The Fokker-Planck equation for charged particles moving in random electromagnetic fields

The derivation of the Fokker-Planck equation is based on the Liouville equation to provide a description of the motion of charged particles in a random electromagnetic field which is valid for all pitch angles. The validity of the Markovian assumptions are assessed, demonstrating that the turbulent magnetic fields must be sufficiently small to develop a meaningful Fokker-Planck solution. The magnitude of the fields are quantified in terms of cosmic-ray particles that are moving in a static turbulent magnetic field superimposed on a uniform background magnetic field. Two forms of the equation are found, one of which is useful in the calculation of cosmic-ray diffusion coefficients although it cannot be applied to pitches near 90 degrees. (C.C.S.)