Resonant Generation of an Alfvén Wave by a Substorm Injected Electron Cloud: A Van Allen Probe Case Study

Abstract

Ultra-low frequency (ULF) waves are regularly observed in the Earth's magnetosphere. They are a convenient magnetospheric diagnosing tool because they interact with energetic charged particles. ULF waves of the Pc4-5 (40-600 s period) ranges most often are Alfvén waves standing along the magnetic field line between magnetically conjugated points in the ionosphere. Besides, the observed Alfvén waves differ in polarization (Anderson et al., 1990): if the radial component of the wave's magnetic field is much larger than the azimuthal component, then such a wave is called a poloidal Alfvén wave, and in the opposite case a wave is called a toroidal one. Poloidal Alfvén waves can interact with charged particles via the drift or drift-bounce resonances (Klimushkin et al., 2021), since they have significant azimuthal component of the wave electric field coinciding with particle drift direction, which leads to acceleration or deceleration of the particles. These resonant interactions are important for the dynamics of the ring current (Southwood et al., 1969) and radiation belt (Schulz & Lanzerotti, 1974) particles. Moreover, through these types of resonances poloidal Alfvén waves can be generated by two types of instabilities: the gradient instability caused by a steep earthward particle density gradient at a resonant energy, and the bump-on-tail instability, when a velocity distribution of the particles is inverted around the resonant energy, that is there is a bump at the energetic part of the distribution (Chen & Hasegawa, 1988;Karpman et al., 1977;Southwood, 1976). Most of the observed poloidal waves are the second harmonic of the Alfvén wave. They are asymmetric in the electric field relative to the equator and are generated by the drift-bounce resonance (

Polarization and Spatial Distribution Features of Pc4 and Pc5 Waves in the Magnetosphere

“…These waves can be excited by a moving source, for example, a substorm-injected cloud of ions (Mager & Klimushkin, 2007, 2008. Eastward drifting ULF waves reported in previous studies were observed at dawn and night sectors (James et al, 2013(James et al, , 2016Mikhailova et al, 2022;Yamamoto et al, 2019;Zolotukhina et al, 2008), but its occurrence rate is small according to Figure 4a. Poloidal and toroidal waves may be observed at the same time, but different energy sources result in different spatial distribution.…”

“…A pp must be higher than 0.5 nT (it corresponds to 0.25 nT wave amplitude) for at least five wave periods in order to distinguish quasi-sinusoidal oscillations from pulses at the same frequency. We chose A pp = 0.5 nT threshold empirically, after comparison with the background noise level and earlier case studies (Mager, 2021;Mikhailova et al, 2022). Usually, quasi-sinusoidal waves have much more oscillation periods, but the wave amplitude gradually increases at the beginning of the observation and gradually decreases at the end.…”

Diagnostics of the Ionospheric Conductivity Based on Spacecraft Observations of the Magnetospheric ULF Waves

“…We revealed several peculiarities during the 27 October 2012 event studying, that were not mentioned in Mikhailova et al (2022). Figure 1 presents the wave field components, the electric field energy density w E and the parallel Poynting flux S ‖ , and their values averaged over the wave period T = 100 s are presented.…”

“…The wave interacted with electrons via the drift resonance and was generated through the gradient instability. The detailed study of the event is presented in Mikhailova et al (2022).…”

Characteristics of Electron Precipitation Directly Driven by Poloidal ULF Waves

“…Another important factor of driving radiation belt dynamics is ultralow‐frequency (ULF) waves, especially those in the Pc4‐5 ranges (from 2 to 22 mHz), which can lead to energy exchange and radial transport of energetic electrons via wave‐particle drift‐resonant interaction (Fei et al., 2006; Klimushkin et al., 2021; Mann et al., 2013; Mikhailova et al., 2022; Su et al., 2015; Zong et al., 2017). Typically, ULF waves are categorized into toroidal and poloidal branches (Hughes, 1994), although they are often coupled with each other (Lee & Lysak, 1989; Wright & Elsden, 2020).…”