Some diffusion equations in plasma physics

Unstable diffusion equations of the form partial/subt/-partial/subx/D (x) partial/subx/ f (x,t) =γ (x) f (x,t) are studied. In the absence of the dissipation function γ (x), the Green's function of the equation when Dapprox. =x-/subn/ (n is an even integer) is derived. Considering the propagation of unstable modes, the overall growth rate of the distribution of the modes, when γ (x) is a sharply peaked function, is evaluated. The three-dimensional propagation of unstable modes for the case D=C/subt//sube/ are also considered. It is shown that the diffusion may suppress the instability of the modes