Computational Methods For Collisional Plasma Physics

Modeling the high density, high temperature plasmas produced by intense laser or particle beams requires accurate simulation of a large range of plasma collisionality. Current simulation algorithms accurately and efficiently model collisionless and collision-dominated plasmas. The important parameter regime between these extremes, semi-collisional plasmas, has been inadequately addressed to date. LLNL efforts to understand and harness high energy-density physics phenomena for stockpile stewardship require accurate simulation of such plasmas. We have made significant progress towards our goal: building a new modeling capability to accurately simulate the full range of collisional plasma physics phenomena. Our project has developed a computer model using a two-pronged approach that involves a new adaptive-resolution, ''smart'' particle-in-cell algorithm: complex particle kinetics (CPK); and developing a robust 3D massively parallel plasma production code Z3 with collisional extensions. Our new CPK algorithms expand the function of point particles in traditional plasma PIC models by including finite size and internal dynamics. This project has enhanced LLNL's competency in computational plasma physics and contributed to LLNL's expertise and forefront position in plasma modeling. The computational models developed will be applied to plasma problems of interest to LLNL's stockpile stewardship mission. Such problems include semi-collisional behavior in hohlraums, high-energy-density physics experiments, and the physics of high altitude nuclear explosions (HANE). Over the course of this LDRD project, the world's largest fully electromagnetic PIC calculation was run, enabled by the adaptation of Z3 to the Advanced Simulation and Computing (ASCI) White system. This milestone calculation simulated an entire laser illumination speckle, brought new realism to laser-plasma interaction simulations, and was directly applicable to laser target physics. For the first time, magnetic fields driven by Raman scatter have been observed. Also, Raman rescatter was observed in 2D. This code and its increased suite of dedicated diagnostics are now playing a key role in studies of short-pulse, high-intensity laser matter interactions. In addition, a momentum-conserving electron collision algorithm was incorporated into Z3. Finally, Z3's portability across diverse MPP platforms enabled it to serve the LLNL computing community as a tool for effectively utilizing new machines.

Assuming no prior knowledge of plasma physics or numerical methods, Computational Methods in Plasma Physics covers the computational mathematics and techniques needed to simulate magnetically confined plasmas in modern magnetic fusion experiments and future magnetic fusion reactors. Largely self-contained, the text presents the basic concepts neces

Because magnetically confined plasmas are generally not found in a state of thermodynamic equilibrium, they have been studied extensively with methods of applied kinetic theory. In closed magnetic field line confinement devices such as the tokamak, non-Maxwellian distortions usually occur as a result of auxiliary heating and transport. In magnetic mirror configurations even the intended steady state plasma is far from local thermodynamic equilibrium because of losses along open magnetic field lines. In both of these major fusion devices, kinetic models based on the Boltzmann equation with Fokker-Planck collision terms have been successful in representing plasma behavior. The heating of plasmas by energetic neutral beams or microwaves, the production and thermalization of a-particles in thermonuclear reactor plasmas, the study of runaway electrons in tokamaks, and the performance of two-energy compo nent fusion reactors are some examples of processes in which the solution of kinetic equations is appropriate and, moreover, generally necessary for an understanding of the plasma dynamics. Ultimately, the problem is to solve a nonlinear partial differential equation for the distribution function of each charged plasma species in terms of six phase space variables and time. The dimensionality of the problem may be reduced through imposing certain symmetry conditions. For example, fewer spatial dimensions are needed if either the magnetic field is taken to be uniform or the magnetic field inhomogeneity enters principally through its variation along the direction of the field.

The physics of plasmas is an extremely rich and complex subject as the variety of topics addressed in this book demonstrates. This richness and complexity demands new and powerful techniques for investigating plasma physics. An outgrowth from his graduate course teaching, now with corrections, Tajima's text provides not only a lucid introduction to computational plasma physics, but also offers the reader many examples of the way numerical modeling, properly handled, can provide valuable physical understanding of the nonlinear aspects so often encountered in both laboratory and astrophysical plasmas. Included here are computational methods for modern nonlinear physics as applied to hydrodynamic turbulence, solitons, fast reconnection of magnetic fields, anomalous transports, dynamics of the sun, and more. The text contains examples of problems now solved using computational techniques including those concerning finite-size particles, spectral techniques, implicit differencing, gyrokinetic approaches, and particle simulation.

In this book, we report on research in methods of computational magneto hydrodynamics supported by the United States Department of Energy under Contract EY-76-C-02-3077 with New York University. The work has re sulted in a computer code for mathematical analysis of the equilibrium and stability of a plasma in three dimensions with toroidal geometry but no sym metry. The code is listed in the final chapter. Versions of it have been used for the design of experiments at the Los Alamos Scientific Laboratory and the Max Planck Institute for Plasma Physics in Garching. We are grateful to Daniel Barnes, Jeremiah Brackbill, Harold Grad, William Grossmann, Abraham Kadish, Peter Lax, Guthrie Miller, Arnulf Schliiter, and Harold Weitzner for many useful discussions of the theory. We are especially indebted to Franz Herrnegger for theoretical and pedagogical comments. Constance Engle has provided outstanding assistance with the typescript. We take pleasure in acknowledging the help of the staff of the Courant Mathematics and Com puting Laboratory at New York University. In particular we should like to express our thanks to Max Goldstein, Kevin McAuliffe, Terry Moore, Toshi Nagano and Tsun Tam. Frances Bauer New York Octavio Betancourt September 1978 Paul Garabedian v Contents Chapter 1. Introduction 1 1. 1 Formulation of the Problem 1 1. 2 Discussion of Results 2 Chapter 2. The Variational Principle 4 4 2. 1 The Magnetostatic Equations 6 2. 2 Flux Constraints in the Plasma . 7 2. 3 The Ergodic Constraint.

The collision of electrons with molecules and molecular ions is a fundamental pro cess in atomic and molecular physics and in chemistry. At high incident electron en ergies, electron-molecule collisions are used to deduce molecular geometries, oscillator strengths for optically allowed transitions, and in the case of electron-impact ionization, to probe the momentum distribution of the molecule itself. When the incident electron energy is comparable to or below those of the molecular valence electrons, the physics involved is particularly rich. Correlation and exchange effects necessary to describe such collision processes bear a close resemblance to similar efft:cts in the theory of electronic structure in molecules. Compound state formations, in the form of resonances and vir tual states, manifest themselves in experimental observables which provide details of the electron-molecule interactions. Ro-vibrational excitations by low-energy electron collisions exemplify energy transfer between the electronic and nuclear motion. The role of nonadiabatic interaction is raised here. When the final vibrational state is in the continuum, molecular dissociation occurs. Dissociative recombination and dissociative attachment are examples of such fragmentation processes. In addition to its fundamental nature, the study of electron-molecule collisions is also motivated by its relation to other fields of study and by its technological appli cations. The study of planetary atmospheres and the interstellar medium necessarily involve collision processes of electrons with molecules and molecular ions.

This volume, which contains 15 contributions, is based on a minicourse held at the 1987 IEEE Plasma Science Meeting. The purpose of the lectures in the course was to acquaint the students with the multidisciplinary nature of computational techniques and the breadth of research areas in plasma science in which computation can address important physics and engineering design issues. These involve: electric and magnetic fields, MHD equations, chemistry, radiation, ionization etc. The contents of the contributions, written subsequent to the minicourse, stress important aspects of computer applications. They are: 1) the numerical methods used; 2) the range of applicability; 3) how the methods are actually employed in research and in the design of devices; and, as a compendium, 4) the multiplicity of approaches possible for any one problem. The materials in this book are organized by both subject and applications which display some of the richness in computational plasma physics.

"The physics of plasmas is an extremely rich and complex subject as the variety of topics addressed in this book demonstrates. This richness and complexity demands new and powerful techniques for investigating plasma physics. An outgrowth from his graduate course teaching, now with corrections, Tajima's text provides not only a lucid introduction to computational plasma physics, but also offers the reader many examples of the way numerical modeling, properly handled, can provide valuable physical understanding of the nonlinear aspects so often encountered in both laboratory and astrophysical plasmas. Included here are computational methods for modern nonlinear physics as applied to hydrodynamic turbulence, solitons, fast reconnection of magnetic fields, anomalous transports, dynamics of the sun, and more. The text contains examples of problems now solved using computational techniques including those concerning finite-size particles, spectral techniques, implicit differencing, gyrokinetic approaches, and particle simulation."--Provided by publisher.