Finite element solution of the Fokker-Planck equation in electrostatic magnetic mirror fusion machines
A perturbation method is developed to find solutions of sloshing ion distributions. This method uses an expansion in the ratio of electrostatic potential to average ion energy to simplify the bounce-averaged Fokker-Planck equation. Finite element techniques, which provide rapid numerical solutions for parametric studies of sloshing ions, are used to derive the zeroth-order angular and velocity equations. The first-order two-dimensional equation was also expanded into finite element ''hat functions''. Application of Galerkin's method gives a linear system of equations where all matrix and source elements are calculated analytically. The density ratio and the potential profiles as functions of axial distance are computed. There is excellent agreement with results from the Lawrence Livermore National Laboratory bounce-averaged Fokker-Planck code with as much as 500 times and 50 times less Cray-1 computer time for the zeroth- and the first-order solutions, respectively.
- Research Organization:
- University of Illinois, Nuclear Engineering Program, Fusion Studies Laboratory, Urbana, IL 61801
- OSTI ID:
- 6138400
- Journal Information:
- Nucl. Sci. Eng.; (United States), Vol. 92:1
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
FOKKER-PLANCK EQUATION
COMPUTER CALCULATIONS
NUMERICAL SOLUTION
MAGNETIC MIRRORS
PLASMA CONFINEMENT
PLASMA MICROINSTABILITIES
CRAY COMPUTERS
ELECTROSTATICS
FINITE ELEMENT METHOD
GALERKIN-PETROV METHOD
IONS
LAWRENCE LIVERMORE LABORATORY
MATRICES
PERTURBATION THEORY
SUPERCOMPUTERS
CHARGED PARTICLES
COMPUTERS
CONFINEMENT
DIFFERENTIAL EQUATIONS
DIGITAL COMPUTERS
EQUATIONS
INSTABILITY
ITERATIVE METHODS
NATIONAL ORGANIZATIONS
OPEN PLASMA DEVICES
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA INSTABILITY
THERMONUCLEAR DEVICES
US AEC
US DOE
US ERDA
US ORGANIZATIONS
700107* - Fusion Energy- Plasma Research- Instabilities
700101 - Fusion Energy- Plasma Research- Confinement
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