By Frances Bauer
During this booklet, we record on learn in equipment of computational magneto hydrodynamics supported by means of the us division of power lower than agreement EY-76-C-02-3077 with ny college. 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. models 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 lots of worthy discussions of the speculation. we're specifically indebted to Franz Herrnegger for theoretical and pedagogical reviews. Constance Engle has supplied extraordinary assistance with the typescript. We enjoy acknowledging assistance from the employees of the Courant arithmetic and Com puting Laboratory at big apple college. particularly we should always prefer to convey our due to Max Goldstein, Kevin McAuliffe, Terry Moore, Toshi Nagano and Tsun Tam. Frances Bauer ny Octavio Betancourt September 1978 Paul Garabedian v Contents bankruptcy 1. creation 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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Additional resources for A Computational Method in Plasma Physics
Time step. O:S; Numbers of mesh points in the s, u, and v directions in plasma region. Axially symmetric error criterion. Three-dimensional error criterion. e4 F~,Fj AXIS ERR RO ERR PSI ERR BOO ERR VAC ERR DEL ENER RMA CONS ZMA CONS NRAl NRA2 NZAl NZA2 MKl MK2 MK3 MK4 32 32 32 32 32 32 32 34 36 36 36 36 36 36 36 36 Mathematical Symbol 30 30 Card No. 5 Format 1 :::;; 1:::;; 1:::;; 1:::;; 00:::;; 00:::;; 00:::;; 00:::;; NRAl :::;; 7 NRA2:::;; 7 NZAl :::;; 7 NZA2:::;; 7 MKl :::;; 33 MK2:::;; 33 MK3:::;; 33 MK4:::;; 33 0< e4 Range Plot parameter for Plot parameter for Plot parameter for Plot parameter for Plot parameter for Plot parameter for Plot parameter for Plot parameter for Fourier coefficients.
Fourier coefficients of outer wall. Fourier coefficients of outer wall. Inverse major radius. Plasma-to-wall radius ratio. If e > 0, number of periodic sections; if length. Run identification number. 3 315 0< Tv 0 The difficulties stemming from the nonlinearity and nonstandard type of the magnetostatic equations in three-dimensional space are too ~reat to allow for a rigorous mathematical proof. 8 Iterative Schemes for Elliptic Equations A simple and powerful tool for analyzing iterative schemes for elliptic partial differential equations is their interpretation as discrete approximations of time-dependent equations. Thus by writing down appropriate artificially time-dependent equations we can arrive at a variety of iterative schemes of practical interest.
A Computational Method in Plasma Physics by Frances Bauer
The difficulties stemming from the nonlinearity and nonstandard type of the magnetostatic equations in three-dimensional space are too ~reat to allow for a rigorous mathematical proof. 8 Iterative Schemes for Elliptic Equations A simple and powerful tool for analyzing iterative schemes for elliptic partial differential equations is their interpretation as discrete approximations of time-dependent equations. Thus by writing down appropriate artificially time-dependent equations we can arrive at a variety of iterative schemes of practical interest.