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

• 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
• ISSN: 1070-664X; 1089-7674
• DOI: 10.1063/1.4754004

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.