DOCSLIB.ORG

High-Order Finite Element Method for Plasma Modeling*

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read 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. (1) and of f , which gives the multi-fluid plasma model. and ion sound speeds, and the speed of light. A general model s for atomic reactions has been developed and is incorporated in [1] the multi-fluid plasma model. The multi-fluid plasma algorithm The principal variables for each species of the multi- is implemented in a flexible code framework (WARPX) that fluid plasma model are derived by computing moments of the allows easy extension of the physical model to include multiple distribution functions. fluids and additional physics. The code runs on multi-processor Z machines and is being adapted with OpenCL to many-core ρ =m f (v)dv (2) systems, characteristic of the next generation of high performance s s s computers. The algorithm is applicable to study advanced physics Z calculations of plasma dynamics including magnetic plasma con- ρsus =ms vfs(v)dv (3) finement and astrophysical plasmas. The discontinuous Galerkin Z method has also been applied to solve the Vlasov-Poisson kinetic P =m wwf (v)dv (4) model. Recently, a blended finite element algorithm has been s s s developed and implemented which exploits the expected physical Z behavior to apply either a discontinuous or continuous finite Hs =ms wwwfs(v)dv (5) element representation, which improves computational efficiency without sacrificing accuracy. The 5M model directly evolves the variables given by Eqs. (2,3) and the tensor contraction of Eq. (4), Z I. INTRODUCTION 1 2 ps = ρsTs = ms w fs(v)dv; (6) Owing to the complexity of plasma phenomena, a thorough 3 understanding requires validated physical models, verified where Ts is the temperature. The 13M model [2] directly computational simulations, and well-diagnosed experiments. evolves the variables given by Eqs. (2,3,4), and the tensor This paper focuses on developing computational methods for contraction of Eq. (5), plasma models with sufficient physical and numerical fidelity 1 Z to generate insight and predictability. h = m w2wf (v)dv (7) s 2 s s II. CONTINUUM PLASMA MODELS The system of moment equations is truncated, retaining only variables with a physical meaning. Higher moment variables Discrete models that account for each constituent particle that appear in the evolution equation are related to lower are not particularly useful for the numerical treatment of realis- moment variables. tic plasmas where the number of particles (N) and the number of interactions (> N 2) are not computationally tractable. The multiple fluids are coupled to each other and to the Instead an ensemble average is performed to give a statistical electromagnetic fields through Maxwell’s equations and inter- action source terms, such as the Lorentz force. Including elastic *This work is supported by a grant from the U.S. Air Force Office of scattering and reacting collisions (e.g. ionization, recombina- Scientific Research. tion, charge exchange) introduces additional source terms that TABLE I. TYPICAL TIME SCALES (IN SECONDS) FOR LABORATORY AND IONOSPHERIC PLASMAS SHOWING THE LARGE SEPARATION. Laboratory FRC Ionosphere F Region −14 −8 1=!pe 5 × 10 6 × 10 L=c 3 × 10−9 7 × 10−2 −8 −3 1=!ci 10 4 × 10 −5 1 L=vA 10 3 × 10 −5 4 L=vT i 4 × 10 10 −3 5 τeq 10 10 couple the fluids. For example, the governing equations for the electron fluid for an interacting three-fluid model (electron, ion, Fig. 1. Schematic representation of a discontinuous, high-order solution neutral) is given by within each element Ω having continuous fluxes. @ρ e + r · (ρ u ) = m Γion − m Γrec (8) @t e e e i e n benefit from high-order accuracy. The general approach of @ρeue ie en FE methods expands the solution vector using a set of basis + r · (ρeueue + peI + Πe) = −Ri + Re functions, vk(r). @t (9) ρee ion rec X − (E + ue × B) + meunΓi − meueΓn q(r) = qkvk(r) (13) me @" k e + r · (((" + p ) I + Π ) · u + h ) = Qie + Qen @t e e e e e e e The governing equation is then projected onto test functions using a Galerkin method as rec me ion ρee ie en −Qe + Qn − ue · E + Ri − Re Z Z Z mn me @q vk dV + vkr · FdV = vkSdV (14) 1 2 rec 1 2 ion Ω @t Ω Ω − meve Γn + mevn − φion Γi 2 2 where an integral equation is generated for each basis (test) (10) function. Integrating by parts and applying the divergence where the source and sink rates are computed by the appro- theorem gives priate convolution integrals, such as the ion source rate from Z @q I Z Z electron impact ionization with neutrals vk dV + vkF·dS− F·rvkdV = vkSdV (15) Ω @t @Ω Ω Ω Z Z Γion = f (v0) f (v)σ (jv − v0j) jv − v0j dvdv0: This equation is valid in general but is inconvenient for realistic i n e ion domains with complicated geometries. Instead, the domain is (11) divided into finite elements, and the integral equation is applied See Ref. [3] for the details of the 5M multi-fluid plasma model. to each element with some assumption of continuity at the Additional moment models can be found in Refs. [4]–[7]. element boundaries. The governing equations for the 5M or 13M model can be If the solution is assumed to be continuous (C0), the fluxes expressed in balance law form as are automatically continuous, and the result is the usual finite element method. During assembly of the global system for the @ Ω q + r · F = S; (12) simultaneous solution for all qk , the surface integral term in @t Eq. (15) cancels everywhere except at the domain boundaries. where q is the vector of conserved variables, F is the flux Volume integrals are evaluated by quadrature. The continuous tensor, and S is vector of source terms. Combining the fluid FE method works well for many elliptic and parabolic systems eigenvalues computed from the flux Jacobian (@F =@Q) with on complicated geometries; however, spurious oscillations can the characteristics of Maxwell’s equations and of the source occur at discontinuities (shocks) for hyperbolic systems, which terms provides the characteristic speeds and frequencies, and means the method is not suitable for many plasma simulations. thereby the time scales given by the plasma model. Table I shows typical values for a laboratory FRC plasma and an If the solution is allowed to be discontinuous, but with ionospheric plasma in the F region. The large separation of the continuous fluxes, which is the only feature required by the physical time scales makes the equation system mathematically conservation law, the resulting finite element system is the stiff, which can complicate an accurate numerical solution. discontinuous Galerkin (DG) method. [8], [9] See Fig. 1 for a schematic representation of the DG method. Fluxes in the surface integral term in Eq. (15) are evaluated using an upwind III. FINITE ELEMENT METHODS method such as an approximate Riemann solver [4], [10] with Finite element (FE) methods offer high-order spatial accu- solution values on either side of the interface. racy in an unsplit approach that tightly couples the flux and 1 1 X F = F+ + F− − l q+ − q− jλ j r (16) source terms in Eq. (12). High-order accurate FE methods are @Ω 2 2 k k k appropriate for problems that have strong anisotropies, com- k plicated geometries, or stiff governing equations. Magnetized Limiting is accomplished by locally reducing the expansion plasma simulations of realistic devices using the continuum order. Time is advanced using a Runge-Kutta method, for kinetic or the multi-fluid plasma models are examples that example the third-order, TVD method. [11] of 106. The effect has been investigated using a high-order finite element method to solve the anisotropic heat conduction equation. @T + r · (−D · rT ) = 0 (18) @t where D = Djj(x; y; z) + D?(x; y; z). The problem is ini- tialized in 3D with a Gaussian temperature profile aligned with a toroidal magnetic field.
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]
  • 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]
  • Hybrid Simulation of Low Temperature Plasmas: a Brief Tutorial
    Tutorial Hybrid Simulation of Low Temperature Plasmas: A Brief Tutorial Demetre J. Economou* Modeling and simulation of low temperature plasmas is widely accepted as a useful tool from both physics and plasma reactor design points of view. Of the modeling approaches, hybrid models strive to combine the predictability of kinetic models with the lower computational burden of fluid models. This paper presents a brief tutorial of hybrid plasma modeling and representa- tive simulation results using hybrid models. When- ever possible, these results are compared to kinetic and/or fluid simulations as well as experimental data. 1. Introduction One of the main challenges of LTP modeling and simulation is the disparity in length and time scales Plasma modeling and simulation has emerged as an (Figure 1). Length scales range from atomic (A˚ , crystal indispensable activity in low temperature plasma (LTP) lattice), to microscopic (nm to mm, feature size), to science and engineering. It is most impactful when mesoscopic (mm, sheath, cluster of features), to macro- supported by experimental plasma diagnostics. Plasma scopic (m, reactor, wafer). The range of time scales is also modeling and simulation can be useful for: (a) unravelling extremely wide, from ps for the collision cascade during new physics (and chemistry); (b) providing insights into ion-surface interaction, to ns response time of electrons plasma and reactor behavior; (c) explaining experimental (inverse of plasma frequency), to ms response time of data and/or suggesting new experiments; (d) performing ions, to 10–100 s ms for heavy species chemistry and gas ‘‘computer experiments’’ to predict physical quantities that residence time, to minutes for the duration of etching or are difficult to measure; (e) providing a platform for the deposition processes.
    [Show full text]