RECURRENT FORMULAS OBTAINED FROM BOLTZMANN EQUATION DISTRIBUTION FUNCTION EXPANSION OVER SPHERICAL HARMONICS

I.A. Litvinenko, Yu.I. Matveenко
VANT. Ser.: Mat. Mod. Fiz. Proc 1993. Вып.2. С. 30-35.

      The approximate solution of Boltzmann equation (in electromagnetic fields) widely uses electron or ion distribution function expansion over spherical harmonics. The higher expansion terms should be accounted when the requirement E/N* > l0³Td is met (where 1 Td =10^-21 Vm²). To find the distribution function within the accuracy of N order a system consisting of (N + 1)² heterogeneous differential equations is solved for (N + 1)² unknown expansion coefficients. This paper presents the derivation of recurrent formulas of reconstruct the differential system.
      A system consisting of 36 equations is written to find the distribution function within the accuracy of fifth order terns.