By Frances Bauer
During this ebook, we record on examine in equipment of computational magneto hydrodynamics supported by means of the USA 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. 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 invaluable discussions of the speculation. we're in particular indebted to Franz Herrnegger for theoretical and pedagogical reviews. Constance Engle has supplied amazing information with the typescript. We enjoy acknowledging the aid of the workers of the Courant arithmetic and Com puting Laboratory at long island college. particularly we must always prefer to exhibit our because of 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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Additional info for A Computational Method in Plasma Physics
Of the artificial time equations has a large imaginary part that makes the energy and the residuals oscillate as functions of t. 4. In addition to the energy itself, there are several other physical and geometric quantities that we use to analyze the solution. The most important are the Fourier coefficients of R, ro, zo, and g, which determine the plasma displacements as functions of t, and the Jacobian D of the coordinate transformation as well as the residuals in the equations, which measure the magnetostatic forces.
For the latter, the number of mesh points in the u direction is most important. Only high f3 cases are found to be unstable by the code for the kind of mesh sizes we are able to use. The accuracy of the equilibrium computation can be checked by considering various exact solutions and seeing how well the code reproduces them. This has been done for several different versions of the screw pinch, and the results are satisfactory. Axially symmetric solution: To validate the implementation of toroidal effects in the code, we have made a comparison with a family of exact solutions in the axially symmetric case.
1t should be decreased until the energy inequality is recovered. 42 4 Description of the Computer Code The best way to find the right time step is to make a short run of about 100 iterations with small descent coefficients ei = 1. In this case, the equations are not dissipative, and if the Courant-Friedrichs-Lewy criterion is satisfied, the residuals should oscillate without growing exponentially. We should not expect the iterations to converge nor the eneJ;gy inequality to be satisfied because we have not provided adequate descent.
A Computational Method in Plasma Physics by Frances Bauer