magnetic field of the strength such that the electrons are strongly magnetized while the ions remain unmagnetized can induce the similar effect as using a dual frequency.

This simulation study supports our experimental results, where we have also observed almost 55.6 % reduction in the sheath width at 7.0 mT of transverse magnetic field [c.f fig-3]. It is also noteworthy to mention that although in past a model for sheath width estimation for the magnetized CCRF discharge has been reported by Park et al [6]. However, the model requires plasma density as an input parameter which is usually measured using a Langmuir probe. The application of probes is not desirable in industrial plasma processing reactors due to limitations such as high oscillating potential, contamination & perturbation introduced by the probe [13]. The method presented here thus becomes imperative where only external measurements have been used to estimate the sheath width.

Summary and Conclusions: In this paper, maximum sheath width is estimated non- invasively using the electrical measurements. Effect of discharge current, pressure and magnetic field on the sheath width is investigated. The ion dynamics is not directly influenced by the magnetic field as ions are unmagnetized in B=7.0 mT. However, magnetic field influences the electron plasma density and the sheath voltage which inturn controls the ion flux and ion energy in the sheath region. Therefore, the ion dynamics is basically getting controlled by the sheath dynamics. The present work also confirms the PIC simulation study by Sharma et al [3] which reported almost 60 % reduction in the sheath width in presence of magnetic field. Our experimental work confirms

114 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India these results and we report almost 55.5 % reduction in the sheath width for the argon discharge operating at 1.0 Pa background pressure and 7.0 mT of applied magnetic field.

In conclusion, the results suggest that the magnetic field can be used as a controlling knob to tune the sheath width/ ion bombarding energy in a single frequency CCRF discharge. This can enable the user to optimize the processing window in a desirable manner.

References [1] T. Panagopoulos and D. J. Economou. Journal of Applied Physics 85.7 pp. 3435–3443 (1999). [2] M.M. Hatami, Physics of Plasmas 22.4, p. 043510, (2015). [3] S. Sharma et al, Physics of Plasmas 25.8, p. 080704, (2018). [4] J. Moritz et al, Physics of Plasmas 23.6, p. 062509(2016). [5] N. S. Krasheninnikova, X.Tang, and V. S. Roytershteyn, Physics of Plasmas 17.5, p. 057103(2010). [6] J.C. Park and B. Kang, IEEE Transactions on Plasma Science 25.3, pp. 499– 506, (June 1997). [7] S. J. You et al, Surface and Coatings Technology 171.1,pp. 226–230, (2003). [8] S. Binwal et al, Physics of Plasmas 25.3, p. 033506(2018). [9] J. K Joshi et al, Journal of Applied Physics 123.11, p. 113301, (2018). [10] S. Binwal et al, Physics of Plasmas 27.3, p. 033506, (2020). [11] M. A. Lieberman and A. J. Lichtenberg. “Principles of plasma discharges and materials processing”. In: MRS Bulletin 30.12 (1994). [12] P. Chabert and N. Braithwaite. Physics of radio-frequency plasmas. Cambridge University Press, (2011). [13] S.K. Karkari, A.R. Ellingboe, and C. Gaman, Applied Physics Letters 93.7, p. 071501, (2008).

115 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

PSC- 12

Dynamics of dust ion acoustic waves in the Low Earth Orbital (LEO) plasma region

S. P. Acharya1, a, A. Mukherjee2, b, and M. S. Janaki1, c 1Saha Institute of Nuclear Physics, Kolkata, India 2National University of Science and Technology, “MISiS”, Moscow, Russia e-mail: [email protected], b [email protected], c [email protected]

Abstract

We consider the system consisting of the plasma environment in the Low Earth Orbital (LEO) region in presence of charged space debris objects. This system is modelled for the first time as a weakly coupled dusty plasma; where the charged space debris objects are treated as weakly coupled dust particles with two dimensional space and time dependences. The dynamics of the ion acoustic waves in the system is found to be governed by a forced Kadomtsev-Petviashvili (KP) type model equation, where the forcing term depends on the distribution of debris objects. Exact accelerated planar solitary wave solutions are obtained from the forced KP equation upon transferring the frame of reference, and applying a specific non holonomic constraint condition. For a different constraint condition, the forced KP equation also admits lump wave solutions. The dynamics of exact accelerated lump wave solutions, which are happened to be pinned, is also explored. Approximate dust ion acoustic wave solutions with time dependent amplitudes and velocities for different types of localized space debris functions are analyzed. Our work provides a much clearer insight of the debris dynamics in the plasma medium in the LEO region, revealing some novel results that are immensely helpful for various space missions. Different perspectives for practical applications of our theoretical results are discussed in detail. .

Key words: Space debris, Low Earth Orbital, forced Kadomtsev-Petviashvili equation, planar soliton, lump wave.

Introduction:

Upsurge in research endeavours encompassing dynamics of space debris objects in near-earth atmospheres has been gaining significant attention by numerous scientists across countries from recent years. Space debris objects [1] include dead satellites, meteoroids, destroyed spacecrafts, other inactive materials resulting from many natural phenomena etc. which are being levitated in extraterrestrial regions especially in near-earth space. The space debris objects are substantially found in the Low Earth Orbital (LEO) [2] and Geosynchronous Earth Orbital (GEO) regions. Also, their number is continuously being increased nowadays due to various artificial space missions which result in dead satellites, destroyed spacecrafts etc. and many natural hazards occurring in space. These debris objects are of varying sizes and shapes, and move with different

116 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India velocities [3]; thus, cause significant harm to running spacecrafts. Therefore, to avoid these deteriorating effects, active debris removal (ADR) has become a challenging problem in twenty-first century. Some indirect detection techniques for space debris have also been developed by different authors [4, 5, 6]. This paper interprets a much more realistic situation; which is not considered by these authors and may provide more justifiable indirect evidence of presence of debris objects.

We model, for the first time, the system consisting of the plasma environment in presence of space debris objects in the Low Earth Orbital (LEO) region as a weakly coupled dusty plasma system. Space debris objects become charged in a plasma medium because of different mechanisms such as photo-emission, electron and ion collection, secondary electron emission [7] etc. These charged debris objects of varying sizes ranging from as small as microns to as big as centimetres, and, in certain conditions, even more than centimetres [3, 8] move with different velocities. Therefore, there can be finite chances that the individual dynamics of charged debris objects are mutually correlated; which results in weak coupling among them. Numerous recent works on dynamics of space debris are performed without taking into account this paramount effect as far as our knowledge goes. In this work, the weak coupling effect among charged debris objects is accomplished with the introduction of a two dimensional space and time dependent forcing function arising out of debris objects. Consequently the forcing function depends physically on the distribution of space debris objects in the LEO plasma region, and their possible relative motions. This new generalized forcing function represents a two dimensional extension of recent works done by Sen et al. [5], and Mukherjee et al. [6].

Derivation of nonlinear evolution equation: We consider the propagation of finite amplitude nonlinear dust ion acoustic waves (DIAWs) in the Low Earth Orbital (LEO) region due to the motion of orbital charged debris objects. The LEO region consists of a low temperature low density plasma along with the abundance of debris objects. We assume that the ion species is treated as a cold species, i.e. the ion pressure is neglected and the electrons obey the Boltzmann distribution. The basic normalized system of equations in this system in (2+1) dimensions is given by , (1) +  + 쳌 ㏨ =, t (2)    t +  + ㏨ 쳌 + = t, (3) ㏨ ㏨ ㏨ t 쳌 쳌 +  + ㏨ + = t , t t t (4) + 쳌 − + − − = (5) + ∇h ㏨ = t (6) where㏨ the following normalizations have been used: + ㏨h∇ ㏨ = t , 쳌  ㏨ t (7) λ 쳌 λ λ t t  ㏨ t where is electron Debye length, Cs is ion acoustic speed, is Boltzmann constant, is electron temperature, is equilibrium electron density, and is equilibrium ion density. Equationsλ (1), (2), (3), and (4) represent ion continuity equation, ion momentum conservation equations in x and y directions,t and Poisson's equation respectively;t where n, u, and denote the density, velocity, and electrostatic potential of the ion species respectively. Similarly, , , and denote dust charge in electron units, dust density, and dust velocity respectively,t and equations (5) and (6) represent dust continuity and dust momentum equation respectively. The term㏨ S(x, y, t) in the RHS of equation (4) represents a charge density source arising due to the weakly coupled charged debris objects having two dimensional space and time dependences. Therefore, S(x, y, t) also depends on the distribution of debris objects in the LEO region. In the

117 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India pioneering work done by Sen et al. [5], they have considered the source term to have one dimensional space and time dependences. Also, Sen et al. have taken both ion acoustic solution and forcing term to have the form of line solitons with constant amplitudes and constant velocities; which is subsequently generalized by Mukherjee et al. [6] by considering more realistic time dependent amplitudes and velocities for both ion acoustic solution and forcing term. We generalize both the work done by Sen et al. and Mukherjee et al. to consider a forcing term in two spatial and one temporal dimensions in order to accomplish the weakly coupled nature of orbital debris objects. We do not follow any restrictions as taken by Sen et al. as well. We derive the evolution equation corresponding to the nonlinear DIAWs in our system following the well-known reductive perturbation technique (RPT) [9]; where we expand the dependent variables of the system as: , (8) h , (9) v = v + h+ ,+ (10) v  =  +  + , (11) v ㏨ = ㏨ + h㏨ + , v (12) t = t + t + v = v + + , + (13) where is a small dimensionless expansion parameter characterizing the strength of nonlinearity v in the system.= t We+ considert + a weak space-time dependent localized debris function which vanishes at space infinities. After scaling we have , (14) where f(x, y,h t) can have any spatially localized form that is consistent with the weakly coupled charged,쳌, = debris ,쳌, dynamics as per our approach. Similarly, the independent variables are also rescaled as: , (15) where is the phase velocity of the wave in x direction. Putting these expanded and rescaled variables = − in ㏨ equation = (1) and = collecting 쳌 different powers of , we get ㏨ , (16) v v  : − ㏨ + = t . (17) v ㏨v Similarly, using equation (2), we get : − ㏨ + +  + vv + = t , (18) v tv : − ㏨ + = t . (19)  v v t Again, using equation (3), we get : − ㏨ + + v + = t . (20) ㏨v tv Finally,h equation (4) yields: : − ㏨ + = t , (21) v v . (22) : − t + = t tv tv From equations (16), (18), (20) and (21), we obtain : − t − + = (23) ㏨v tv Then, upon differentiating equation (22) wrt partially, and substituting equations (17), (19) and v = tv = v ㏨ = v = h (23), we get the final nonlinear evolution equation after some simplifications as: (24) which is the forced Kadomtsev-Petviashvili (KP) equation, i.e. the generalization of forced KdV v v v v v equation, with the subscripts+ denote+ partial + derivatives.= , In order to get a convenient form, we apply the frame transformation: (25) Then, equation (24) reduces to v v =h=== = h

118 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

, (26) The above equation represents the final evolution equation which is analysed extensively in the following subsections.h + hh + h + h = Solutions of nonlinear evolution equation: We know that KP, modified KP, coupled KP [10], generalized KP [11], and nonplanar KP [12] equations are very well-known and different methods of solutions are already known [13, 14]. Also, KP Burgers equation, different solutions [15] and their dynamical evolution have been analysed for plasmas. These analyses have been performed without taking into account the forcing term. We analyse different types of solutions of forced KP equation (26) in this section. (A) Planar solitary wave solution: The equation (26), upon applying a transformation and , admits exact dust ion acoustic accelerated planar soliton solution when the forcing function satisfies a non holonomic constraint: − − , (27) where represents the time dependent amplitude of the forcing function Here, we generalize + hh the constraint+ h condition+ =− taken h by Mukherjee et al. [6] to solve forced Korteweg-de Vries (KdV) equation to two dimension in order to apply the same for forced KP equation.h Then, after some simplifications, the exact dust ion acoustic accelerated planar soliton solution is given by , (28) 쳌 쳌 쳌 whereh ,,and = represent + the 伸andcomponents + + of wave+ number, + and denotes the phase of the solitary wave solution respectively. Typically this planar soliton solution is as shown in figure 쳌 1. 쳌

Fig. 1: Planar solution at T=1.5 .

Similarly, the forcing function is given by . (29) Therefore, it is concluded that both amplitude and velocity of the forcing function change 쳌 쳌 whereas ,, only velocity=− of the伸 dust ion + acoustic + soliton + changes. + This is two dimensional extension of the recent work done by Mukherjee et al. [6] on exact accelerated solitons. (B) Lump wave solution: The lump wave solution of the forced KP equation (26) are discussed below. (i) Solution by constraint condition: Following Yong et al. [16], we approximate the forcing function as: . (30) In contrast to Yong et al., we have taken a slightly different constraint condition =− , (31) then it satisfies lump wave solution which is typically of the form = + h . h −+vthy− +−yhh (32) h = v+ −+vthy−v +−yhh This is obtained using the famous Hirota bilinear method [17]. This lump wave solution is plotted in figure 2.

119 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Fig.2: Lump solution at T=0.

(ii) Solution by frame transformation: We apply a frame transformation:

(33) along with the approximation = + thatt =. As a= result, equation (26) turns into an unforced KP equation = h , (34) which admits theh solution: + hh + h + h = t

. (35) −+t ++ − + + +v This showsh ,, accelerating= +t features ++ due to presence− + of+ the terrm+v . (C) Perturbative solution: We can also approximate the solution of forced KP equation (26) through perturbation technique following the work done by Morozt [18]. We get a perturbative solution, in this case, as , (36) where and denote zeroth and first order perturbed quantities respectively. Here, t v represents the solutionh = of h equation+ h + (26) in absence of external forcing . The other perturbed t v t quantitiesh dependh upon and the nature of forcing function . This perturbed solution is moreh realistic as compared to solutions by constraint conditions. ht Discussions and applications: In this work, we obtain exact accelerated lump wave solutions, as explored in previous section, due to the presence of forcing function in (2+1) dimensions. Again, these accelerated lump solutions are happened to be 'pinned', i.e. both source or forcing function and analytical solution move with the same velocity. We also obtain accelerated planar solitary wave solution when the forcing function satisfies a certain constraint condition as represented by equation (27), and lump wave solutions when the constraint condition changes to that represented by equation (31). But the condition that forcing function obey a certain constraint is not more realistic. Therefore, from a practical point of view, there are more chances that pinned accelerated lump wave solutions are to be resulted as consequences of the presence of weakly coupled debris objects, which are self-consistently related to the dust ion acoustic solution. We obtain this inference after we generalize the debris problem taken by Sen et al. [5] to two dimensions to model as a weakly coupled dusty plasma system in order to make the solutions more realistic and practicable, after considering time dependent amplitudes of the forcing functions. We know that lump wave solutions are special kinds of rational function solutions that are localized in all directions in space whereas solitary wave solutions are exponentially localized solutions in certain directions. Therefore, lump waves can be more stable as compared to solitary waves resulting from KP equation and are detectable by external means. Recently, Sen et al. [5] devise an indirect method of detection of centimetre-sized debris objects by observation of precursor line solitons. But they neglected many crucial effects including the time dependence of amplitudes of forcing function which represents debris objects. This may imply the observation of a debris object even when no line soliton is to be detected in its vicinity. Therefore, our observation of pinned accelerated lump wave solutions due to presence of debris objects may pave a novel way of detection of debris objects through observation of lump waves irrespective of the sizes and shapes of debris objects by advanced sensors or technologies equipped in

120 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India space-crafts. This also happens to be the generalization of the work done by Kulikov et al. [4] where they conclude the detection of debris objects through growth of amplitudes. From an abstract point of view, our work provides a much clearer insight of space debris dynamics in the LEO plasma region through mathematical modelling.

Conclusions: . Our work provides a detailed theoretical investigation of space debris dynamics in the LEO plasma region through mathematical modeling. This will be extremely helpful for different space missions by various space agencies in the world. References: [1] H. Klinkrad, Space Debris: Models and Risk Analysis, Springer Praxis Books, Praxis Publishing Ltd, Chichester, UK. [2] J. C. Sampaio, E. Wnuk, R. Vilhena de Moraes, and S. S. Fernandes, Resonant Orbital Dynamics in LEO Region: Space Debris in Focus, Mathematical Problems in Engineering, Volume 2014, Article ID 929810. [3] Rules of Thumb and Data for Space Debris Studies, Australian Space Academy. [4] I. Kulikov and M. Zak, Detection of Moving Targets Using Soliton Resonance Effect, Advances in Remote Sensing, Vol. 1, No. 3, December 2012. [5] A. Sen, S. Tiwari, S. Mishra and P. Kaw, Nonlinear wave excitations by orbiting charged space debris objects, Advances in Space Research, Vol. 56, Issue 3, Pages 429-435, 1 August 2015. [6] A. Mukherjee, S. P. Acharya, and M. S. Janaki, Exact accelerated solitons by orbiting charged space debris, arXiv:2001.11817v1 [nlin.PS], 26 Jan 2020. [7] M. Horanyi, Charged dust dynamics in the solar system, Annual Review of Astronomy and Astrophysics, Vol. 34, Pages 383-418, November 2003. [8] Technical Report on Space Debris, United Nations Publication, ISBN 92-1-100813-1, New York, 1999. [9] R. A. Kraenkel, J. G. Pereira and M. A. Manna, The reductive perturbation method and the Korteweg-de Vries hierarchy, Acta Appl Math 39, 389-403 (1995). [10] M. Lin, and W. Duan, The Kadomtsev-Petviashvili (KP), MKP, and coupled KP equations for two-ion-temperature dusty plasmas, Chaos, Solitons and Fractals, Volume 23, Issue 3, Pages 929-937, 2005. [11] J. Yu, F. Wang, W. Ma, Y. Sun, and C. M. Khalique, Multiple-soliton solutions and lumps of a (3+1)-dimensional generalized KP equation, Nonlinear Dynamics, Vol. 95, pages 1687{1692 (2019). [12] S. Reyad, M. M. Selim, A. EL-Depsy, and S. K. El-Labany, Solutions of nonplanar KP-equations for dusty plasma system with GE-method Physics of Plasmas, Vol. 25, 083701 (2018). [13] A. R. Seadawy, and K. El-Rashidy, Dispersive solitary wave solutions of Kadomtsev-Petviashvili and modi_ed Kadomtsev-Petviashvili dynamical equations in unmagnetized dust plasma, Results in Physics, Volume 8, Pages 1216-1222, 2018. [14] A. A. Minzoni, and N. F. Smyth, Evolution of lump solutions for the KP equation, Wave Motion, Vol. 24, Issue 3, Pages 291-305, 1996. [15] M. S. Janaki, B. K. Som, B. Dasgupta, and M. R. Gupta, K-P Burgers Equation for the Decay of Solitary Magnetosonic Waves Propagating Obliquely in a Warm Collisional Plasma, Journal of the Physical Society of Japan, Vol. 60, No. 9, Pages 2977-2984, 1991. [16] X. Yong, W. X. Ma, Y. Huang, and Y. Liu, Lump solutions to the Kadomtsev-Petviashvili I equation with a self-consistent source, Computers and Mathematics with Applications 75 (2018) 3414-3419. [17] R. Hirota, Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons Phys. Rev. Lett. 27, 1192 (1971). [18] I. M. Moroz, The Kadomtsev-Petviashvili equation under rapid forcing, Journal of Mathematical Physics 38, 3110 (1997).

121 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

PSC -13

Large amplitude ion-acoustic solitons in plasmas with positrons and two superthermal electrons

S. K. Jain1, P. C. Singhadiya2 and J. K. Chawla 1Govt. College, Dholpur, Rajasthan, India-328001 2Seth RLS Govt. College, Kaladera, Rajasthan, India-303801 Department of Physics, Govt. College Tonk, Rajasthan, India-304001

e-mail: [email protected]

Abstract

The large amplitude of ion-acoustic solitons in plasma consisting of ions, positrons and cold and hot superthermal electrons is considered the pseudo-potential method (SPM). An energy integral equation for the system has been derived with the help of SPM. It is found that compressive solitons exist in the plasma system for selected set of plasma parameters. The effect of the spectral indexes of hot electrons (kh), spectral indexes of cold electrons (kc), temperature ratio of two species of electron 1),( positron concentration ),( ionic temperature ratio  ),( positron temperature ratio  )( and Mach number (M) on the characteristics of the large amplitude ion-acoustic solitons are discussed in detail. The amplitude of the solitons increases with increase in positron concentration ),( ionic temperature ratio  ),( positron temperature ratio  )( and Mach number (M) however an decrease in spectral indexes (kh, kc), increases the amplitude of the solitons. The present study of this paper may be helpful in space and astrophysical plasma system where positrons and superthermal electrons are present.

Key words: Large amplitude, pseudo-potential method , superthermal electrons , soliton Introduction: The study of the linear and nonlinear wave phenomena in electron-positron-ion (EPI) plasma has been a subject of significant importance for researchers. The pair production generate naturally electron-positron plasmas such as pulsar magnetosphere [1,3], in early universe [2,4], in nucleon stars, active galactic nuclei [6] and star atmosphere [8]. Several authors [7,10,20] studied the ion-acoustic waves in EPI plasmas. Many researchers using the SPM for study large amplitude ion-acoustic waves with two distinct groups of hot electrons [5,15], negative ion [9], EPI [11,15], charge dust grains [14,18], superthermal electrons [19] in plasmas. Bharuthram and Shukla [5] investigated the effect of two distinct groups of hot electrons on large amplitude ion-acoustic solitons (IASLs) in plasmas. The effect of superthermal electrons observed in astrophysical environment deviates from Maxwellian distribution and found to obey kappa distribution. The effect of superthermal electrons on ion-acoustic waves in plasmas has been studied by Hellberg et al. [12] and Boubakour et al. [13]. El-shamy [16] studied the characteristics of the ion acoustic solitary waves in plasmas with superthermal electrons. Saini et al. [17] examined that effect of hot and cold superthermal electrons on ion-acoustic waves in magnetized plasma.

122 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Basic equations: We consider a collisionless plasma consisting of ions, positrons and superthermal electrons. The dynamics of the plasma is given by the continuity equation, equation of motion and Poisson’s equation:

xt nvn  0)(

(1) t x vvv x   x nn 2 (2)  pchx 1  nnnn (3) The superthermal electrons having two distinct temperature follow kappa distribution and positrons may be given by k  2/1     c     nc 1  (4)  kc  2/3 

k  2/1     h   1  (5) nh 1   kh  2/3 

  3322       p en 1 ... (6)  62 

nc0 nh0 n p0  kc  121  1 kh 12  Where   ,   ,   , 1   , ne0 ne0 ne0 kc  32  kh  )32( 2 22  kc  141  1  k h 14     c,h 2 2 2 and k is the k-distribution corresponding to cold and kc  322  k h  )32(2 hot species of electrons. In the above equations n, np, nc and nh and v are denote the normalized density of ions, positron, T cold and hot electrons, fluid velocity of the ion respectively. The ion-acoustic speed C  e s m T and   e is the normalized electrostatic wave potential. The space variable (x) and time e T   e variable (t) have been normalized by Debye length D 2 and inverse of the ion 4 0en m  1      plasma frequency in the mixture pi 2 , respectively. TT ep ,/ TT ei ,/ and 4 0en

 1  / TT hc are the ratio of positron and electron temperature, the ratio of ion and electron temperature, the ratio of cold to hot electron temperature respectively.

Stationary solitons solution : Let us find out the Sagdeev pseudopotential from basic equations (1) – (3) with introduce the usual transformation   Mtx (7) where M is the Mach number of DLs. Using the equation (7) in Eqs. (1) – (3), the fluid equations be written as

123 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

 nvnM  0)( (8)

  vvvM     nn 2 (9)  pe 1  nnn (10) Using the Eqs. (4) – (6), in the equation (10) and integrating Eqs. (8) - (9) with using appropriate boundary conditions for the unperturbed plasma at   , n = 1, v = 0,    0 and d  .0 Find the quadratic equations  4 (Mn 2  )2 Mn 22  0 (11) From equation (11) the ion density (n) is given by 2M n  (12) 2/1 2/1  2 2 2 2  M 2  M   42  M    Integrating equation (10) with respect to , we obtain

1 2   Vd    0 (13) 2  where V  is the Sagdeev potential which is given by 3 3  k   k    2   2 h  2  2 c     1        V    11    11   1 e   1   23 kh    23 kc      

 2 2 2 2   M    M  4)2(2  M   M 1    4M 2  (14)   2 2/3  2 2 2 2   3M    M  4)2(2  M      1  M 2    3  For the existence of large amplitude solitons, the Sagdeev potential must satisfy the following conditions

V   ,0 and Vd    ,0 at   0 (15) V    ,0 Vd    0    (16)  m  m m 0

V    0 for   m ,0 (17)

124 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Here  m , represents the maximum value of potential. 3 3  k   k  2 h 2 c   2    2      1 m     m   m  11    11   1 e  1   23 kh    23 kc        2  2 2   2   M m   M m 4)2(2 M   M 1    4M 2    2 2/3  2 2 2 2   3M  m   M m  4)2(2  M      1  M 2    0  3  (18)

……. for m ……….. and …>0 …….. for  m Results and Discussion: In the present investigation, it is found that for the selected set of plasma parameters, the system supports only IACSs depending upon the spectral indexes of hot electrons (kh), spectral indexes of cold electrons (kc), temperature ratio of two species of electron 1 ),( positron concentration ),( ionic temperature ratio  ),( positron temperature ratio  )( and Mach number (M). In fig. (1), Sagdeev potential  )( curves have been plotted to investigate the effect of spectral indexes of hot electrons (kh). The graphical representation reveals that for decreasing the value of kh, the amplitude of the IACSs increases. In fig. (2), Sagdeev potential  )( curves have been plotted to investigate the effect of spectral indexes of cold electrons (kc). The graphical representation reveals that for decreasing the value of kc, the amplitude of the IACSs increases. In figure 3 the Sagdeev potential  )( against potential  for different values of positron temperature ratio . It is found that increasing values of  results increases in amplitude of the SP of the ion-acoustic compressive soliton. In figure 4 the Sagdeev potential  )( against potential  for different values of positron concentration ).( It is found that increasing values of  results increases in amplitude of the SP of the ion-acoustic compressive soliton.

Fig. Cap. Fig. (1) Variation of the Sagdeev potential V )( with potential  of the compressive ion-acoustic solitons for M = 2.1, kh = 2,  = 0.1,  1 = 0.1,  = 0.01,  = 0.001 and  = 0.001 having different values of kc = 8.0 (red color dashed line), 9.0 (blue color dotted line) and 1.9259 (black color solid line). Fig. (2) Variation of the Sagdeev potential V )( with potential  of the compressive ion-acoustic solitons for M = 2.1, kc = 8,  = 0.1,  1 = 0.1,  = 0.01,  = 0.001 and  = 0.001 having different values of kh = 2.0 (red color dashed line), 2.01 (blue color dotted line) and 1.9259 (black color solid line).

125 8th. PSSI-PLASMA SCHOLARS COLLOQUIUM (PSC-2020) October 8-9, 2020, KIIT University, Bhubaneswar-751024, Odisha, India

Fig. (6) Variation of the Sagdeev potential V )( with potential  of the compressive ion-acoustic solitons for kh = 2.0, kc = 8, M = 2.1,  = 0.1,  1 = 0.1,  = 0.01 and  = 0.001 having different values of  = 0.001 (red color dashed line), 0.005 (blue color dotted line) and 0.009 (black color solid line). Fig. (7) Variation of the Sagdeev potential V )( with potential  of the compressive ion-acoustic solitons for kh = 2.0, kc = 8, M = 2.1,  = 0.1,  1 = 0.1,  = 0.01 and  = 0.001 having different values of  = 0.001 (red color dashed line), 0.01 (blue color dotted line) and 0.1 (black color solid line). Conclusions: In the present paper, the effect of spectral indexes of cold and hot electrons, temperature ratio of two species of electron, positron concentration, ionic temperature ratio, positron temperature ratio and Mach number on the large amplitude of the IACSs are investigated in plasmas. For given set of plasma parameters on increasing indexes of cold and hot electrons, the amplitude of IACSs decreases, but it decreases with increase in positron concentration and positron temperature ratio. The finding results of this paper may be useful for understanding of nonlinear ion-acoustic solitons in plasma containing positrons, ions and nonthermal electrons in space and laboratory plasmas. References [1] P. Goldreich and W. H. Julian, Astrophys. J. 157, 869 (1969). [2] W. Misner, K. S. Throne and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973), p. 763. [3] F. C. Michel, Rev. Mod. Phys. 54, 1 (1982). [4] M. J. Rees, in The Very Early Universe, edited by G. W. Gibbons, S. W. Hawking and S. Siklas (Cambridge University Press, Cambridge, 1983). [5] R. Bharuthram and P. K. Shukla, Phys. Fluids 29, 3214 (1986). [6] H. R. Miller and P. J. Witter, Active Galactic Nuclei, Springer, Berlin 1987 p. 202. [7] F. B. Rizzato, Plasma Phys. Control. Fusion 40, 289 (1988). [8] E. Tandberg–Hansen and A. G. Emshie, The Physics of Solar Flares (Cambridge University Press, Cambridge, 1988), p. 124. [9] S. L. Jain, R. S. Tiwari and S. R. Sharma, Can. J. Phys 68, 474 (1990). [10] S. I. Popel, S. V. Vladimirov, P. K. Shukla, Phys. Plasmas 2, 716 (1995). [11] Y. N. Nejoh, Phys. Plasma 3, 1447 (1996). [12] M. A. Hellberg, R. L. Mace, T. K. Baluku, I. Kourakis and N. S. Saini, Phys. Plasmas 16, 094701 (2009). [13] N. Boubakour, M. Tribeche and K. Aoutou, Phys. Scr. 79, 065503 (2009). [14] R. S. Tiwari, S. L. Jain and M. K. Mishra, Phys Plasmas 18, 083702 (2011). [15] S. K. Jain and M. K. Mishra, J Plasma Physics 79, 893 (2013). S. K. Jain and M. K. Mishra, Astrophys Space Sci 346, 395 (2013). [16] E. F. El-Shamy, Phys. Plasmas 21, 082110 (2014). [17] N. S. Saini, B. S. Chahal, A. S. Bains and C. Bedi, Phys. Plasmas, 21, 022114 (2014). [18] S. L. Jain, R. S. Tiwari and M. K. Mishra, Astrophys Space Sci 357, 57 (2015). S. L. Jain, R. S. Tiwari and M. K. Mishra, J. Plasma Phys 81, 1 (2015). [19] K. Kumar and M. K. Mishra, AIP Advances 7, 115114 (2017). [20] J. K. Chawla, P. C. Singhadiya, R. S. Tiwari, Pramana J. Phys. 94, 13 (2020).

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