On the particle number conservation inherent in the diffusion approach of the Fokker-Planck equation

Starting from the Fokker-Planck equation we show that, in a strict sense, the usual diffusive transport of charged particles in weak magnetic field fluctuations is not valid until the space-integrated number of particles per velocity interval has reached its final overall constant value and is conserved. Large anisotropies are thus not compatible with diffusion. Diffusion becomes exactly valid after an infinite time, but has reached a good approximation to the real transport before that. The particle-number conservation holds for quite general mean magnetic field configurations, and is not limited to the case of a constant mean field.