By Frances Bauer

During this ebook, we record on learn in tools of computational magneto hydrodynamics supported by means of the us division of strength less than agreement EY-76-C-02-3077 with big apple 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 amazing advice with the typescript. We enjoy acknowledging the aid of the workers of the Courant arithmetic and Com puting Laboratory at manhattan college. specifically we should always prefer to convey our because of 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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**Example text**

Scaling constant. Perturbation amplitude. Pressure distribution exponent. Maximum pressure. Rotational transform 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

Card 16 FUX(I), 1= 1, ... 5): These are the Fourier coefficients of the initial perturbation of the flux surfaces, where the perturbation is given by b = AMP[FUX(I) cos (V) + FUX(2) cos (2U) + FUX(3) cos (3U) + FUX(4) cos (2U - V) + FUX(5) cos (3U - V) + FUX(6) cos (2[U - V]) + FUX(7) cos (3[U - V])]. If there is a vacuum region present, we initialize the free boundary function by means of the formula g(u, v) = g(u) [1 + b], where g(u) is obtained from an axially symmetric calculation. This results in a perturbation of every flux surface.

Maximum error of free boundary equation. Maximum error of vacuum equations. Increment of energy Average r coordinate of magnetic axis. Descent coefficient for free boundary equation. Total poloidal and toroidal fluxes in vacuum region. 1 Historical Development of the Code The method we present here has been developed in several stages. As a first model, we considered a sharp boundary plasma with skin current [5,6]. Our first code was applied to the problem of finding stellarator equilibria. It was also used to analyze high fJ Tokamaks of low aspect ratio.