Velocity Space Diffusion from Weak Plasma Turbulence in a Magnetic Field

TLDR

Quasi‑linear velocity‑space diffusion is studied for waves of any branch propagating at arbitrary angles to a uniform magnetic field in a spatially uniform plasma. The analysis assumes the space‑averaged distribution function evolves slowly relative to the gyroperiod and wave timescales, and neglects nonlinear mode coupling. An H‑like theorem demonstrates that both resonant and nonresonant quasi‑linear diffusion push distributions toward marginal stability, yet the marginally stable plateau is generally unattainable because it would require particles to diffuse to infinite energies; resonant particles with velocities much larger than the phase velocity scatter mainly in pitch angle, while particles with velocities near or below the phase velocity scatter in energy at a comparable rate.

Abstract

The quasi-linear velocity space diffusion is considered for waves of any oscillation branch propagating at an arbitrary angle to a uniform magnetic field in a spatially uniform plasma. The space-averaged distribution function is assumed to change slowly compared to a gyroperiod and characteristic times of the wave motion. Nonlinear mode coupling is neglected. An H-like theorem shows that both resonant and nonresonant quasi-linear diffusion force the particle distributions towards marginal stablity. Creation of the marginally stable state in the presence of a sufficiently broad wave spectrum in general involves diffusing particles to infinite energies, and so the marginally stable plateau is not accessible physically, except in special cases. Resonant particles with velocities much larger than typical phase velocities in the excited spectrum are scattered primarily in pitch angle about the magnetic field. Only particles with velocities the order of the wave phase velocities or less are scattered in energy at a rate comparable with their pitch angle scattering rate.