Fast ions scattering in a fixed background of electrons. The kinetic
equation for the ions is
where vt2=Te/mi. Treat only the one-dimensional case.
Chapman Engskog procedure gives a fluid equation
for this system in the limit . The zeroth- and
first-order distributions are
The resulting fluid equation is a simple diffusion equation
There is only one fluid equation since the collision operator only conserves density. This simple diffusion equation also has an analytic solution in terms of Green's functions.
Scheme involves solving eqs. (4) and (7)
simultaneously. Number conservation for the combined system gives
and transfer is implemented with