DOCSLIB.ORG

Space Plasma Physics Thomas Wiegelmann, 2012 Space Plasma Physics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Space Plasma Physics Thomas Wiegelmann, 2012 Space Plasma Physics 4/18/2012 Space Plasma Physics Thomas Wiegelmann, 2012 Space Plasma Physics 1. Basic Plasma Physics concepts 2. Overview about solar system plasmas Physical Processes Plasma Models 8. Plasma Waves, instabilities and shocks 9. Magnetic Reconnection 3. Single particle motion, Test particle model 4. Statistic description of plasma, BBGKY- Applications Hierarchy and kinetic equations 10. Planetary Magnetospheres 5. Fluid models, Magneto-Hydro-Dynamics 11. Solar activity 6. Magneto-Hydro-Statics 7. Stationary MHD and Sequences of Equilibria 12. Transport Processes in Plasmas Used Material What is plasma? • Lecture notes from Eckart Marsch 2007 In plasma physics we study ionized gases • Baumjohann&Treumann: Basic Space Plasma Physics under the influence of • Schindler: Physics of space plasma activity electro-magnetic fields. • Priest: Solar MHD • Kulsrud: Plasma Physics for Astrophysics • Krall & Trivelpiece: Principles of Plasma Physics • Chen: Introduction to plasma physics and controlled fusion • Balescu: Plasma Transport (3 volumes) Levi Tonks (1897-1971) and William Crookes (1832-1919) • Spatschek: Theoretische Plasmaphysik Irving Langmuir (1881- called ionized matter in a gas 1957, photo) first used the discharge (Crookes-tube, photo) term plasma for a 4th state of matter • Wikipedia, Google and YouTube collection of charged (Phil. Trans 1879) particles (Phys. Rev. 1929) Source: Wikipedia Industrial Plasmas Natural Plasmas on Earth Lightning Electric Arcs St. E Fire Semi conducter Nuclear Fusion, Neon-lights, Fluorescent device fabrication lamps,Plasma globes here a Tokamak Ball lightning Aurorae Source: Wikipedia 1 4/18/2012 Space Plasmas Accretion discs Interior and atmosphere of Sun+Stars Source: Wikipedia Planetary magnetospheres, solar wind, inter-planetary medium Comparison: Gas and Plasma Source: Wikipedia Plasmas studied in this lecture What is a plasma? • Non-relativistic particle velocities v<<c • Spatial and temporal scales are large compared to • A fully or partly ionized gas. Planck length (1.6 10-35 m) and time (5.4 10-44 s) • Collective interaction of charged particles More precise: Any action variables like is more important than particle-particle (momentum x spatial dimension, Energy x time) are collisions. large compared to Planck constant (h= 6.6 10-34 Js) Classic plasma, no quantum-mechanic effects. • Charged particles move under the influence of • Plasmas violating these conditions electro-magnetic fields (Lorentz-force) (Quark-Gluon Plasma, relativistic plasma) are active • Charged particles cause electric fields, areas of research, but outside the scope of this moving charged particles cause electric currents introductory course. and thereby magnetic fields (Maxwell equations). 2 4/18/2012 Plasma models What is a plasma? - Test particles: Study motion of individual charged particles under the influence of external electro-magnetic (EM) fields • In principle we can study a plasma by solving the Lorentz-force and Maxwell- - Kinetic models: equations selfconsistently. Statistic description of location and velocity of • With typical 10^20-10^50 particles in space particles and their interaction + EM-fields. plasmas this is not possible. (Vlasov-equation, Fokker-Planck eq.) (Using some 10^9 or more particles with this approach is possible on modern computers) - Fluid models: Study macroscopic quantities like density, pressure, => Plasma models flow-velocity etc. + EM-fields (MHD + multifluid models) - Hybrid Models: Combine kinetic + fluid models Electromagnetic forces Maxwell equations for electro-magnetic fields The motion of charged particles in space is strongly influenced by the self- generated electromagnetic fields, which evolve according to A and The motion of charged particles in space is F (induction) laws (in this lecture we use the SI-system): determined by the electrostatic Coulomb force and magnetic Lorentz force: where q is the charge and v the velocity of any charged particle. If we deal with electrons and various ionic species (index, s), the charge and current densities are obtained, respectively, by summation over all kinds of species as where 0 and 0 are the vacuum dielectric constant and free-space follows: magnetic permeability, respectively. The charge density is and the current density j. The electric field obeys Gauss law and the magnetic field is always free of divergence, i.e. we have: which together obey the continuity equation, because the number of charges is conserved, i.e. we have: Electro-static effects Debye-length A plasma is quasi-neutral • On large scales the positive (ions) and negative charges cancel each other. • On small scales charge separations occur. Can we estimate these scales? => Do calculations on blackboard. Remark: Some text-books drop the factor sqrt(3/2)~1.2 3 4/18/2012 Debye-length Debye shielding • Electric potential for a charge in vacuum: • Electric potential in a plasma: => Debye shielding Source: Chen, Wikipedia Debye shielding Plasma Oscillations • How does a charged particle (say an electron) move in a non-magneticed plasma? • Solve electrostatic Maxwell equation selfconsistently with equation of motion, here for the Coulomb force • => Do calculations on blackboard. Source: Technik-Lexikon Plasma Oscillations Plasma parameter • Plasma frequency • The plasma paramter g indicates the number of particles in a Debye sphere. • Electron plasma frequency • Plasma approximation: g << 1. is often used to specify the • For effective Debye shielding and electron density of a plasma. statistical significants the number of How? => Dispersion relation of EM-waves particles in a Debye sphere must be high. See lecture of plasma waves. 4 4/18/2012 Plasma parameter g Collisions: Mean free path g gives a measure how collective effects • • The mean free path is the distance a particle dominate over single particle effects. moves in average before it suffers a collision. • Contrast between neutral gas and plasma: • Cross section for interaction of particles -Interaction region of a neutral atom is the during collisions in a plasma is approximated atomic radius R and with the Debye-length. -Interaction region in a plasma is the • Mean free path: Debye sphere and Collision frequency: • Plasma state can be derived from expansion of • exact many body equations with g. Magnetized Plasmas Induction equation Using Maxwell equations for slow time variations, In order to study the transport of plasma and without the displacement current yields the magnetic field lines quantitatively, let us combine induction equation (with constant conductivity ): M equations with the simple 0 phenomenological O law, relating the electric field in the plasma frame with its current: Convection Diffusion (Later we will derive O law more systematically Exercise: Derive this equation for a spatial from kinetic plasma theory) constant conductivity. How does the equation look if the conductivity varies spatially? Magnetic diffusion Hydromagnetic theorem Assuming the plasma be In an ideal collisionless at rest, the induction plasma in motion with equation becomes a pure infinite conductivity the diffusion equation: induction equation becomes: with the magnetic diffusion coefficient D = ( )-1. m 0 0 The field lines are constrained to move with the plasma -> frozen-in field. If plasma patches on different sections Under the influence of finite resistivity the magnetic field of a bundle of field lines move oppositely, then the lines diffuses across the plasma, and field inhomogenities are will be deformed accordingly. Electric field in plasma smoothed out at time scale, = L 2, with scale length L . d 0 0 B B frame, E' = 0, -> voltage drop around closed loop is zero. 5 4/18/2012 Magnetic reconnection Field line merging and reconnection in the Assuming the plasma streams at bulk speed V, then E the induction equation can be written in simple dimensional form as: The ratio of the first to second term gives the so-called magnetic Reynolds number, Rm = 0 0LBV, which is useful to decide whether a plasma is diffusion or convection dominated. Current sheet with converging flows -> magnetic merging at points where Rm 1. Field lines form X-point and separatrix. magnetopaus magnetotail e Waves in plasmas Plasma waves are not generated at random. To exist they must satisfy two conditions: In a plasma there are many reasons for spatio-temporal variations (waves or more generally fluctuations): High -> their amplitude must exceed the thermal noise level -> they must obey appropriate dynamic plasma equations temperature required for ionization ( H = 13.6 eV 158000 K) implies fast thermal particle motion. As a consequence There is a large variety of wave modes which can be excited in -> microscopic fluctuating charge separations and currents a plasma. The mode structure depends on the composition, -> fluctuating electromagnetic fields. boundary conditions and theoretical description of the plasma. There are also externally imposed disturbances which may propagate through the plasma and spread their energy in the We may represent any wave disturbance, A(x,t), by its whole plasma volume. The relevant frequency ranges are: Fourier components (with amplitude, A(k, ), wave vector k, and frequency, ): Ultra-low, extremely-low, and very-low frequency waves Phase velocity (wave front propagation) Group velocity (energy flow) Wave-particle interactions Summary Plasma waves in a warm plasma interact with particles through: • Plasma is a quasi-neutral ionized gas moving Cyclotron resonance: - k·v = ± gi,e under the influence
Load more

Recommended publications
  • Verification of Gyrokinetic Codes: Theoretical Background & Numerical Implementations
    N.Tronko 1, T.Goerler 2 , A.Bottino 2 , B.D.Scott 2, E.Sonnendrücker 1 Verification of Gyrokinetic codes: Theoretical background & Numerical implementations NumKin 2016, IRMA, Strasbourg, France 1 NMPP, Max Planck Institute für Plasmaphysik 2 TOK, Max Planck Institute für Plasmaphysik VeriGyro Project Participants Enabling Research Project on Verification of Gyrokinetic codes • Germany! Max Planck Insitute for Plasma Physics (Garching and Greifswald) • Switzerland SPC-EPFL, Lausanne • Finland! Aalto Univeristy • Great Britain University of Warwick • France CEA Cadarache, Université Paris IV, Rennes, Toulouse, Lorraine, Bretagne IRMA, Maison de la Simulation (Saclay) • USA Saint Michel’s College, VT NumKin 2016 VeriGyro Project @ IPP Garching Interdisciplinary Project in IPP Max Planck (Garching) NMPP Division (Numerical Methods for Plasma Physics) • Development and implementation of new algorithms for fusion and astrophysical plasma modeling • Development of libraries (i.e. Selalib) • Verification of existing codes • Participants: N. Tronko, E. Sonnendrücker Enabling Research Project VeriGyro TOK (Tokamak Theory) • Development of major codes • Plasma modeling and comparison with experimental results (ASDEX Upgrade) • Participants: T. Görler, A. Bottino, B. D. Scott NumKin 2016 VeriGyro Project: Motivation • Verification of Global (Electromagnetic) Gyrokinetic codes: Why? • Most popular tools for magnetised plasmas simulations: • Significant Development since last 10 years • Electrostatic gyrokinetic implementations : well established ! [Dimits
    [Show full text]
  • 1 the Derivation of Particle Monte Carlo Methods for Plasma Modeling
    The derivation of Particle Monte Carlo methods for plasma modeling from transport equations. Savino Longo Dipartimento di Chimica dell'Università and CNR/IMIP, Via Orabona 4, 70126 Bari, Italy. e-mail: [email protected] Abstract: We analyze here in some detail, the derivation of the Particle and Monte Carlo methods of plasma simulation, such as Particle in Cell (PIC), Monte Carlo (MC) and Particle in Cell / Monte Carlo (PIC/MC) from formal manipulation of transport equations. Keywords: Charged Particle Transport, Boltzmann Equation, Monte Carlo Methods, Particle-in-Cell, Vlasov/Boltzmann equation 1 1.Introduction An accurate calculation of the velocity distribution of charged particles in non equilibrium plasmas is necessary in order to evaluate the rate at which collisional elementary processes take place in these media as well as their transport properties [1]. In doing so, one has to take into account the effect of inertia, scattering, externally applied and self-coherent fields, all affecting the particle transport. To this aim, different particle simulation techniques have been used extensively, as an alternative to the grid-based solution of transport equations [1] by finite differences or finite element techniques. To these belong the very well-know Test Particle Monte Carlo (TPMC, or simply Monte Carlo, MC [1]), the Particle in Cell (PIC [2,3]) and Particle in Cell / Monte Carlo methods (PIC/MC [4]). No explicit description of the methods will be given here because of their widespread application within the plasma modelling community, and we assume in the following that they are already known to the reader.
    [Show full text]
  • Computational Plasma Physics
    Computational plasma physics S. Possanner and E. Sonnendr¨ucker Max-Planck-Institut f¨urPlasmaphysik und Zentrum Mathematik, TU M¨unchen Lecture notes Sommersemester 2019 April 26, 2019 Contents 1 Introduction2 1.1 Scientific computing..........................2 1.2 Plasmas.................................4 1.3 Model equations.............................4 1.3.1 The N-body model.......................6 1.3.2 Kinetic models.........................7 1.3.3 Fluid models..........................9 1 Chapter 1 Introduction 1.1 Scientific computing Understanding an experiment in physics relies on a model which is generally a differential equation or a partial differential equation or a system involving many of these. In sufficiently simple cases analytical solutions of these models exist and then this can be used to predict the behaviour of a similar experiment. However in many cases, especially when the model is based on first principles, it is so complex that there is no analytical solution available. Then there are two options: the first is to simplify the model until it can be analytically solved, the second is to compute an approximate solution using a computer. In practice both are usually done, the simplified models being used to verify that the code is working properly. Due to the enormous development of computer resources in the last 50 years, quite realistic simulations of physical problems become now possible. A large amount of theoretical work in physics and related disciplines, in particular in plasma physics, now relies quite heavily on numerical simulation. Computational sciences have emerged next to theory and experiments as a third pillar in physics and engineering. Designing efficient, robust and accurate simulation codes is a challenging task that is at the interface of the application domain, plasma physics in our case, applied mathematics and computer science.
    [Show full text]
  • Computational Modeling of Fully Ionized Magnetized Plasmas Using the fluid Approximationa…
    PHYSICS OF PLASMAS 13, 058103 ͑2006͒ Computational modeling of fully ionized magnetized plasmas using the fluid approximationa… ͒ D. D. Schnackb Center for Energy and Space Science, Science Applications International Corporation, 10260 Campus Point Drive, San Diego, California 92121 D. C. Barnes Center for Integrated Plasma Studies, University of Colorado, 2000 Colorado Avenue, Boulder, Colorado 80309 D. P. Brennan General Atomics, P.O. Box 85608, San Diego, California 92186 C. C. Hegna Department of Engineering Physics, University of Wisconsin, 1500 Engineering Drive, Madison, Wisconsin 53706 E. Held Department of Physics, Utah State University, Logan, Utah 84322 C. C. Kim Department of Engineering Physics, University of Wisconsin, 1500 Engineering Drive, Madison, Wisconsin 53706 and Plasma Science and Innovation Center, University of Washington, P.O. Box 352250, Seattle, Washington 98195 S. E. Kruger TechX Corporation, 5621 Arapahoe Avenue, Suite A, Boulder, Colorado 80303 A. Y. Pankin Center for Energy and Space Science, Science Applications International Corporation, 10260 Campus Point Drive, San Diego, California 92121 C. R. Sovinec Department of Engineering Physics, University of Wisconsin, 1500 Engineering Drive, Madison, Wisconsin 53706 ͑Received 20 October 2005; accepted 6 January 2006; published online 11 May 2006͒ Strongly magnetized plasmas are rich in spatial and temporal scales, making a computational approach useful for studying these systems. The most accurate model of a magnetized plasma is based on a kinetic equation that describes the evolution of the distribution function for each species in six-dimensional phase space. High dimensionality renders this approach impractical for computations for long time scales. Fluid models are an approximation to the kinetic model.
    [Show full text]
  • Particle-In-Cell Simulations of Highly Collisional Plasmas on the GPU in 1 and 2 Dimensions
    Particle-In-Cell Simulations Of Highly Collisional Plasmas On The GPU In 1 And 2 Dimensions A thesis for the degree of PHILOSOPHIAE DOCTOR Presented to DUBLIN CITY UNIVERSITY By Nina Hanzlikova B.Sc. School of Physical Sciences Dublin City University Research Supervisor: Prof. Miles M. Turner March 2015 Declaration I hereby certify that this material, which I now submit for assessment on the programme of study leading to the award of Philosophiae Doctor is entirely my own work, and that I have exercised reasonable care to ensure that the work is original, and does not to the best of my knowledge breach any law of copyright, and has not been taken from the work of others save and to the extent that such work has been cited and acknowledged within the text of my work. Signed: ........................................................ Nina Hanzlikova ID No.: 56459501 Date: 27th December 2014 Contents List of Figures xii List of Symbols xiii 1 Introduction 1 1.1 Overview . 2 1.2 Plasma Fundamentals . 4 1.2.1 Debye Length . 4 1.2.2 Plasma Frequency . 5 1.2.3 Collisions . 7 1.2.4 Diffusion . 9 1.2.5 Plasma Sheath . 11 1.2.6 Driving Potential and Heating . 14 1.3 Atmospheric Pressure Plasmas . 15 1.3.1 Atmospheric Plasma Sources . 15 1.3.2 Atmospheric Plasma Characteristics . 16 ii CONTENTS 1.4 Plasma Modelling . 21 1.4.1 Particle Modelling . 22 1.4.2 Atmospheric Plasma Modelling . 23 1.5 Chapter Summary . 25 2 Introduction To High Performance Computing 27 2.1 Graphical Processing Unit (GPU) .
    [Show full text]
  • Semiclassical Modeling of Multiparticle Quantum Mechanics
    UNIVERSITY OF CALIFORNIA Los Angeles Semiclassical Modeling of Quantum-Mechanical Multiparticle Systems using Parallel Particle-In-Cell Methods A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by Dean Edward Dauger 2001 © Copyright by Dean Edward Dauger 2001 To my parents, Alan and Marlene, who were always fully supportive of my work and my endeavors. And Charlie and Allegra, my cats. And to all those who have a vision, a dream of something new and inspiring, to express that Idea, limited only by its own conclusion if it has one. iii Contents I. Introduction A. Motivation ···················································································1 B. Existing Methods ···················································································6 C. Outline ···················································································8 D. Conventions ···················································································9 II. Theory A. The Approach ·················································································11 B. Feynman Path Integrals···············································································13 C. The Semiclassical Approximation·······························································18 D. Initial Position and Final Momentum·························································21 E. The Matrix ··················································································23 F. The Determinant
    [Show full text]
  • Arxiv:1809.02473V1 [Physics.Plasm-Ph] 7 Sep 2018 These Applications Are Only Emerging, and a Brief Discus- Tal Understanding and for Technological Applications
    Towards an integrated modeling of the plasma-solid interface M Bonitz1, A Filinov1;2;3, J W Abraham1, K Balzer4, H Kählert1, E Pehlke1, FX Bronold5, M Pamperin5, M M Becker2, D Loffhagen2, H Fehske5 1 Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität, Leibnizstr. 15, D-24098 Kiel, Germany 2 Leibniz-Institut für Plasmaforschung und Technologie e.V. (INP), Felix-Hausdorff-Str. 2, D-17489 Greifswald, Germany 3 Joint Institute for High Temperatures RAS, Izhorskaya Str. 13, 125412 Moscow, Russia 4 Rechenzentrum der Christian-Albrechts-Universität Kiel and 5 Institut für Physik, Universität Greifswald Solids facing a plasma are a common situation in many astrophysical systems and laboratory setups. More- over, many plasma technology applications rely on the control of the plasma-surface interaction, i.e. of the particle, momentum and energy fluxes across the plasma-solid interface. However, presently often a fundamen- tal understanding of them is missing, so most technological applications are being developed via trial and error. The reason is that the physical processes at the interface of a low-temperature plasma and a solid are extremely complex, involving a large number of elementary processes in the plasma, in the solid as well as fluxes across the interface. An accurate theoretical treatment of these processes is very difficult due to the vastly different system properties on both sides of the interface: quantum versus classical behavior of electrons in the solid and plasma, respectively; as well as the dramatically differing electron densities, length and time scales. Moreover, often the system is far from equilibrium. In the majority of plasma simulations surface processes are either neglected or treated via phenomenological parameters such as sticking coefficients, sputter rates or secondary electron emission coefficients.
    [Show full text]
  • Fluid Modeling of Transport and Instabilities in Magnetized Low-Temperature Plasma Sources Sarah Sadouni
    Fluid modeling of transport and instabilities in magnetized low-temperature plasma sources Sarah Sadouni To cite this version: Sarah Sadouni. Fluid modeling of transport and instabilities in magnetized low-temperature plasma sources. Physics [physics]. Université Paul Sabatier - Toulouse III, 2020. English. NNT : 2020TOU30014. tel-02978476 HAL Id: tel-02978476 https://tel.archives-ouvertes.fr/tel-02978476 Submitted on 26 Oct 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THÈSE En vue de l’obtention du DOCTORAT DE L’UNIVERSITÉ DE TOULOUSE Délivré par l'Université Toulouse 3 - Paul Sabatier Présentée et soutenue par Sarah SADOUNI Le 27 février 2020 Modélisation fluide du transport et des instabilités dans une source plasma froid magnétisé Ecole doctorale : GEET - Génie Electrique Electronique et Télécommunications : du système au nanosystème Spécialité : Ingénierie des Plasmas Unité de recherche : LAPLACE - Laboratoire PLAsma et Conversion d'Énergie - CNRS-UPS-INPT Thèse dirigée par Gerjan HAGELAAR et Andrei SMOLYAKOV Jury Mme Anne BOURDON, Rapporteure Mme Sedina TSIKATA, Rapporteure M. Pierre FRETON, Examinateur M. Jan VAN DIJK, Examinateur M. Gerjan HAGELAAR, Directeur de thèse M. Andrei SMOLYAKOV, Co-directeur de thèse Contents R´esum´e 4 Abstract 5 Introduction 6 Plasma devices and applications .
    [Show full text]
  • Test Cases for Grid-Based Direct Kinetic Modeling of Plasma Flows
    Plasma Sources Science and Technology PAPER Related content - Numerical analysis of azimuthal rotating Test cases for grid-based direct kinetic modeling spokes in a crossed-field discharge plasma of plasma flows R Kawashima, K Hara and K Komurasaki - Hollow cathode modeling: I. A coupled plasma thermal two-dimensional model To cite this article: Kentaro Hara and Kyle Hanquist 2018 Plasma Sources Sci. Technol. 27 065004 Gaétan Sary, Laurent Garrigues and Jean- Pierre Boeuf - Sheaths in laboratory and space plasmas Scott Robertson View the article online for updates and enhancements. Recent citations - Interaction of biased electrodes and plasmas: sheaths, double layers, and fireballs Scott D Baalrud et al - Ion kinetics and nonlinear saturation of current-driven instabilities relevant to hollow cathode plasmas Kentaro Hara and Cameron Treece - An overview of discharge plasma modeling for Hall effect thrusters Kentaro Hara This content was downloaded from IP address 150.135.159.43 on 05/01/2021 at 00:18 Plasma Sources Science and Technology Plasma Sources Sci. Technol. 27 (2018) 065004 (14pp) https://doi.org/10.1088/1361-6595/aac6b9 Test cases for grid-based direct kinetic modeling of plasma flows Kentaro Hara1 and Kyle Hanquist2 1 Texas A&M University, College Station, Texas, United States of America 2 University of Michigan, Ann Arbor, Michigan, United States of America E-mail: [email protected] Received 19 January 2018, revised 1 May 2018 Accepted for publication 22 May 2018 Published 18 June 2018 Abstract Grid-based kinetic models are promising in that the numerical noise inherent in particle-based methods is essentially eliminated. Here, we call such grid-based techniques a direct kinetic (DK) model.
    [Show full text]
  • Three-Dimensional Particle-In-Cell Simulation of a Pulsed Plasma Thruster: Modeling and Challenges
    Three-dimensional Particle-In-Cell Simulation of a Pulsed Plasma Thruster: Modeling and Challenges IEPC-2011-116 Presented at the 32nd International Electric Propulsion Conference, Wiesbaden, Germany September 11–15, 2011 J. Neudorfer∗ Institut f¨ur Aerodynamik und Gasdynamik, Universit¨at Stuttgart, 70550 Stuttgart, Germany German Research School for Simulation Sciences GmbH, 52062 Aachen, Germany T. Stindl† Institut f¨ur Raumfahrtsysteme, Universit¨at Stuttgart, 70550 Stuttgart, Germany R. Schneider‡ Karlsruher Institut f¨ur Technologie, Institut f¨ur Hochleistungsimpuls- und Mikrowellentechnik, 76021 Karlsruhe, Germany S. Roller§ German Research School for Simulation Sciences GmbH, 52062 Aachen, Germany Applied Supercomputing in Engineering, RWTH Aachen University, 52062 Aachen, Germany C.-D. Munz¶ Institut f¨ur Aerodynamik und Gasdynamik, Universit¨at Stuttgart, 70550 Stuttgart, Germany and M. Auweter-Kurtz German Aerospace Academy ASA, 71304 B¨oblingen, Germany In order to simulate the rarefied plasma flow within pulsed plasma thrusters (PPTs), a fully kinetic approach for the Boltzmann-Maxwell equations is under development by IAG (Institute of Aerodynamics and Gas Dynamics, Universit¨at Stuttgart), IRS (Institute of Space Systems, Universit¨at Stuttgart), ASE (Applied Supercomputing in Engineering, German Research School for Simulation Sciences) and IHM (Institute for Pulsed Power and Microwave Technology, Karlsruher Institut f¨ur Technologie). An attractive numerical method to solve the Boltzmann-Maxwell problem without collisions
    [Show full text]
  • High-Order Finite Element Method for Plasma Modeling*
    HIGH-ORDER FINITE ELEMENT METHOD FOR PLASMA MODELING* U. Shumlak, R. Lilly, S. Miller, N. Reddell, E. Sousa Aerospace and Energetics Research Program University of Washington, Seattle, USA, 98195-2250 Email: [email protected] Abstract—High-order accurate finite element methods provide description. Plasmas may be most accurately modeled using unique benefits for problems that have strong anisotropies and kinetic theory, where distribution functions, fs(x; v; t), are complicated geometries and for stiff equation systems that are governed by a Boltzmann equation coupled through large source terms, e.g. Lorentz force, collisions, @f @f q @f @f or atomic reactions. Magnetized plasma simulations of realistic s + v · s + s (E + v × B) · s = s (1) devices using the kinetic or the multi-fluid plasma models are @t @x ms @v @t collisions examples that benefit from high-order accuracy. The multi-fluid plasma model only assumes local thermodynamic equilibrium for each species s, e.g. ions, electrons, neutrals. Combined within each fluid, e.g. ion and electron fluids for the two- with Maxwell’s equations, the system leads to the continuum fluid plasma model. The algorithm implements a discontinu- kinetic plasma model, as well as the particle kinetic plasma ous Galerkin method with an approximate Riemann solver to model. Kinetic models, in their most general form, are six- compute the fluxes of the fluids and electromagnetic fields at dimensional, but reduced models with limited dimensionality the computational cell interfaces. The multi-fluid plasma model can also be meaningful, e.g. gyrokinetic. Further reduced has time scales on the order of the electron and ion cyclotron plasma models result by taking moments over velocity space frequencies, the electron and ion plasma frequencies, the electron of Eq.
    [Show full text]
  • Miniapps and Proxy Apps for Fusion/Plasma Physics and Practical Programming Studies Using Npbs
    Miniapps and Proxy Apps for Fusion/Plasma Physics and Practical Programming Studies using NPBs Alice Koniges, Jean-Luc Vay, Rebecca Yuan (LBNL) Viktor Decyk, (UCLA) Stephane Ethier and Weixing Wang (PPPL) Berkeley UPC Group FROM: Using Application Proxies for Co-design of Future HPC Computer Systems and Applications SC12 Full Day Tutorial Michael A. Heroux, Alice E. Koniges, David F. Richards, Richard F. Barrett, Thomas Brunner Fusion Mini/Proxy Apps and NPBs 1 Value of Proxy Apps BIG + small Processor EXPERIMENT (ITER) MODELING CODES COMPACTGenerator APPS SKELETON APPS (Tensilica) Base CPU OCD Application-optimized processor implementation Apps Datapaths Cache Timer Extended Registers FPU ITERATE PROGRAMMING APPLIED Apply and Benchmark MODELS MATH Fusion Mini/Proxy Apps and NPBs 2 We will study examples of Compact and Skeleton Apps Relevant to Fusion • Example Compact App: PIC Electrostatic, GTC_simple – Reduced I/O, No diagnostics, Possible reduced physics and dimensionality • Example Skeleton App: Shifter BIG small Fusion Mini/Proxy Apps and NPBs 3 Fusion Energy* is the answer to our energy future • One gallon of sea water same energy as 300 gallons gasoline • Fifty cups of water equals 2 tons of coal • Fusion power plant produces no climate changing gases • Dramatically lower radioactive bi-products than fission plants • No danger of runaway reaction or core melt down • Two major approaches: Magnetic and Inertial, each with own issues • Simulation is key to saving big $$ per discharge/shot • Extreme range of time/space scale for magnetic
    [Show full text]