Moment expansions and the neoclassical approximation for a model kinetic equation

A simple, model kinetic equation proposed by D. Pfirsch is solved by moment expansions techniques and the results are examined for convergence and compared with the neoclassical approximate solution. The model equation v ∂f/∂x + E sin x ∂f/∂v = ν ∂/∂v {∂f/∂v + (v-ud)f} involves the three parameters ν, where 1/ν is the collisionality of the system, ud is the mean velocity to which the system is driven, and E, the perturbing potential. The domain of interest is one in which E, ud, and ν are all small. Limitations and domains of utility of various approximations are compared with the numerical results. It is clear that the origin in (E, ud, ν) space is a highly singular point, and properties of the solution near the origin depend on the path of approach to the origin