Orbit-averaged guiding-center Fokker–Planck operator for numerical applications

A guiding-center Fokker–Planck operator is derived in a coordinate system that is well suited for the implementation in a numerical code. This differential operator is transformed such that it can commute with the orbit-averaging operation. Thus, in the low-collisionality approximation, a three-dime...

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Bibliographic Details
Published in:Physics of plasmas 2010-11, Vol.17 (11), p.112513-112513-12
Main Authors: Decker, J., Peysson, Y., Brizard, A. J., Duthoit, F.-X.
Format: Article
Language:English
Subjects:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
BOOTSTRAP CURRENT
CHARGED-PARTICLE TRANSPORT
CURRENTS
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
ELECTRIC CURRENTS
EQUATIONS
FOKKER-PLANCK EQUATION
FUNCTIONS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
PLASMA SIMULATION
RADIATION TRANSPORT
SIMULATION
THREE-DIMENSIONAL CALCULATIONS
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Summary:A guiding-center Fokker–Planck operator is derived in a coordinate system that is well suited for the implementation in a numerical code. This differential operator is transformed such that it can commute with the orbit-averaging operation. Thus, in the low-collisionality approximation, a three-dimensional Fokker–Planck evolution equation for the orbit-averaged distribution function in a space of invariants is obtained. This transformation is applied to a collision operator with nonuniform isotropic field particles. Explicit neoclassical collisional transport diffusion and convection coefficients are derived, and analytical expressions are obtained in the thin orbit approximation. To illustrate this formalism and validate our results, the bootstrap current is analytically calculated in the Lorentz limit.
ISSN:1070-664X
1089-7674
DOI:10.1063/1.3519514