D. Mourenas

Consequences of geomagnetic activity on energization and loss of radiation belt electrons by oblique chorus waves

Statistics of amplitudes and obliquity of lower band chorus whistler mode waves have been obtained from Cluster measurements in Earths outer radiation belt and fitted as functions of L, latitude, magnetic local time, and three geomagnetic activity ranges for Dst ∈ [+10,-80] nT. Very oblique chorus waves have generally a much smaller average intensity than quasi-parallel waves, especially on the nightside. Nevertheless, analytical estimates and full numerical calculations of quasi-linear diffusion rates show that dayside very oblique waves (θ>60°) dominate pitch angle scattering of energetic electrons during moderately disturbed periods. As geomagnetic activity increases, leading to higher wave amplitudes, electron lifetimes are only slightly reduced, due to a decrease of the wave obliquity probably related to Landau damping by stronger incoming fluxes from the plasma sheet. As a result, electron energization by chorus waves for Dst>-80 nT generally occurs in a loss-dominated regime in which energization increases at lower L. However, at L≥6 the most disturbed periods (Dst<-40 nT) produce a stronger energization independent of losses. Double-belt structures may therefore arise when Dst<-40 nT, with two peaks of energization located just outside the plasmapause and at L~6. The variability of lower band chorus wave obliquity with geomagnetic activity could actually account for some part of the observed variability of energization and loss in the outer belt. It is also suggested that quasi-linear pitch angle diffusion by very oblique waves together with energy diffusion by parallel waves might contribute to the steep wave growth observed in the day sector between the equator and 25°.

Non-diffusive resonant acceleration of electrons in the radiation belts

We describe a mechanism of resonant electron acceleration by oblique high-amplitude whistler waves under conditions typical for the Earth radiation belts. We use statistics of spacecraft observations of whistlers in the Earth radiation belts to obtain the dependence of the angle θ between the wave-normal and the background magnetic field on magnetic latitude λ. According to this statistics, the angle θ already approaches the resonance cone at λ∼15° and remains close to it up to λ∼30°–40° on the dayside. The parallel component of the electrostatic field of whistler waves often increases around λ∼15° up to one hundred of mV/m. We show that due to this increase of the electric field, the whistler waves can trap electrons into the potential well via wave particle resonant interaction corresponding to Landau resonance. Trapped electrons then move with the wave to higher latitudes where they escape from the resonance. Strong acceleration is favored by adiabatic invariance along the increasing magnetic field, wh...

Very oblique whistler generation by low‐energy electron streams

Whistler mode chorus waves are present throughout the Earths outer radiation belt as well as at larger distances from our planet. While the generation mechanisms of parallel lower band chorus waves and oblique upper band chorus waves have been identified and checked in various instances, the statistically significant presence in recent satellite observations of very oblique lower band chorus waves near the resonance cone angle remains to be explained. Here we discuss two possible generation mechanisms for such waves. The first one is based on Landau resonance with sporadic very low energy (<4 keV) electron beams either injected from the plasma sheet or produced in situ. The second one relies on cyclotron resonance with low-energy electron streams, such that their velocity distribution possesses both a significant temperature anisotropy above 3–4 keV and a plateau or heavy tail in parallel velocities at lower energies encompassing simultaneous Landau resonance with the same waves. The corresponding frequency and wave normal angle distributions of the generated very oblique lower band chorus waves, as well as their frequency sweep rate, are evaluated analytically and compared with satellite observations, showing a reasonable agreement.

Evidence of stronger pitch angle scattering loss caused by oblique whistler‐mode waves as compared with quasi‐parallel waves

Wave normal distributions of lower-band whistler-mode waves observed outside the plasmapause exhibit two peaks: one near the parallel direction and the other at very oblique angles. We analyze a number of conjunction events between the Van Allen Probes near the equatorial plane and Polar Orbiting Environmental Satellites (POES) at conjugate low altitudes, where lower-band whistler-mode wave amplitudes were inferred from the two-directional POES electron measurements over 30–100 keV, assuming that these waves were quasi-parallel. For conjunction events, the wave amplitudes inferred from the POES electron measurements were found to be overestimated as compared with the Van Allen Probes measurements primarily for oblique waves and quasi-parallel waves with small wave amplitudes (< ~20 pT) measured at low latitudes. This provides plausible experimental evidence of stronger pitch angle scattering loss caused by oblique waves than by quasi-parallel waves with the same magnetic wave amplitudes, as predicted by numerical calculations.

Wave energy budget analysis in the Earth/'s radiation belts uncovers a missing energy

Whistler-mode emissions are important electromagnetic waves pervasive in the Earth’s magnetosphere, where they continuously remove or energize electrons trapped by the geomagnetic field, controlling radiation hazards to satellites and astronauts and the upper-atmosphere ionization or chemical composition. Here, we report an analysis of 10-year Cluster data, statistically evaluating the full wave energy budget in the Earth’s magnetosphere, revealing that a significant fraction of the energy corresponds to hitherto generally neglected very oblique waves. Such waves, with 10 times smaller magnetic power than parallel waves, typically have similar total energy. Moreover, they carry up to 80% of the wave energy involved in wave–particle resonant interactions. It implies that electron heating and precipitation into the atmosphere may have been significantly under/over-valued in past studies considering only conventional quasi-parallel waves. Very oblique waves may turn out to be a crucial agent of energy redistribution in the Earth’s radiation belts, controlled by solar activity.

Nonlinear electron acceleration by oblique whistler waves: Landau resonance vs. cyclotron resonance

This paper is devoted to the study of the nonlinear interaction of relativistic electrons and high amplitude strongly oblique whistler waves in the Earths radiation belts. We consider electron trapping into Landau and fundamental cyclotron resonances in a simplified model of dipolar magnetic field. Trapping into the Landau resonance corresponds to a decrease of electron equatorial pitch-angles, while trapping into the first cyclotron resonance increases electron equatorial pitch-angles. For 100 keV electrons, the energy gained due to trapping is similar for both resonances. For electrons with smaller energy, acceleration is more effective when considering the Landau resonance. Moreover, trapping into the Landau resonance is accessible for a wider range of initial pitch-angles and initial energies in comparison with the fundamental resonance. Thus, we can conclude that for intense and strongly oblique waves propagating in the quasi-electrostatic mode, the Landau resonance is generally more important than the fundamental one.

Unraveling the excitation mechanisms of highly oblique lower band chorus waves

Excitation mechanisms of highly oblique, quasi-electrostatic lower band chorus waves are investigated using Van Allen Probes observations near the equator of the Earths magnetosphere. Linear growth rates are evaluated based on in situ, measured electron velocity distributions and plasma conditions and compared with simultaneously observed wave frequency spectra and wave normal angles. Accordingly, two distinct excitation mechanisms of highly oblique lower band chorus have been clearly identified for the first time. The first mechanism relies on cyclotron resonance with electrons possessing both a realistic temperature anisotropy at keV energies and a plateau at 100–500 eV in the parallel velocity distribution. The second mechanism corresponds to Landau resonance with a 100–500 eV beam. In both cases, a small low-energy beam-like component is necessary for suppressing an otherwise dominating Landau damping. Our new findings suggest that small variations in the electron distribution could have important impacts on energetic electron dynamics.

Fast transport of resonant electrons in phase space due to nonlinear trapping by whistler waves

We present an analytical, simplified formulation accounting for the fast transport of relativistic electrons in phase space due to wave-particle resonant interactions in the inhomogeneous magnetic field of Earths radiation belts. We show that the usual description of the evolution of the particle velocity distribution based on the Fokker-Planck equation can be modified to incorporate nonlinear processes of wave-particle interaction, including particle trapping. Such a modification consists in one additional operator describing fast particle jumps in phase space. The proposed, general approach is used to describe the acceleration of relativistic electrons by oblique whistler waves in the radiation belts. We demonstrate that for a wave power distribution with a hard enough power law tail P(Bw2)∝Bw−η such that η < 5/2, the efficiency of nonlinear acceleration could be more effective than the conventional quasi-linear acceleration for 100 keV electrons.

Strong enhancement of 10–100 keV electron fluxes by combined effects of chorus waves and time domain structures

Time domain structures (TDSs) are trains of intense electric field spikes observed in large numbers during plasma injections in the outer radiation belt. Here we explore the question of their importance in energetic electron acceleration and loss in this region. Although the most common TDSs can preaccelerate low-energy electrons up to 1–5 keV energies, they often cannot produce by themselves the seed population of 30–150 keV electrons, which are needed for a subsequent energization up to relativistic energies during storms or substorms. However, we demonstrate by numerical simulations that modifications of the low-energy electron pitch angle and energy distributions due to interactions with TDS lead to more efficient scattering of electrons by chorus waves toward both higher and lower pitch angles, ultimately leading to both significantly higher fluxes in the 10–100 keV energy range and more intense 1–100 keV precipitation into the atmosphere, potentially affecting the outer radiation belt dynamics.

Inner belt and slot region electron lifetimes and energization rates based on AKEBONO statistics of whistler waves

Global statistics of the amplitude distributions of hiss, lightning-generated, and other whistler mode waves from terrestrial VLF transmitters have been obtained from the EXOS-D (Akebono) satellite in the Earths plasmasphere and fitted as functions of L and latitude for two geomagnetic activity ranges (Kp 3). In particular, the present study focuses on the inner zone L∈[1.4,2] where reliable in situ measurements were lacking. Such statistics are critically needed for an accurate assessment of the role and relative dominance of each type of wave in the dynamics of the inner radiation belt. While VLF waves seem to propagate mainly in a ducted mode at L∼1.5–3 for Kp 3). Hiss waves are generally the most intense in the inner belt, and lightning-generated and hiss wave intensities increase with geomagnetic activity. Lightning-generated wave amplitudes generally peak within 10° of the equator in the region L<2 where magnetosonic wave amplitudes are weak for Kp<3. Based on this statistics, simplified models of each wave type are presented. Quasi-linear pitch angle and energy diffusion rates of electrons by the full wave model are then calculated. Corresponding electron lifetimes compare well with decay rates of trapped energetic electrons obtained from Solar Anomalous and Magnetospheric Particle Explorer and other satellites at L∈[1.4,2].