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W e propose an adaptive mesh method for the numerical solution of differential equations which causes the mesh lines to move closer together in regions where higher resolution in some physical quantity T is desired. coefficient D>O i s introduced into the equipotential zoning equations, where D depends on the gradient of T. The equations are inverted, leading to nonlinear elliptic equations for the mesh coordinates with source terms which depend on the gradient o f D. A A functional form of D is proposed.

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A multi-group diffusion method is derived for the slowing down and spatial transport of energetic positive ions in a hot plasma. A diffusion coefficient which is “flux-limited” is used to provide better accuracy when slowing-down is dominated by Coulomb collisions with electrons and the mean free path is long. This results in a fast, flexible, small-memory computer program for calculating the behaviour of energetic charged particles. Calculated results are presented for 3.5-MeV alpha-particles slowing down in a 50-keV deuterium-tritium plasma of uniform density. Various spatial distributions of the alpha-particle source were tested in spherical geometry and compared with the results of suitable Monte-Carlo calculations. Generally, fair to good agreement was obtained for the energy deposition in space and time with as few as ten energy groups, and good to excellent agreement was obtained with 100 groups. It was found that the multi-group method using 100 groups was appreciably faster than the Monte-Carlo method, while for only 10 groups it was at least an order of magnitude faster. This method is expected to give good results for temperature, density, and charged-particle source distributions which are typical of laser fusion reactors, and may also be applicable to certain astrophysical problems.

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