Charged Particle Simulation Under the Guiding Center Approximation
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Laboratory Investigation of the Dynamics of Shear Flows in a Plasma Boundary Layer by Ami Marie DuBois A dissertation submitted to the Graduate Faculty of Auburn University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy Auburn, Alabama December 14, 2013 Copyright 2013 by Ami Marie DuBois Approved by Edward Thomas, Jr., Chair, Professor of Physics William Amatucci, Staff Scientist at Naval Research Laboratory Uwe Konopka, Professor of Physics David Maurer, Professor of Physics Abstract The laboratory experiments presented in this dissertation investigate a regime of instabilities that occur when a highly localized, radial electric field oriented perpendicular to a uniform background magnetic field gives rise to an azimuthal velocity shear profile at the boundary between two interpenetrating plasmas. This investigation is motivated by theoretical predictions which state that plasmas are unstable to transverse and parallel inhomogeneous sheared flows over a very broad frequency range. Shear driven instabilities are commonly observed in the near-Earth space environment when boundary layers, such as the magnetopause and the plasma sheet boundary layer, are compressed by intense solar storms. When the shear scale length is much less than the ion gyro- radius, but greater than the electron gyro-radius, the electrons are magnetized in the shear layer, but the ions are effectively un-magnetized. The resulting shear driven instability, the electron-ion hybrid instability, is investigated in a new interpenetrating plasma configuration in the Auburn Linear EXperiment for Instability Studied (ALEXIS) in the absence of a magnetic field aligned current. In order to truly understand the dynamics at magnetospheric boundary layers, the EIH instability is studied in the presence of a density gradient located at the boundary layer between two plasmas. -
View Technical Report
CH9700652 LRP 581/97 August 1997 Global approach to the spectral problem of MICROINSTABILITIES IN TOKAMAK PLASMAS USING A GYROKINETIC MODEL S. Brunner CRPP Centre de Recherches en Physique des Plasmas ECOLE POLYTECHNIQUE Association Euratom - Confederation Suisse FEDERALE DE LAUSANNE Centre de Recherches en Physique des Plasmas (CRPP) Association Euratom - Confederation Suisse Ecole Poly technique Federate de Lausanne PPB, CH-1015 Lausanne, Switzerland phone: +41 21 693 34 82 17 —fax +41 21 693 51 76 Centre de Recherches en Physique des Plasmas - Technologle de la Fusion (CRPP-TF) Association Euratom - Confederation Suisse Ecole Poly technique Federate de Lausanne CH-5232 Vllligen-PSI, Switzerland phone: +41 56 310 32 59 —fax +41 56 310 37 29 LRP 581/97 August 1997 Global approach to the spectral problem of MICROINSTABILITIES IN TOKAMAK PLASMAS USING A GYROKINET1C MODEL S. Brunner EPFL 1997 Abstract Ion temperature gradient (ITG) -related instabilities are studied in tokamak-like plas mas with the help of a new global eigenvalue code. Ions are modeled in the frame of gyrokinetic theory so that finite Larmor radius effects of these particles are retained to all orders. Non-adiabatic trapped electron dynamics is taken into account through the bounce-averaged drift kinetic equation. Assuming electrostatic perturbations, the sys tem is closed with the quasineutrality relation. Practical methods are presented which make this global approach feasible. These include a non-standard wave decomposition compatible with the curved geometry as well as adapting an efficient root finding al gorithm for computing the unstable spectrum. These techniques are applied to a low pressure configuration given by a large aspect ratio torus with circular, concentric mag netic surfaces. -
Partially Ionized Plasmas in Astrophysics
Space Sci Rev (2018) 214:58 https://doi.org/10.1007/s11214-018-0485-6 Partially Ionized Plasmas in Astrophysics José Luis Ballester1 · Igor Alexeev2 · Manuel Collados3 · Turlough Downes4 · Robert F. Pfaff5 · Holly Gilbert6 · Maxim Khodachenko7 · Elena Khomenko3 · Ildar F. Shaikhislamov8 · Roberto Soler1 · Enrique Vázquez-Semadeni9 · Teimuraz Zaqarashvili7,10 Received: 29 June 2017 / Accepted: 2 February 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract Partially ionized plasmas are found across the Universe in many different as- trophysical environments. They constitute an essential ingredient of the solar atmosphere, molecular clouds, planetary ionospheres and protoplanetary disks, among other environ- ments, and display a richness of physical effects which are not present in fully ionized plasmas. This review provides an overview of the physics of partially ionized plasmas, in- cluding recent advances in different astrophysical areas in which partial ionization plays a B J.L. Ballester [email protected] I. Alexeev [email protected] M. Collados [email protected] T. Downes [email protected] R.F. Pfaff [email protected] H. Gilbert [email protected] M. Khodachenko [email protected] E. Khomenko [email protected] I.F. Shaikhislamov [email protected] R. Soler [email protected] E. Vázquez-Semadeni [email protected] T. Zaqarashvili [email protected] 58 Page 2 of 149 J.L. Ballester et al. fundamental role. We outline outstanding observational and theoretical questions and dis- cuss possible directions for future progress. Keywords Plasmas · Magnetohydrodynamics · Sun · Molecular clouds · Ionospheres · Exoplanets 1 Introduction Plasma pervades the Universe at all scales, and the term plasma universe was coined by Hannes Alfvén to point out the important role played by plasmas across the universe (Alfven 1986). -
Guiding Center Motion
GUIDING CENTER MOTION H.J. de Blank FOM Institute DIFFER – Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM, P.O. Box 1207, 3430 BE Nieuwegein, The Netherlands, www.differ.nl. ABSTRACT Secondly, the Coulomb force is a long range interaction. In a well-ionized plasma, particles rarely suffer large-angle The motion of charged particles in slowly varying electro- deflections in two-particle collisions. Rather, their orbits are magnetic fields is analyzed. The strength of the magnetic deflected through weak interactions with many particles si- field is such that the gyro-period and the gyro-radius of the multaneously. Hence, the effects of collisions can be best particle motion around field lines are the shortest time and described statistically, in terms of distributions of particles. length scales of the system. The particle motion is described The kinetic equation for the particle distribution function as the sum of a fast gyro-motion and a slow drift velocity. will be discussed at the end of this chapter, with emphasis on the role of the particle orbits, not the collisions. The equations of motion of a particle with mass m and I. INTRODUCTION charge q in electromagnetic fields E(x, t) and B(x, t) are, The interparticle forces in ordinary gases are short-ranged, q x˙ = v, v˙ = (E + v B), (1) so that the constituent particles follow straight lines between m × collisions. At low densities where collisions become rare, N the gas molecules bounce up and down between the walls of where the dot denotes the time derivative. Each of the the containing vessel before experiencing a collision. -
Guiding-Center Equations for Electrons in Ultraintense Laser Fields Joel E
ARTICLES Guiding-center equations for electrons in ultraintense laser fields Joel E. Moore and Nathaniel J. Fisch Princeton Plasma Physics Laboratory, Princeton University, P.O. Box 4.51, Princeton, New Jersey 08543 (Received 25 October 1993, accepted 31 January 1994) The guiding-center equations are derived for electrons in arbitrarily intense laser fields also subject to external fields and ponderomotive forces. Exhibiting the relativistic mass increaseof the oscillating electrons, a simple frame-invariant equation is shown to govern the behavior of the electrons for sufficiently weak background fields and ponderomotive forces. The parameter regime for which such a formulation is valid is made precise, and some predictions of the equation are checked by numerical simulation. I. INTRODUCTION but a different form of the equations derived here can be applied to this case as well. The increasing degree of interest in high-intensity la- Various accelerator schemes- attempt some sort of sers (a = eEdmcw - 1) motivates a theoretical examina- conversion of the intense transversefields of a laser into a tion of the behavior of electrons oscillating in the fields of more useful form, and constraints on when such conver- such lasers. The electron motion is well understood when sion can occur are given here. The general constraints the only forces presentare those from the wave,’ this paper given here confirm and generalizethe constraint found by examines the motion of electrons when other fields are Apollonov ef aL4 for a specific accelerator design, and also present in addition to the wave. explain the optimal parameters Kawata er al. found nu- The nonlinearity parameter a can be understood as the merically for two accelerator designs.5’6Essentially these ratio of the momentum imparted by the wave field in a accelerator designs convert some of the relativistic quiver single oscillation to mc. -
Ion-Cyclotron Resonance Heating of O+ in the Topside Ionosphere and Mapping Outflows Ot the Magnetosphere
Dissertations and Theses 9-2014 Ion-Cyclotron Resonance Heating of O+ in the Topside Ionosphere and Mapping Outflows ot the Magnetosphere Anthony W. Pritchard Follow this and additional works at: https://commons.erau.edu/edt Part of the Atmospheric Sciences Commons, and the Engineering Physics Commons Scholarly Commons Citation Pritchard, Anthony W., "Ion-Cyclotron Resonance Heating of O+ in the Topside Ionosphere and Mapping Outflows ot the Magnetosphere" (2014). Dissertations and Theses. 234. https://commons.erau.edu/edt/234 This Thesis - Open Access is brought to you for free and open access by Scholarly Commons. It has been accepted for inclusion in Dissertations and Theses by an authorized administrator of Scholarly Commons. For more information, please contact [email protected]. ION-CYCLOTRON RESONANCE HEATING OF O+ IN THE TOPSIDE IONOSPHERE AND MAPPING OUTFLOWS TO THE MAGNETOSPHERE BY ANTHONY W. PRITCHARD A Thesis Submitted to the Department of Physical Sciences and the Committee on Graduate Studies In partial fulfillment of the requirements for the degree of Master in Science in Engineering Physics 09/2014 Embry-Riddle Aeronautical University Daytona Beach, Florida c Copyright by Anthony W. Pritchard 2014 All Rights Reserved ii Abstract This thesis considers the heavy ion dynamics due to ion-cyclotron resonance en- ergization processes that take place in the turbulent region of the Earth’s topside, high latitude ionosphere. We simulate the impact of this transverse heating process upon energies and velocity distribution functions of outflowing oxygen ions (O+) in the approximate altitude range of 800 km to 15,000 km. To do so most effectively, we use a single particle tracing model that precisely reproduces the small-scale wave-particle interaction of broadband extremely low frequency (BBELF) waves with the ions’ cyclotron motions, leading to the upward acceleration of ions in type-II ion outflows and ion conics. -
Observation of the Hot Electron Interchange Instability in a High Beta Dipolar Confined Plasma
Observation of the Hot Electron Interchange Instability in a High Beta Dipolar Confined Plasma Eugenio Enrique Ortiz Submitted in Partial Fulfillment of the Requirement for the degree of Doctorate of Philosphy in the Graduate School of Arts and Sciences Columbia University 2007 Observation of the Hot Electron Interchange Instability in a High Beta Dipolar Confined Plasma Eugenio Enrique Ortiz Abstract In this thesis the first study of the high beta, hot electron interchange (HEI) instability in a laboratory, dipolar confined plasma is presented. The Levitated Dipole Experiment (LDX) is a new research facility that explores the confinement and stability of plasma created within the dipole field produced by a strong superconducting magnet. In initial experiments long- pulse, quasi-steady state microwave discharges lasting more than 10 sec have been produced with equilibria having peak beta values of 20%. Creation of high-pressure, high beta plasma is possible only when intense HEI instabilities are stabilized by sufficiently high background plasma density. In LDX the HEI instability is found to occur under three conditions: during the low density regime, as local high beta relaxation events, and as global intense energy relaxation bursts. Each regime is characterized by how the plasma behaves in response to heating and fueling. Measurements of the HEI instability are made using high-impedance, floating potential probes and fast Mirnov coils. Analysis of these signals reveals the extent of the transport during high beta plasmas. For intense enough high beta HEI instabilities, fluctuations at the edge significantly exceed the magnitude of the equilibrium field generated by the high beta electrons and energetic electron confinement ends in under 100 µsec. -
Fundamentals of Plasma Physics and Controlled Fusion Kenro Miyamoto
Fundamentals of Plasma Physics and Controlled Fusion Kenro Miyamoto (Received Sep. 18, 2000) NIFS-PROC-48 Oct. 2000 Fundamentals of Plasma Physics and Controlled Fusion by Kenro Miyamoto i Fundamentals of Plasma Physics and Controlled Fusion Kenro Miyamoto Contents Preface 1 Nature of Plasma ....................................................................1 1.1 Introduction .......................................................................... 1 1.2 Charge Neutrality and Landau Damping ..............................................1 1.3 Fusion Core Plasma ...................................................................3 2 Plasma Characteristics ..............................................................7 2.1 Velocity Space Distribution Function, Electron and Ion Temperatures ..................7 2.2 Plasma Frequency, Debye Length ......................................................8 2.3 Cyclotron Frequency, Larmor Radius ..................................................9 2.4 Drift Velocity of Guiding Center ..................................................... 10 2.5 Magnetic Moment, Mirror Confinement, Longitudinal Adiabatic Constant ............12 2.6 Coulomb Collision Time, Fast Neutral Beam Injection ................................14 2.7 Runaway Electron, Dreicer Field .....................................................18 2.8 Electric Resistivity, Ohmic Heating ...................................................19 2.9 Variety of Time and Space Scales in Plasmas .........................................19 3 Magnetic -
General Plasma Physics I Notes AST 551
General Plasma Physics I Notes AST 551 Nick McGreivy Princeton University Fall 2017 1 Contents 0 Introduction5 1 Basics7 1.1 Finals words before the onslaught of equations . .8 1.1.1 Logical framework of Plasma Physics . .9 1.2 Plasma Oscillations . 10 1.3 Debye Shielding . 13 1.4 Collisions in Plasmas . 17 1.5 Plasma Length and Time Scales . 21 2 Single Particle Motion 24 2.1 Guiding Center Drifts . 24 2.1.1 E Cross B Drift . 25 2.1.2 Grad-B drift . 29 2.1.3 Curvature Drift . 31 2.1.4 Polarization Drift . 35 2.1.5 Magnetization Drift and Magnetization Current . 37 2.1.6 Drift Currents . 38 2.2 Adiabatic Invariants . 40 2.2.1 First Adiabatic Invariant µ ................. 44 2.2.2 Second Adiabatic Invariant J ................ 46 2.3 Mirror Machine . 46 2.4 Isorotation Theorem . 48 2.4.1 Magnetic Surfaces . 49 2.4.2 Proof of Iso-rotation Theorem . 50 3 Kinetic Theory 54 3.1 Klimantovich Equation . 57 3.2 Vlasov Equation . 60 3.2.1 Some facts about f . 62 3.2.2 Properties of Collisionless Vlasov-Maxwell Equations . 63 3.2.3 Entropy of a distribution function . 64 3.3 Collisions in the Vlasov Description . 66 3.3.1 Heuristic Estimate of Collision Operator . 66 3.3.2 Strongly and Weakly Coupled Plasmas . 67 3.3.3 Properties of Collision Operator . 68 3.3.4 Examples of Collision Operators . 69 3.4 Lorentz Collision Operator . 70 3.4.1 Lorentz Conductivity . 72 4 Fluid and MHD Equations 74 4.1 Deriving Fluid Equations . -
Magnetic Confinement of Charged Particles
Magnetic confinement of charged particles Thomas Sunn Pedersen Max-Planck Institute for Plasma Physics and University of Greifswald, Germany Overview •Motivation for studying single particle orbits in magnetic fields •Motion in a straight uniform B-field (basic review) •The guiding center approximation •Motion including a static electric field, or gravity •Motion in inhomogeneous and bent B-fields and the first adiabatic invariant •Mirror confinement •Time variation (no derivation) Lecture on guiding center approximation 2 The need for magnetic field confinement •The easiest fusion process to reach is D-T fusion •This requires particle kinetic energies in the range 10-100 keV •Even at the particle energy of peak D-T fusion reactivity, non-fusion collisions (scattering) dominate over the fusion collisions By two orders of magnitude •Must confine plasma at T>10 keV (~120 M Kelvin) for many collisions •Thermal speed of D and T is on the order of 106 m/s at these temperatures (and even higher for electrons) – μs confinement if you have no confining field? •Electric fields alone won’t work: Confine only one species •Magnetic fields may work (must Be Bent!) •Gravity works on the sun, But not on Earth Lecture on guiding center approximation 3 Charged particle motion in a straight magnetic field •A charged particle performs a screw-like path if it is confined by a straight uniform magnetic field and it feels no other forces •Start with Newton’s 2nd law and the Lorentz force: F = ma = qv × B B B zˆ = 0 € Lecture on guiding center approximation -
Advanced Space Plasma Physics
Advanced Space Plasma Physics Rudolf A. Treumann & Wolfgang Baumjohann Max-Planck-Institut fur¨ extraterrestrische Physik, Garching and Osterreichische¨ Akademie der Wissenschaften Institut fur¨ Weltraumforschung, Graz Revised Edition, Imperial College Press, London, 2001 Preface This book is the second volume of our introductory text on Space Plasma Physics. The first volume is published under the title Basic Space Plasma Physics and covers the more fundamental aspects, i.e., single particle dynamics, fluid equilibria, and waves in space plasmas. This second volume extends the material to the more advanced fields of plasma instabilities and nonlinear effects. Actually, there are already a number of monographs, where the general nonlinear plasma methods are described in considerable detail. But many of these books are quite specialized. The present book selects those methods, which are applied in space plasma physics, and, on the expense of detailedness, tries to make them accessible to the more practically oriented student and researcher by putting the new achievements and methods into the context of general space physics. The first part of the book is concerned with the evolution of linear instabilities in plasmas. Instabilities have turned out to be the most interesting and important phenom- ena in physics. They arise when free energy has accumulated in a system which the system wants to get rid of. In plasma physics there is a multitude of reasons for the excitation of instabilities. Inhomogeneities may evolve both in real space and in veloc- ity space. These inhomogeneities lead to the generation of instabilities as a first linear and straightforward reaction of the plasma to such deviations from thermal equilibrium. -
Trajectories of Charged Particles Trapped in Earth's Magnetic Field
Trajectories of charged particles trapped in Earth’s magnetic field M. Kaan Ozt¨urk¨ Yeditepe University, Information Systems and Technologies, Istanbul, Turkey∗ (Dated: December 16, 2011) I outline the theory of relativistic charged-particle motion in the magnetosphere in a way suitable for undergraduate courses. I discuss particle and guiding center motion, derive the three adiabatic invariants associated with them, and present particle trajectories in a dipolar field. I provide twelve computational exercises that can be used as classroom assignments or for self-study. Two of the exercises, drift-shell bifurcation and Speiser orbits, are adapted from active magnetospheric research. The Python code provided in the supplement can be used to replicate the trajectories and can be easily extended for different field geometries. I. INTRODUCTION Ions and electrons trapped in the Earth’s magnetic field may affect our technology and our daily lives in sig- nificant ways. Energetic plasma particles may penetrate satellites and disable them temporarily or permanently. They can also pose serious health hazards for astronauts in space. Spectacles like the aurora are created by parti- cles that enter the Earth’s atmosphere at polar regions; on the other hand, aircraft personnel and frequent flyers may accumulate a significant dose of radiation due to the same particles.1 All of these effects are enhanced at pe- riods of solar maximum, the next one being expected to happen between 2012 and 2014. Occasional extreme so- FIG. 1. A schematic view of the Earth’s magnetosphere. The lar events may induce currents in the ionosphere, which solar wind comes from the left.