Abstract We report correlated data on nightside chorus waves and energetic electrons during two small storm periods: 1 November 2012 ( D s t ≈−45) and 14 January 2013 ( D s t ≈−18). The Van Allen Probes simultaneously observed strong chorus waves at locations L = 5.8–6.3, with a lower frequency band 0.1–0.5 f ce and a peak spectral density ∼10 −4 nT 2 /Hz. In the same period, the fluxes and anisotropy of energetic (∼10–300 keV) electrons were greatly enhanced in the interval of large negative interplanetary magnetic field B z . Using a bi‐Maxwellian distribution to model the observed electron distribution, we perform ray tracing simulations to show that nightside chorus waves are indeed produced by the observed electron distribution with a peak growth for a field‐aligned propagation approximately between 0.3 f ce and 0.4 f ce , at latitude <7°. Moreover, chorus waves launched with initial normal angles either θ <90° or >90° propagate along the field either northward or southward and then bounce back either away from Earth for a lower frequency or toward Earth for higher frequencies. The current results indicate that nightside chorus waves can be excited even during weak geomagnetic activities in cases of continuous injection associated with negative B z . Moreover, we examine a dayside event during a small storm C on 8 May 2014 ( D s t ≈−45) and find that the observed anisotropic energetic electron distributions potentially contribute to the generation of dayside chorus waves, but this requires more thorough studies in the future.
Abstract Whistler mode wave is a crucial emission which can significantly affect the electron dynamics in the magnetosphere. The nonlinear three‐wave interaction between whistler mode waves has been frequently observed, while the four‐wave interaction between these waves is seldom reported. Here, we present two multiband whistler mode wave events by Van Allen Probes, in which the relatively weak wave bands occur exactly corresponding to the strong wave bands. We find that the frequencies of the weak and strong bands satisfy the frequency matching conditions of the four‐wave interaction, and the wave normal angles of the weak bands are almost within the possible ranges calculated from the wave vector matching conditions. Additionally, the cross‐correlation coefficients between the amplitudes of the weak bands and that of strong bands approach 0.80. These results indicate that the weak bands are very likely to be produced by the four‐wave interaction between whistler mode waves. Similar to the three‐wave interaction, the four‐wave interaction can extend the frequency of whistler mode waves from close to 0.5 f ce to a wider range in both the lower (0.26 f ce ) and upper (0.78 f ce ) bands, and thus potentially play an important role in the electron dynamics.
Earth's cusp proton aurora occurs near the prenoon and is primarily produced by the precipitation of solar energetic (2–10 keV) protons. Cusp auroral precipitation provides a direct source of energy for the high-latitude dayside upper atmosphere, contributing to chemical composition change and global climate variability. Previous studies have indicated that magnetic reconnection allows solar energetic protons to cross the magnetopause and enter the cusp region, producing cusp auroral precipitation. However, energetic protons are easily trapped in the cusp region due to a minimum magnetic field existing there. Hence, the mechanism of cusp proton aurora has remained a significant challenge for tens of years. Based on the satellite data and calculations of diffusion equation, we demonstrate that EMIC waves can yield the trapped proton scattering that causes cusp proton aurora. This moves forward a step toward identifying the generation mechanism of cusp proton aurora.
Abstract Auroral kilometric radiations (AKR) are widely existing superluminous waves in the magnetosphere. Due to rarely available measurements of AKR magnetic field components, we derive the explicit expression of diffusion coefficients in terms of electric field components, which can be applied to various space plasma waves. Using Van Allen Probes data, we calculate diffusion coefficients with different harmonic orders for two AKR events. It is found that the first (higher) harmonic order contributes to diffusion coefficients at small (larger) pitch angles. The effect of higher harmonic orders becomes more significant as the electron energy increases. These results are contrary to the case of chorus wave, in which the first order usually contributes much to wave‐particle interactions. Estimations show that the phase space density of 0.5 MeV electrons can increase ∼ 10 times within 6 hr by AKR. This study is important for better modeling of AKR‐induced radiation belt electron dynamics.
Abstract Quasi‐electrostatic magnetosonic (QEMS) waves have been recently reported, referring to a distinct type of magnetosonic (MS) wave with only the electric fluctuation being detectable. Here a statistical study of QEMS waves is carried out with the Van Allen Probes data. 83% of 40,466 QEMS samples are observed with plasma density n e < 20 cm −3 , and intense QEMS waves tend to appear in the lower density region. QEMS waves become strong in the case of more pronounced proton rings around 10 keV and larger suprathermal proton populations. High occurrence rates and large amplitudes of QEMS waves are confined near the dayside equator (|MLAT| < 3°). The wave frequencies are typically slightly below the n th harmonic of proton gyro‐frequency, and the wave intensity gradually decreases with an increasing harmonic number n . Our results further demonstrate that low plasma densities and abundant suprathermal protons are beneficial for intensifying QEMS waves and contribute to the establishment of QEMS wave model.
In this study, we utilize a recently introduced relativistic kappa‐type (KT) distribution function to model the omnidirectional differential flux of energetic electrons observed by the SOPA instrument on board the 1989–046 and LANL‐01A satellites at geosynchronous orbit. We derive a useful correlation between the differential flux and the distribution of particles which can directly offer those best fitting parameters (e.g., the number density N , the thermal characteristic speed θ and the spectral index κ ) strongly associated with evaluation of the electromagnetic wave instability. We adopt the assumption of a nearly isotropic pitch angle distribution (PAD) and the typical LMFIT function in the program IDL to perform a non‐linear least squared fitting, and find that the new KT distribution fits well with the observed data during different universal times both in the lower and higher energies. We also carry out the direct comparisons with the generalized Lorentzian (kappa) distribution and find that kappa distribution fits well with observational data at the relatively lower energies but display deviations at higher energies, typically above hundreds of keV. Furthermore, the fitting spectral index κ basically takes 4, 5 or 6 while the fitting parameters N and θ are quite different due to different differential fluxes of electrons at different universal times. These results, which are applied to the case of a nearly isotropic PAD, demonstrate that the particle flux satisfies the power law not only at the lower energies but also at the relativistic energies, and the new KT distribution may present valuable insights into the dynamical features in those space plasmas (e.g., the Earth's outer radiation belts and the inner Jovian magnetosphere) where highly energetic particles exist.
Abstract During the 13–14 November 2012 storm, Van Allen Probe A simultaneously observed a 10 h period of enhanced chorus (including quasi‐parallel and oblique propagation components) and relativistic electron fluxes over a broad range of L = 3–6 and magnetic local time = 2–10 within a complete orbit cycle. By adopting a Gaussian fit to the observed wave spectra, we obtain the wave parameters and calculate the bounce‐averaged diffusion coefficients. We solve the Fokker‐Planck diffusion equation to simulate flux evolutions of relativistic (1.8–4.2 MeV) electrons during two intervals when Probe A passed the location L = 4.3 along its orbit. The simulating results show that chorus with combined quasi‐parallel and oblique components can produce a more pronounced flux enhancement in the pitch angle range ∼45°–80°, consistent well with the observation. The current results provide the first evidence on how relativistic electron fluxes vary under the drive of almost continuously distributed chorus with both quasi‐parallel and oblique components within a complete orbit of Van Allen Probe.
Abstract Frequency distribution is a vital factor in determining the contribution of whistler mode chorus to radiation belt electron dynamics. Chorus is usually considered to occur in the frequency range 0.1–0.8 f ce_eq (with the equatorial electron gyrofrequency f ce_eq ). We here report an event of intense low‐frequency chorus with nearly half of wave power distributed below 0.1 f ce_eq observed by Van Allen Probe A on 27 August 2014. This emission propagated quasi‐parallel to the magnetic field and exhibited hiss‐like signatures most of the time. The low‐frequency chorus can produce the rapid loss of low‐energy (∼0.1 MeV) electrons, different from the normal chorus. For high‐energy (≥0.5 MeV) electrons, the low‐frequency chorus can yield comparable momentum diffusion to that of the normal chorus but much stronger (up to 2 orders of magnitude) pitch angle diffusion near the loss cone.
The electromagnetic ion cyclotron (EMIC) wave has long been suggested to be responsible for the rapid loss of radiation belt relativistic electrons. The test‐particle simulations are performed to calculate the bounce‐averaged pitch angle advection and diffusion coefficients for parallel‐propagating monochromatic EMIC waves. The comparison between test‐particle (TP) and quasi‐linear (QL) transport coefficients is further made to quantify the influence of nonlinear processes. For typical EMIC waves, four nonlinear physical processes, i.e., the boundary reflection effect, finite perturbation effect, phase bunching and phase trapping, are found to occur sequentially from small to large equatorial pitch angles. The pitch angle averaged finite perturbation effect yields slight differences between the transport coefficients of TP and QL models. The boundary reflection effect and phase bunching produce an average reduction of >80% in the diffusion coefficients but a small change in the corresponding average advection coefficients, tending to lower the loss rate predicted by QL theory. In contrast, the phase trapping causes continuous negative advection toward the loss cone and a minor change in the corresponding diffusion coefficients, tending to increase the loss rate predicted by QL theory. For small amplitude EMIC waves, the transport coefficients grow linearly with the square of wave amplitude. As the amplitude increases, the boundary reflection effect, phase bunching and phase trapping start to occur. Consequently, the TP advection coefficients deviate from the linear growth with the square of wave amplitude, and the TP diffusion coefficients become saturated with the amplitude approaching 1 nT or above. The current results suggest that these nonlinear processes can cause significant deviation of transport coefficients from the prediction of QL theory, which should be taken into account in the future simulations of radiation belt dynamics driven by the EMIC waves.
Abstract Recent studies have shown that chorus can efficiently accelerate the outer radiation belt electrons to relativistic energies. Chorus, previously often observed above 0.1 equatorial electron gyrofrequency f ce , was generated by energetic electrons originating from Earth's plasma sheet. Chorus below 0.1 f ce has seldom been reported until the recent data from Van Allen Probes, but its origin has not been revealed so far. Because electron resonant energy can approach the relativistic level at extremely low frequency, relativistic effects should be considered in the formula for whistler mode wave growth rate. Here we report high‐resolution observations during the 14 October 2014 small storm and firstly demonstrate, using a fully relativistic simulation, that electrons with the high‐energy tail population and relativistic pitch angle anisotropy can provide free energy sufficient for generating chorus below 0.1 f ce . The simulated wave growth displays a very similar pattern to the observations. The current results can be applied to Jupiter, Saturn, and other magnetized planets.
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