Transport of energetic particles in turbulent space plasmas: pitch-angle scattering, telegraph, and diffusion equations - Shalchi, Andreas (Frontiers in Astronomy and Space Sciences, 2024)
In the current article we revisit the pitch-angle scattering equation describing the propagation of energetic particles through a magnetized plasma. In this case particles such as solar energetic particles and cosmic rays interact with magnetohydrodynamic turbulence and experience stochastic changes of the pitch-angle. Since this happens over and extended period of time, a pitch-angle isotropization process occurs leading to parallel spatial diffusion. This process is described well by the pitch-angle scattering equation. However, the latter equation is difficult to solve analytically even if special cases for the scattering coefficient are considered. In the past a so-called subspace approximation was proposed which has important applications in the theory of perpendicular diffusion. Alternatively, an approach based on the telegraph equation (also known as telegrapher's equation) has been developed. We show that the two-dimensional subspace approximation and the description based on the telegraph equation are equivalent. However, it is also shown that the obtained distribution functions contain artifacts and inaccuracies which cannot be found in the numerical solution to the problem. Therefore, an N-dimensional subspace approximation is proposed corresponding to a semi-analytical/semi-numerical approach. This is a useful alternative compared to standard numerical solvers. Depending on the application, the N-dimensional subspace approximation can be orders of magnitude faster. Furthermore, the method can easily be modified so that it can be used for any pitch-angle scattering equation.