Van Allen Probes Observations of Drift‐Bounce Resonance and Energy Transfer Between Energetic Ring Current Protons and Poloidal Pc4 Wave

Abstract

A poloidal Pc4 wave and proton flux oscillations are observed in the inner magnetosphere on the dayside near the magnetic equator by the Van Allen Probes spacecraft on 2 March 2014. The flux oscillations are observed in the energy range of 67.0 to 268.8 keV with the same frequency of the poloidal Pc4 wave. We find pitch angle and energy dispersion in the phase difference between the poloidal magnetic field and the proton flux oscillations, which are features of drift-bounce resonance. We estimate the resonance energy to be~120 keV for pitch angle (α) of 30°or 150°and 170-180 keV for α = 50°or 130°. To examine the direction of energy flow between protons and the wave, we calculate the sign of the gradient of proton phase space density (df/dW) on both the inbound and outbound legs of the orbit. We find the gradient to be outward on both legs, which means that energy is transferred from the protons to the wave. During the poloidal Pc4 wave event, the Dst* index shows a measurable increase of~6.7 nT. We estimate the total energy loss of the ring current from the recovery of the Dst* index and from the variation of proton flux by the drift-bounce resonance. We suggest that energy transfer from the ring current protons to the poloidal Pc4 wave via the drift-bounce resonance contributes to up to~85% of the increase of the Dst* index.Poloidal ULF waves are capable of resonating with charged particles through their azimuthal wave electric fields. This wave-particle interaction is known as drift-bounce resonance. Drift-bounce resonant condition is expressed aswhere ω is the wave angular frequency, ω d is the particle drift frequency, ω b is the particle bounce frequency, and N is an integer (Southwood et al., 1969). The drift-bounce resonance condition can be satisfied with odd mode ULF waves when N = 2k (k is an integer), while it can be satisfied with even mode ULF waves when OIMATSU ET AL. 3421

Eastward Propagating Second Harmonic Poloidal Waves Triggered by Temporary Outward Gradient of Proton Phase Space Density: Van Allen Probe A Observation

“…Proton fluxes with conjugate pitch angles ( α , 180°− α ) show out‐of‐phase oscillations. This is a typical feature of the pitch angle distributions in the drift‐bounce resonance of P2 waves (e.g., Oimatsu et al, ; Takahashi et al, ). Figure c shows PSD of B ν and Δ f H+ .…”

“…The poloidal ultralow frequency (ULF) wave is one of the most prominent waves in the inner magnetosphere and at the geosynchronous orbit. Studies have shown that the poloidal Pc 4–5 (a frequency range of 1.67–22.2 mHz) waves are excited through drift/drift‐bounce resonance with ~100 keV protons (Dai et al, ; Min et al, ; Oimatsu et al, ; Takahashi et al, ) or bounce resonance of ~10 keV protons (Hughes et al, ; Liu et al, ; Takahashi et al, ). These waves are notable because they can also resonate with and modify inner magnetospheric electron populations (Claudepierre et al, ; Hao et al, ; Mann et al, ).…”

“…Southwood et al () gave where q is the electric charge of the particle, B eq is the magnitude of the magnetic field at the equator of the Earth's surface, and R E is the radius of the Earth. Several studies found that df / dW > 0 when poloidal waves were observed (Min et al, ; Oimatsu et al, ; Takahashi et al, ).…”

Ion Energies Dominating Energy Density in the Inner Magnetosphere: Spatial Distributions and Composition, Observed by Arase/MEP‐i

“…Mass-dependent acceleration may be possible in the plasma sheet with magnetic and electric field perturbations (e.g., Catapano et al, 2016), in the reconnection region and around the separatrix between closed and open magnetic fields (where the Hall electric field exists; Liang et al, 2017), around a dipolarization front (i.e., a reconnection jet front) where the magnetic field increases in less than seconds and a strong electric field is thus induced (Runov et al, 2015), near the transition region from the stretched magnetic field to the dipole-like field where a fast flow associated with reconnection slows down and the electric field is induced by the magnetic field pileup (Nakayama et al, 2016). Possible waves are dispersive Alfvén waves (e.g., Chaston et al, 2016), which can accelerate O+ that are simultaneously extracted from the topside ionosphere and/or preexist on the same field lines; waves/fluctuations with a frequency range of electron-ion cyclotron waves (e.g., Nosé et al, 2014); and ULF waves (e.g., Mitani et al, 2018;Oimatsu et al, 2018), which can resonate with drifting and bouncing ring current ions. However, as higher-energy O+ are more difficult to transport to the inner magnetosphere, it is still a controversial issue whether a large number of those accelerated O+ can penetrate to around/inside geosynchronous orbit.…”

Selective Acceleration of O+ by Drift‐Bounce Resonance in the Earth's Magnetosphere: MMS Observations

“…ω b and ω d in a dipole magnetic field are provided as ω b = and ω d = − + + Ω E , where m i is the ion mass, R E is the Earth's radius, α E is the pitch angle at the geomagnetic equator, B E is the equatorial magnetic field at the surface of the Earth, q is the electric charge, φ is the eastward angle from the midnight, Ω E is the angular frequency of the corotation of the Earth, and ψ 0 is the electric potential of the convection electric field obtained from the Volland‐Stern model (Maynard & Chen, ; Stern, ; Volland, ). We also utilized the following equations: T (sin α E ) = 1.351 − 0.925sin α E + 0.558sin 2 α E − 0.248sin 3 α E and P (sin α E ) = 0.340 + 0.226sin α E − 0.154sin 2 α E + 0.088sin 3 α E (Hamlin et al, ; Oimatsu, Nosé, Takahashi, et al, ; Yang, Zong, Fu, Li, et al, ).…”