The Second Order Pitch-Angle Approximation for the Cosmic Ray Fokker-Planck Kinetic Equations

The diffusive particle propagation and its pitch angle scattering is studied using kinetic equation of the Fokker Planck form. The case is considered when charged particles preferable propagate along the strong mean magnetic field direction and undergo the pitch angle scattering with respect to it. The paper deals with solution of the equation for particle distribution function in the second order approximation in the pitch angle. The exact analytical solution is obtained in an integral form. The well known solution in the first order pitch angle approximation can be restored performing the small time limit in the result. Unlike the first order solution the obtained solution in the second approximation rightly shows that the pitch angle diffusion is closely connected with the particle transport along the mean magnetic field.