We present a comprehensive analysis of the processes that lead to quasilinear pitch-angle-scattering loss of electrons from the L < 4 region of the Earth's inner magnetosphere during geomagnetically quiet times. We consider scattering via Coulomb collisions, hiss waves, lightning-generated whistler (LGW) waves, waves from ground-based very-low-frequency (VLF) transmitters, and electromagnetic ion cyclotron (EMIC) waves. The amplitude, frequency, and wave normal angle spectra of these waves are parameterized with empirical wave models, which are then used to compute pitch-angle diffusion coefficients. From these coefficients, we estimate the decay timescales, or lifetimes, of 30 keV to 4 MeV electrons and compare the results with timescales obtained from in-situ observations. We demonstrate good quantitative agreement between the two over most of the L and energy range under investigation. Our analysis suggests that the electron decay timescales are very sensitive to the choice of plasmaspheric density model. At L < 2, where our theoretical lifetimes do not agree well with the observations, we show that including Coulomb energy drag (ionization energy loss) in our calculations significantly improves the quantitative agreement with the observed decay timescales. We also use an accurate model of the geomagnetic field to provide an estimate of the effect that the drift-loss cone has on the theoretically calculated electron lifetimes, which are usually obtained using an axisymmetric dipole field.

This brief technique paper presents a method of reconstructing the global, time-varying distribution of some physical quantity Q that has been sparsely sampled at various locations within the magnetosphere and at different times. The quantity Q can be essentially any measurement taken on the satellite including a variety of waves (chorus, hiss, magnetosonic, and ion cyclotron), electrons of various energies ranging from cold to relativistic, and ions of various species and energies. As an illustrative example, we chose Q to be the electron number density (inferred from spacecraft potential) measured by three Time History of Events and Macroscale Interactions during Substorms (THEMIS) probes between 2008 and 2014 and use the SYM-H index, taken at a 5 min cadence for the 5 h preceding each observed data point as the main regressor, although the predictor can also be any suitable geomagnetic index or solar wind parameter. Results show that the equatorial electron number density can be accurately reconstructed throughout the whole of the inner magnetosphere as a function of space and time, even capturing the dynamics of elementary plasmaspheric plume formation and corotation, suggesting that the dynamics of various other physical quantities could be similarly captured. For our main model, we use a simple, fully connected feedforward neural network with two hidden layers having sigmoidal activation functions and an output layer with a linear activation function to perform the reconstruction. The training is performed using the Levenberg-Marquardt algorithm and gives typical RMS errors of ~1.7 and regression of >0.93, which is considered excellent. We also present a discussion on the different applications and future extensions of the present model, for modeling various physical quantities.

Recent test particle simulations have shown that energetic electrons traveling through fast magnetosonic (MS) wave packets can experience an effect which is specifically associated with the tight equatorial confinement of these waves, known as transit time scattering. However, such test particle simulations can be computationally cumbersome and offer limited insight into the dominant physical processes controlling the wave-particle interactions, that is, in determining the effects of the various wave parameters and equatorial confinement on the particle scattering. In this paper, we show that such nonresonant effects can be effectively captured with a straightforward analytical treatment that is made possible with a set of reasonable, simplifying assumptions. It is shown that the effect of the wave confinement, which is not captured by the standard quasi-linear theory approach, acts in such a way as to broaden the range of particle energies and pitch angles that can effectively resonate with the wave. The resulting diffusion coefficients can be readily incorporated into global diffusion models in order to test the effects of transit time scattering on the dynamical evolution of radiation belt fluxes.

Equatorially mirroring energetic electrons pose an interesting scientific problem, since they generally cannot resonate with any known plasma waves and hence cannot be scattered down to lower pitch angles. Observationally it is well known that the flux of these equatorial particles does not simply continue to build up indefinitely, and so a mechanism must necessarily exist that transports these particles from an equatorial pitch angle of 90 down to lower values. However, this mechanism has not been uniquely identified yet. Here we investigate the mechanism of bounce resonance with equatorial noise (or fast magnetosonic waves). A test particle simulation is used to examine the effects of monochromatic magnetosonic waves on the equatorially mirroring energetic electrons, with a special interest in characterizing the effectiveness of bounce resonances. Our analysis shows that bounce resonances can occur at the first three harmonics of the bounce frequency (nωb, n = 1, 2, and 3) and can effectively reduce the equatorial pitch angle to values where resonant scattering by whistler mode waves becomes possible. We demonstrate that the nature of bounce resonance is nonlinear, and we propose a nonlinear oscillation model for characterizing bounce resonances using two key parameters, effective wave amplitude à and normalized wave number k≈z. The threshold for higher harmonic resonance is more strict, favoring higher à and k≈z, and the change in equatorial pitch angle is strongly controlled by k≈z. We also investigate the dependence of bounce resonance effects on various physical parameters, including wave amplitude, frequency, wave normal angle and initial phase, plasma density, and electron energy. It is found that the effect of bounce resonance is sensitive to the wave normal angle. We suggest that the bounce resonant interaction might lead to an observed pitch angle distribution with a minimum at 90.

We compute quasilinear diffusion rates due to pitch angle scattering by various mechanisms in the Earth's electron radiation belts. The calculated theoretical lifetimes are compared with observed decay rates, and we find excellent qualitative agreement between the two. The overall structure of the observed lifetime profiles as a function of energy and L is largely due to plasmaspheric hiss and Coulomb scattering. The results also reveal a local minimum in lifetimes in the inner zone at lower energy ( ∼ 50 keV), attributed to enhanced scattering via ground-based very low frequency transmitters, and a reduction in lifetimes at higher L and energy ( > 1 MeV), attributed to enhanced electromagnetic ion cyclotron wave scattering. In addition, we find significant quantitative disagreement at L<3.5 , where the theoretical lifetimes are typically a factor of ∼ 10 larger than the observed, pointing to an additional loss process that is missing from current models. We discuss potential factors that could contribute to this disagreement.

Recent ray tracing suggests that plasmaspheric hiss can originate from chorus observed outside of the plasmapause. Although a few individual events have been reported to support this mechanism, the number of reported conjugate events is still very limited. Using coordinated observations between Time History of Events and Macroscale Interactions during Substorms (THEMIS) and Van Allen Probes, we report on an interesting event, where chorus was observed at a large L shell (∼9.8), different from previously reported events at L < 6, but still exhibited a remarkable correlation with hiss observed in the outer plasmasphere (L ∼ 5.5). Ray tracing indicates that a subset of chorus can propagate into the observed location of hiss on a timescale of ∼5-6 s, in excellent agreement with the observed time lag between chorus and hiss. This provides quantitative support that chorus from large L shells, where it was previously considered unable to propagate into the plasmasphere, can in fact be the source of hiss.

Plasmaspheric hiss is known to play an important role in controlling the overall structure and dynamics of radiation belt electrons inside the plasmasphere. Using newly available Van Allen Probes wave data, which provide excellent coverage in the entire inner magnetosphere, we evaluate the global distribution of the hiss wave frequency spectrum and wave intensity for different levels of substorm activity. Our statistical results show that observed hiss peak frequencies are generally lower than the commonly adopted value (~550-Hz), which was in frequent use, and that the hiss wave power frequently extends below 100-Hz, particularly at larger L shells (>-~3) on the dayside during enhanced levels of substorm activity. We also compare electron pitch angle scattering rates caused by hiss using the new statistical frequency spectrum and the previously adopted Gaussian spectrum and find that the differences are up to a factor of ~5 and are dependent on energy and L shell. Moreover, the new statistical hiss wave frequency spectrum including wave power below 100-Hz leads to increased pitch angle scattering rates by a factor of ~1.5 for electrons above ~100-keV at L~5, although their effect is negligible at L-≤-3. Consequently, we suggest that the new realistic hiss wave frequency spectrum should be incorporated into future modeling of radiation belt electron dynamics. Key Points Hiss wave power is activity dependent and frequently extends below 100-Hz Hiss peak frequency is dependent on L and lower than the previous value 550-Hz Difference in hiss diffusion rate is up to 5, and realistic spectra should be used

Chorus-like whistler mode waves that are known to play a fundamental role in driving radiation belt dynamics are excited on the Large Plasma Device by the injection of a helical electron beam into a cold plasma. The mode structure of the excited whistler wave is identified using a phase correlation technique showing that the waves are excited through a combination of Landau resonance, cyclotron resonance, and anomalous cyclotron resonance. The dominant wave mode excited through cyclotron resonance is quasi-parallel propagating, whereas wave modes excited through Landau resonance and anomalous cyclotron resonance propagate at oblique angles that are close to the resonance cone. An analysis of the linear wave growth rates captures the major observations in the experiment. The results have important implications for the generation process of whistler waves in the Earth's inner magnetosphere.

Recent ray tracing suggests that plasmaspheric hiss can originate from chorus observed outside of the plasmapause. Although a few individual events have been reported to support this mechanism, the number of reported conjugate events is still very limited. Using coordinated observations between Time History of Events and Macroscale Interactions during Substorms (THEMIS) and Van Allen Probes, we report on an interesting event, where chorus was observed at a large L shell (~9.8), different from previously reported events at L<6, but still exhibited a remarkable correlation with hiss observed in the outer plasmasphere (L~5.5). Ray tracing indicates that a subset of chorus can propagate into the observed location of hiss on a timescale of ~5-6s, in excellent agreement with the observed time lag between chorus and hiss. This provides quantitative support that chorus from large L shells, where it was previously considered unable to propagate into the plasmasphere, can in fact be the source of hiss.

We use measurements from NASA's Van Allen Probes to calculate the decay time constants for electrons over a wide range of energies (30 keV to 4 MeV) and L values ( L = 1.3-6.0) in the Earth's radiation belts. Using an automated routine to identify flux decay events, we construct a large database of lifetimes for near-equatorially mirroring electrons over a 5-year interval. We provide the first accurate estimates of the long decay timescales in the inner zone ( ∼ 100 days), which are highly resolved in energy and free from proton contamination. In the slot region and outer zone, we compare our lifetime calculations with prior empirical estimates and find good quantitative agreement (lifetimes ∼ 1-20 days). The comparisons suggest that some prior estimates may overestimate electron lifetimes between L≈ 2.5-4.5 due to instrumental effects and/or background contamination. Previously reported two-stage decays are explicitly demonstrated to be a consequence of using integral fluxes.