Coherent Pitch-Angle Interaction between Whistler Waves and a Distribution of Energetic Particles (PhD Oral-24)*

How coherent whistler waves interact with energetic particles is a crucial question in magnetospheric plasma physics, as well as in the context of runaway electrons in fusion devices. A recent study \footnote{P. M. Bellan, Phys. Plasmas, 20, 042117} showed that an exact rearrangement of the relativistic particle equation of motion under a circularly-polarized wave leads to an equation describing the motion of the “frequency mismatch” parameter $\xi$ under a pseudo-potential $\psi$. When the shape of the pseudo-potential is two-valleyed and the particle has enough pseudo-energy to undergo two-valley motion, $\xi$ and the pitch-angle changes greatly. In the present study, the analysis is extended to a distribution of particles. A general condition for two-valley motion is first derived. It is then shown via single-particle simulations that particles which satisfy the two-valley condition indeed undergo large pitch-angle changes. Then, the fraction of two-valley particles are calculated assuming that the particle distribution is Maxwell-J\"{u}ttner, which is the relativistic generalization of the Maxwell-Boltzmann distribution. For magnetospheric parameters, at least 1-5\% of the particles undergo two-valley motion, and this fraction is verified by single-particle simulations