A numerical investigation of extending diffusion theory codes to solve the generalized diffusion equation in the edge pedestal
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Floyd, John-Patrick, II
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Abstract
The presence of a large pinch velocity in the edge pedestal of high confinement
(H-mode) tokamak plasmas implies that particle transport in the plasma edge must be
treated by a pinch-diffusion theory, rather than a pure diffusion theory. Momentum
balance also requires the inclusion of a pinch term in descriptions of edge particle
transport. A numerical investigation of solving generalized pinch-diffusion theory using
methods extended from the numerical solution methodology of pure diffusion theory has
been carried out. The generalized diffusion equation has been numerically integrated
using the central finite-difference approximation for the diffusion term and three finite
difference approximations of the pinch term, and then solved using Gauss reduction. The
pinch-diffusion relation for the radial particle flux was solved directly and used as a
benchmark for the finite-difference algorithm solutions to the generalized diffusion
equation. Both equations are solved using several mesh spacings, and it is found that a
finer mesh spacing will be required in the edge pedestal, where the inward pinch velocity
is large in H-mode plasmas, than is necessary for similar accuracy further inward where
the pinch velocity diminishes. An expression for the numerical error of various finite-differencing
algorithms is presented.
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Date
2011-04-05
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