An alternative expression for ad hoc field collision model

An alternative form of ad hoc collision model to the Fokker–Planck field collision operator is proposed. The model is so constructed that the results of exact Fokker–Planck field collision, applied to the low-order Legendre and associated Laguerre polynomials, are used to impose self-adjointness first and then collisional conservation laws. The model is shown to be actually identical to the conventional ad hoc model in the l = 0 and 1 parts in Legendre polynomial expansion in an isothermal case, while it is not limited to extend to the higher order, in contrast to the conventional ad hoc model, in which the collisional conservation laws are imposed primarily, using the exact test collision form of the Fokker–Planck operator. Furthermore, it is discussed that the proposed model is identified to the lowest order in an expansion of formal Hirshman–Sigmar operator, while there is a difference between the formal and conventional Hirshman–Sigmar operators. Numerical examples demonstrate that the proposed model can yield comparable results to those by the exact Fokker–Planck and conventional Hirshman–Sigmar operators.