Spectral Formulation Of The Fokker-Planck-Landau Operator With Velocity Dependent Coulomb Logarithm

In collisional plasmas, the collective effect of small angle, grazing collisions allows the Boltzmann collision operator to be approximated by the Landau or Landau-Fokker-Planck operator [1] . While this approximation is typically performed in terms of a fixed small angle cutoff in the collision cross section, an analysis of the two-body interaction shows that this angular cutoff should in fact be velocity dependent. We perform the grazing collision limit in Fourier space and derive a new, modified Landau collision operator with a velocity dependent Coulomb logarithm. The new operator provides a different relaxation rate to equilibrium, in particular changing the rate at which the bulk and tail relax to equilibrium. Furthermore, the improved velocity dependent CL can be incorporated into many other existing simulation tools without considerably more effort [2] , [3] . We present numerical results showing the effect of this velocity dependence by comparing relaxation to equilibrium using the Boltzmann operator, a Landau operator with velocity dependent $C_L$ , and the classical Landau operator with a constant $C_L$ .