Nonlinear Wave Growth of Whistler-Mode Hiss Emissions in a Uniform Magnetic Field

We conduct electromagnetic particle simulations in a uniform magnetic environment to verify the nonlinear wave growth process of plasmaspheric hiss in the equatorial plasmasphere. The satisfaction of the separability criterion for coexisting multiple frequency waves in the initial stage of wavenumber-time evolution declares that wave packets are coherent and capable of growing nonlinearly. Spatial and temporal evolutions of two typical modes located in wavenumber-time evolution demonstrate the consistency among wave growths, frequency variations, and inhomogeneity factor S in coherent wave packets, showing that rising and falling tones occur at negative and positive S values, respectively, and an obvious wave growth happens in a reasonable range of S satisfying the second-order resonance condition. Wave packets extracted from wave fields in space and time by a frequency band-pass filter confirm a good agreement between the nonlinear theory and simulation results. The nonlinear growth rates of the extracted wave packets possess similar magnitudes to the growth rates of wave packets in the simulation, and they are much greater than the theoretical linear growth rate, indicating that the nonlinear process is essential in the generation of plasmaspheric hiss

Upstream Shift of Generation Region of Whistler-Mode Rising-Tone Emissions in the Magnetosphere

We have performed a series of simulation runs for whistler-mode wave-particle interaction in a parabolic magnetic field with 12 different frequencies of triggering waves and 3 different plasma frequencies specifying cold plasma densities. Under a given plasma condition, a specific frequency range of the triggering wave exists that can generate rising-tone emissions. The generation region of rising-tone emission shifts upstream. The velocity of the wave generation region is dependent on duration of the subpacket, which is controlled by the formation of the resonant current in the generation region. When the source velocity, which is a sum of the resonance and group velocities, is approximately the same as the velocity of the wave generation region, a long-sustaining rising-tone emission is generated. When the spatial and temporal gap between subpackets exists due to damping phase of short subpacket generation, resonant electrons in the gap of the subpackets are carried at the resonance velocity to the upstream region, and the velocity of the wave generation region becomes large in magnitude. When formation of resonant currents is delayed, the velocity of the generation region becomes smaller than the source velocity in magnitude. Below one quarter of the cyclotron frequency, coalescence of subpackets takes place, suppressing formation of the resonant current in the generation region. Since gradual upstream shift of the generation region is necessary for the wave to grow locally, the source velocity should be a small negative value

Precipitation Rates of Electrons Interacting With Lower-Band Chorus Emissions in the Inner Magnetosphere

Electrons trapped in the Earth's magnetic field can be scattered by whistler mode chorus emissions and precipitate into the Earth's upper atmosphere. Whistler mode chorus waves propagating in the Earth's inner magnetic field are usually observed with oblique wave normal angles (WNAs). In this study, we apply 12 chorus wave models with four various WNA sets (the maximum WNA are 0°, 20°, 60°, and 90% of resonance cone angles) and three wave amplitude sets (the maximum wave magnetic fields are 2.1 nT, 307 pT, and 49.4 pT) at L = 4.5. We use test-particle simulations to trace electrons interacting with the waves and create Green's function sets for electrons initially at kinetic energies (K) 10–6, 000 keV and equatorial pitch angles (α) 5°–89°. The simulation results show that in the 2.1 nT cases, the very oblique chorus waves contribute to more electron precipitation than the other three chorus wave models, especially at energies 50–100 keV. Checking the highest initial equatorial pitch angle of the precipitated electrons, we find that the very oblique chorus waves can precipitate electrons with α > 45°. In contrast, the other chorus waves can only precipitate electrons with α < 30°. Furthermore, the precipitation rates reveal that the anomalous trapping effect, which moves low equatorial pitch angle electrons away from the loss cone, in the oblique cases is much weaker than in the parallel case, resulting in higher precipitation rates. Finally, we derive the pitch angle scattering rates and verify the precipitation by nth cyclotron resonances with oblique chorus

Nonlinear triggering process of whistler-mode emissions in a homogeneous magnetic field

We perform an electromagnetic particle simulation of triggered emissions in a uniform magnetic field for understanding of nonlinear wave–particle interaction in the vicinity of the magnetic equator. A finite length of a whistler-mode triggering wave packet with a constant frequency is injected by oscillating an external current at the equator. We find that the first subpacket of triggered emissions is generated in the homogeneous magnetic field. By analyzing resonant currents and resonant electron dynamics in the simulation, we find that the formation of an electron hole in a velocity phase space results in resonant currents, and the currents cause wave amplification and frequency increase. We obtain the interaction time of counter-streaming resonant electrons in a triggering wave packet with a finite width. By changing the duration time of the triggering pulse, we evaluate the interaction time necessary for formation of an electron hole. We conduct 4 runs with different duration times of the triggering pulse, 980, 230, 105, 40 Ωe⁻¹, which correspond to cases with interaction times, 370%, 86%, 39%, and 15% of the nonlinear trapping period, respectively. We find generation of triggered emissions in the three cases of 370%, 86%, and 39%, which agrees with the conventional nonlinear model that the nonlinear transition time, which is necessary for formation of resonant currents, is about a quarter of the nonlinear trapping period

Triggering of Whistler‐Mode Rising and Falling Tone Emissions in a Homogeneous Magnetic Field

We perform a self-consistent one-dimensional electromagnetic particle simulation with a uniform magnetic field and open boundaries. The plasma environment consists of cold isotropic electrons, energetic electrons, and immobile ions. The energetic electrons are initialized with a subtracted-Maxwellian distribution with temperature anisotropy. By oscillating external currents with a constant frequency 0.2 fce, where fce is the electron cyclotron frequency, a whistler-mode wave is injected as a triggering wave from the center of the simulation system, and we investigated the process of interactions between the triggering wave and energetic electrons. We find that both rising-tone and falling-tone emissions are triggered through the formation of an electron hole and an electron hill in the velocity phase space consisting of a parallel velocity and the gyro-phase angle of the perpendicular velocities. The rising-tone emission varies from 0.2 fce to 0.4 fce, while the falling-tone varies from 0.2 fce to 0.15 fce. The generation region of the rising-tone triggered emission starts near the injection point of the triggering wave and moves upstream generating new subpackets. The generation region of the falling-tone triggered emission also moves upstream generating new subpackets. The simultaneous formation of the electron hole and hill is identified by separating small and large wavenumber components corresponding to lower and higher frequencies, respectively, by applying the discrete Fourier transformation to the waveforms in space. Based on the simulation results of the whistler-mode triggered emissions, we conclude that the mechanism of frequency variation of whistler-mode chorus emissions works even in a uniform magnetic field

Particle Simulation of the Generation of Plasmaspheric Hiss

We have conducted a one‐dimensional electromagnetic particle simulation with a parabolic magnetic field to reproduce whistler‐mode hiss emissions in the plasmasphere. We assume a bi‐Maxwellian distribution with temperature anisotropy for energetic electrons injected into the plasmasphere and find that hiss emissions are generated with spectrum characteristics typical of those observed by spacecraft near the magnetic equator. The hiss emissions contain fine structures involving rising tone and falling tone elements with variation in frequencies. The amplitude profile of the spectra agrees with the optimum wave amplitude derived from the nonlinear wave growth theory. The simulation demonstrates that hiss emissions are generated locally near the magnetic equator through linear and nonlinear interactions with energetic electrons with temperature anisotropy. The coherent hiss emissions efficiently scatter resonant electrons of 2.5–80 keV into the loss cone

Occurrence characteristics of electromagnetic ion cyclotron waves at sub-auroral Antarctic station Maitri during solar cycle 24

We present a statistical study of electromagnetic ion cyclotron (EMIC) waves observed at Antarctic station (geographic 70.7° S, 11.8° E, L=5) on quiet and disturbed days during 2011–2017. The data span a fairly good period of both ascending and descending phases of the solar cycle 24, which has witnessed extremely low activity. We noted EMIC wave occurrence by examining wave power in different frequency ranges in the spectrogram. EMIC wave occurrence during ascending and descending phases of solar cycle 24, its local time, seasonal dependence and durations have been examined. There are total 2367 days for which data are available. Overall, EMIC waves are observed for 3166.5 h (≈5.57% of total duration) which has contributions from 1263 days. We find a significantly higher EMIC wave occurrence during the descending phase (≈ 6.83%) as compared to the ascending phase (≈ 4.08%) of the solar cycle, which implies nearly a twofold increase in EMIC wave occurrence. This feature is attributed to the higher solar wind dynamic pressure during descending phase of solar activity. There is no evident difference in the percentage occurrence of EMIC waves on magnetically disturbed and quiet days. On ground, EMIC waves show marginally higher occurrence during winter as compared to summer. This seasonal tendency is attributed to lower electron densities and conductivities in the ionosphere, which can affect the propagation of EMIC waves through ionospheric ducts. In local time, the probability distribution function of EMIC wave occurrence shows enhancement during 11.7–20.7 LT (i.e., afternoon–dusk sector). Daily durations of EMIC waves are in the range of 5–1015 min and it is noted that the longer duration (240–1015 min) events are prevalent on quiet days and are mostly seen during the descending phase of solar cycle

Nonlinear Wave Growth Analysis of Whistler‐Mode Chorus Generation Regions Based on Coupled MHD and Advection Simulation of the Inner Magnetosphere

We show the regions where nonlinear growth of whistler-mode chorus waves is preferred to occur in the inner magnetosphere. A global magnetohydrodynamics (MHD) simulation was used to obtain large-scale electric and magnetic fields under the southward interplanetary magnetic field condition. With the electric and magnetic fields obtained by the MHD simulation, we ran a comprehensive inner magnetosphere-ionosphere model to solve the evolution of phase space density of electrons. Hot electrons originating from the tail region drift sunward and penetrate deep into the inner region due to a combination of convection and substorm-associated electric fields. Cold electrons also drift sunward, resulting in a contraction of the plasmasphere. We obtained the following results. (1) The whistler waves can first grow due to the linear mechanism (pitch angle anisotropy) in the premidnight-prenoon region outside the plasmapause, followed by rapid, nonlinear mechanism accompanied with rising-tone chorus elements. (2) When the solar wind speed is high, the whistler waves grow more efficiently due to linear and nonlinear mechanisms over a wider area because of deep penetration of hot electrons and the large contraction of the plasmasphere. This is consistent with the observation that the outer belt electrons increase for the fast solar wind. (3) For slow solar wind, the linear growth is mostly suppressed, but the nonlinear growth can still take place when external seed waves are present. This may explain the persistence of dawn chorus and large-amplitude chorus waves that are often observed in the premidnight-postdawn region in relatively weak geomagnetic activities

Full Particle Simulation of Whistler-Mode Triggered Falling-Tone Emissions in the Magnetosphere

We perform a one‐dimensional electromagnetic full particle simulation for triggered falling‐tone emissions in the Earth's magnetosphere. The equatorial region of the magnetosphere is modeled with a parabolic magnetic field approximation. The short whistler‐mode waves with a large amplitude are excited and propagate poleward from an artificial current oscillating with a constant frequency and amplitude. Following the excited waves, clear emissions are triggered with a falling frequency. Without the inhomogeneity of the background magnetic field, no triggered emission appears. The falling tone has several subpackets of amplitude and decreases the frequency in a stepwise manner. The positive resonant current formed by resonant electrons in the direction of the wave magnetic field clearly shows that an electron hill is formed in the phase space and causes the frequency decrease. The entrapping of the resonant electrons at the front of the packets and the decrease of the amplitude at the end of packets are essential for the generation of falling‐tone emissions. Each wavefront of the emission has a strongly negative resonant current −JE, which results in the wave growth. In the formation process of the resonant currents, we investigate the inhomogeneous factor S, which controls the nonlinear motion of the resonant electrons interacting with waves. The factor S consists of two terms, a frequency sweep rate and a gradient of the background magnetic field. The resonant current JE in the wave packet changes its sign from negative to positive as the packet moves away from the equator, terminating the wave growth

Upstream motion of chorus wave generation: comparisons with observations

An understanding of the development of strong very low frequency chorus elements is important in the study of the rapid MeV electron acceleration observed during radiation belt recovery events. During such events, chorus elements with long-duration (20–40 ms), strong (|Bw| 0.5–2.0 nT) subpackets with smoothly varying frequency and phase capable of producing nonlinear energy gain of 1%–2% for multi-MeV seed electrons. For such strong chorus elements, we examine the consequences of an upstream motion of the chorus wave generation region using Van Allen Probes observations and nonlinear theory. For a given upstream velocity, vs, resonant electron energy (50–350 keV) and pitch angle (105–115 deg) are uniquely determined for each wave frequency. We examine the effect of an upstream vs on the inhomogeneity factor that controls wave growth. For steadily increasing upstream motion as the chorus element evolves, vs/c ranging over [-0.001, −0.065], nonlinear wave growth takes place at ≥ 50% of the theoretical maximal value during the development of the observed strong subpackets. For the cases examined, resonant electron energies and pitch angles closely match those of the observed injected electron flux enhancements responsible for chorus development and the nonlinear acceleration of MeV radiation belt electrons