Van Allen Probes Observations of Second Harmonic Poloidal Standing Alfv\ en Waves

Long-lasting second-harmonic poloidal standing Alfv\ en 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\textendash300 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\textdegree (southward moving protons) at W \~ 120 keV. This feature is explained by drift-bounce resonance (mωd \~ ωb) of \~120 keV protons with the waves, where ωd and ωb are the proton drift and bounce frequencies. At lower energies, the proton phase space density ( math formula) exhibits a bump-on-tail structure with math formula occurring in the 1\textendash10 keV energy range. This math formula is unstable and can excite P2 waves through bounce resonance (ω \~ ωb), where ω is the wave frequency.