The application of an invariant method for the solution of the Vlasov equation at a plasma edge

Erich Pohn, M. Shoucri, Gerald Kamelander

Research output: Chapter in Book or Conference ProceedingsConference Proceedings with Oral Presentationpeer-review

Abstract

A new computer time saving method is presented for the calculation of the charge Separation and electric field at a plasma edge. This problem has been recently presented in one spatial dimension using an adiabatic equation for the electrons, and a kinetic Vlasov equation for the ions, with three velocity dimensions (M. Shoucri et al., Proceedings of the 2 EPS Conference, Maastricht (1998)). These equations were solved using a method of fractional steps for the solution of the, kinetic equation (M. Shoucri. R. Gagné, J. Comp. Phys. 27, 315 (1978)). Extending these results to two spatial dimensions requires extending the phase-space dimensionality of the ions Vlasov equation from four to five. Also, including a kinetic equation for the electrons will make the computation lengthy and expensive, due to the important, ratio of masses between electrons and ions. This problem, however, can be tackled if we take advantage of exact invariants of the solution present in the Vlasov equation. Expressing the distribution function in terms of the invariant allows to reduce the dimensionality, of the phase-space of the Valsov equation, and makes the solution possible with a reasonable computational power. We apply this method of invariant for the previously presented 1D solution. We are able to reproduce exactly the same results with a gain of a factor of 10 in the computation time. The method is next extended for the 2D problem, in which the ions are treated with a fully kinetic equation, and a drift kinetic equation is used for the magnetized electrons. Preliminary results from the 2D code do confirm the existence of the 1D solution previously presented.
Original languageEnglish
Title of host publicationConference on Controlled Fusion and Plasma Physics 27th European Physical Society Conference on Controlled Fusion and Plasma Physics
Pages109
Number of pages1
Publication statusPublished - 2000
EventConference on Controlled Fusion and Plasma Physics -
Duration: 1 Jan 2000 → …

Conference

ConferenceConference on Controlled Fusion and Plasma Physics
Period1/01/00 → …

Research Field

  • Biosensor Technologies

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