NIM for Fokker-Planck equation applied to electrostatically confined plasmas

Conference · Fri Jan 01 04:00:00 EST 1993 · Transactions of the American Nuclear Society; (United States)

OSTI ID:5926223

McArdle, K R ^[1]

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1. Univ. of Virginia, Charlottesville (United States)

The Fokker-Planck equation is important in the kinetic theory of plasmas because it is used extensively to model the trapping of charged particles in magnetic mirrors and tokamaks. Standard finite difference numerical methods already exist that can compute the loss rates for multispecies linear and nonlinear models; however, these calculations are more difficult for smaller particle leakage (i.e., problems with larger magnetic mirror ratios R, defined as the ratio of the B-field at the end of the mirror to the B-field at the midplane). Approximate analytic estimates for the loss rates, accurate in the limit of large mirror ratios, exist via the Pastukov analytic method 4 but the accuracy is fixed and <20% (Ref. 5) for problems of interest to fusion. A nodal integral method (NIM) has been developed for the steady-state, space-independent Fokker-Planck equation and is now applied to electrostatic trapping of particles in a magnetic mirror. This paper shows that the NIM is superior to the finite difference method (FDM) for problems with less particle leakage and also in the calculation of the energy leakage. Electrostatic trapping, a difficult problem because the formulation becomes singular in the limit of complete trapping (zero leakage), is not as difficult for the NIM because the NIM gives exact one-dimensional solutions in such cases as zero leakage (a normalization constraint is required).

• OSTI ID: 5926223
• Report Number(s): CONF-930601--
• Conference Information: Journal Name: Transactions of the American Nuclear Society; (United States) Journal Volume: 68
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700300* -- Plasma Physics &amp; Fusion Research-- (1992-)
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics &amp; Computers
CALCULATION METHODS
COMPUTERIZED SIMULATION
CONFINEMENT
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE DIFFERENCE METHOD
FINITE ELEMENT METHOD
FOKKER-PLANCK EQUATION
ITERATIVE METHODS
KINETIC EQUATIONS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA CONFINEMENT
RADIATION TRANSPORT
SIMULATION