Modulation of energetic particle fluxes by a mixed mode of transverse and compressional waves

Modulation characteristics of particle fluxes in the presence of a mixed mode of compressional and transverse magnetic waves at hydromagnetic frequencies are investigated through kinetic perturbation of the distribution function. The magnetospheric medium where the particles are modulated contains both the magnetic and pressure gradients. The modulation features are found to be strongly dependent on the energy and pitch angle of the particles. Drifting particles can resonate with waves whose phase velocities are close to their drift velocities. When this occurs, the modulation amplitudes become significantly large and large phase shifts will occur. It is pointed out that resonance is important for particles with mid pitch angles (40-70 deg). The phase shift between the particle modulations and the magnetic field oscillations are strongly controlled by the combined effects of transverse and compressional wave components and/or the occurrence of drift resonance. Numerical calculations are performed using the dispersion relation of drift mirror Alfven waves as an example of waves with both compressional and transverse components.