By Frances Bauer
During this e-book, we record on learn in equipment of computational magneto hydrodynamics supported by means of the us division of power less than agreement EY-76-C-02-3077 with manhattan collage. The paintings has re sulted in a working laptop or computer code for mathematical research of the equilibrium and balance of a plasma in 3 dimensions with toroidal geometry yet no sym metry. The code is indexed within the ultimate bankruptcy. types of it were used for the layout of experiments on the Los Alamos clinical Laboratory and the Max Planck Institute for Plasma Physics in Garching. we're thankful to Daniel Barnes, Jeremiah Brackbill, Harold Grad, William Grossmann, Abraham Kadish, Peter Lax, Guthrie Miller, Arnulf Schliiter, and Harold Weitzner for plenty of invaluable discussions of the speculation. we're in particular indebted to Franz Herrnegger for theoretical and pedagogical reviews. Constance Engle has supplied extraordinary guidance with the typescript. We enjoy acknowledging assistance from the employees of the Courant arithmetic and Com puting Laboratory at long island collage. specifically we must always wish to convey our due to Max Goldstein, Kevin McAuliffe, Terry Moore, Toshi Nagano and Tsun Tam. Frances Bauer manhattan Octavio Betancourt September 1978 Paul Garabedian v Contents bankruptcy 1. advent 1 1. 1 formula of the matter 1 1. 2 dialogue of effects 2 bankruptcy 2. The Variational precept four four 2. 1 The Magnetostatic Equations 6 2. 2 Flux Constraints within the Plasma . 7 2. three The Ergodic Constraint .
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Extra resources for A Computational Method in Plasma Physics
This involves theoretical estimates and trial runs of the program in more complicated cases. Given the input data, the program minimizes the potential energy, and if the iteration is convergent it computes a stable equilibrium. The iteration can diverge either because there is no equilibrium or because the equilibrium is unstable. If the iteration does diverge, we must distinguish between two explanations, namely numerical instabilities and physical instabilities. The former are caused by a wrong choice of the numerical parameters and are characterized by a loss of the energy inequality bE < O.
7 of the indices NR and NZ correspond to the terms 1, sin (V), cos (V), ... , cos (3 V), respectively. This procedure is useful for the study of unstable equilibria when one wants to initialize the plasma column with a given helical excursion or when one wants to examine the properties of a specific mode. For example, it allows the variables Rand 1/1 to adjust while preserving the initial perturbation of the magnetic axis. NAC denotes the number ofthe iteration after which the acceleration scheme for the descent coefficients takes effect.
We have chosen this description for the equation of the outer wall because it includes all the cases, for which results will be presented in the next chapter. Any other expression satisfying the periodicity conditions can be used instead by making appropriate changes in· subroutines ASIN and SURF. Note that because the code has been written so as to minimize truncation errors, not only must the equations for riu, v) and Z2(U, v) be given, but also their u and v deri vati ves. Card 8 n, Po, Po, P ..
A Computational Method in Plasma Physics by Frances Bauer