Comparison of pitch angle diffusion by turbulent and monochromatic whistler waves

A recent Hamiltonian analysis of magnetized test particles acted on by a small monochromatic wave is compared to a quasi-linear formulation of pitch angle diffusion by a turbulent spectrum of whistler waves. The quasi-linear expression has previously been applied to anthropogenic VLF transmissions to conclude that they dominate pitch angle diffusion of inner radiation belt electrons. However, because these transmissions are very narrow in frequency range, the monochromatic approach might be more appropriate. It is shown analytically that the monochromatic limit of the quasi-linear pitch angle diffusion coefficient reduces to the same expression as the diffusive regime of the Hamiltonian treatment. Agreement of the Hamiltonian pitch angle diffusion coefficient with the quasi-linear values is verified numerically using realistic parameters for the spread in frequency and wave-normal angle. As an aside, a simple, alternate derivation of quasi-linear diffusion coefficients is given.