Weak turbulence and quasilinear diffusion for relativistic wave-particle interactions using Markov theory

Quasilinear diffusion theory forms the basis of much of the modelling and interpretation of particle transport and energisation due to interactions with electromagnetic waves in many space plasma physics environments. We present a derivation and discussion of weak turbulence and quasilinear theories for relativistic particle dynamics in both pitch-angle and energy space, due to interactions with field-aligned electromagnetic waves in a uniform background magnetic field. We use a Markovian approach that starts from the consideration of single particle motion in a prescribed electromagnetic field. This Markovian approach has a number of benefits, including: (i) the evident self-consistent relationship between the more general weak turbulence theory and the standard resonant diffusion quasilinear theory (as is commonly used in e.g. radiation belt and solar wind studies); (ii) the general nature of the Fokker-Planck equation that can be derived without any prior assumptions regarding its form; (iii) the clear dependence of the form of the Fokker-Planck equation and the transport coefficients on given specific timescales. The resultant quasilinear theory expressions are not new in and of themselves, but this concise derivation and discussion of the weak turbulence and quasilinear theories using the Markovian framework is both novel and physically very instructive. The results presented herein could form fundamental groundwork for future studies that consider phenomena for which some of the assumptions may be relaxed.