Van Allen Probes Observations of Second Harmonic Poloidal Standing Alfvén Waves

Long-lasting second-harmonic poloidal standing Alfvén waves (P2 waves) were observed by the twin Van Allen Probes (Radiation Belt Storm Probes, or RBSP) spacecraft in the noon sector of the plasmasphere, when the spacecraft were close to the magnetic equator and had a small azimuthal separation. Oscillations of proton fluxes at the wave frequency (∼10 mHz) were also observed in the energy (W) range 50–300 keV. Using the unique RBSP orbital configuration, we determined the phase delay of magnetic field perturbations between the spacecraft with a 2nπ ambiguity. We then used finite gyroradius effects seen in the proton flux oscillations to remove the ambiguity and found that the waves were propagating westward with an azimuthal wave number (m) of ∼−200. The phase of the proton flux oscillations relative to the radial component of the wave magnetic field progresses with W, crossing 0 (northward moving protons) or 180° (southward moving protons) at W ∼ 120 keV. This feature is explained by drift-bounce resonance (mω_d ∼ ω_b) of ∼120 keV protons with the waves, where ω_d and ω_b are the proton drift and bounce frequencies. At lower energies, the proton phase space density (F_H+) exhibits a bump-on-tail structure with ∂F_H+/∂W >0 occurring in the 1–10 keV energy range. This F_H+ is unstable and can excite P2 waves through bounce resonance (ω ∼ ω_b), where ω is the wave frequency.