Multi-temperature representation of electron velocity distribution functions. I. Fits to numerical results

Electron energy distribution functions are expressed as a sum of 6–12 Maxwellians or a sum of 3, but each multiplied by a finite series of generalized Laguerre polynomials. We fitted several distribution functions obtained from the finite difference Fokker-Planck code “FPI” [Matte and Virmont, Phys....

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Bibliographic Details
Published in:Physics of plasmas 2012-10, Vol.19 (10)
Main Authors: Haji Abolhassani, A. A., Matte, J.-P.
Format: Article
Language:English
Subjects:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Alternative energy sources
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COLD PLASMA
DISTRIBUTION FUNCTIONS
Electron energy distribution
ELECTRON TEMPERATURE
ELECTRONS
ENERGY SPECTRA
FINITE DIFFERENCE METHOD
FOKKER-PLANCK EQUATION
HEAT FLUX
Heat transfer
Heat transmission
LAGUERRE POLYNOMIALS
Mathematical analysis
Mathematical models
PLASMA HEATING
Plasmas
Representations
TEMPERATURE GRADIENTS
VELOCITY
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Summary:Electron energy distribution functions are expressed as a sum of 6–12 Maxwellians or a sum of 3, but each multiplied by a finite series of generalized Laguerre polynomials. We fitted several distribution functions obtained from the finite difference Fokker-Planck code “FPI” [Matte and Virmont, Phys. Rev. Lett. 49, 1936 (1982)] to these forms, by matching the moments, and showed that they can represent very well the coexistence of hot and cold populations, with a temperature ratio as high as 1000. This was performed for two types of problems: (1) the collisional relaxation of a minority hot component in a uniform plasma and (2) electron heat flow down steep temperature gradients, from a hot to a much colder plasma. We find that the multi-Maxwellian representation is particularly good if we accept complex temperatures and coefficients, and it is always better than the representation with generalized Laguerre polynomials for an equal number of moments. For the electron heat flow problem, the method was modified to also fit the first order anisotropy f1(x,v,t), again with excellent results. We conclude that this multi-Maxwellian representation can provide a viable alternative to the finite difference speed or energy grid in kinetic codes.
ISSN:1070-664X
1089-7674
DOI:10.1063/1.4754004