Theoretical and numerical studies of chorus waves: A review

Theoretical and numerical models of chorus waves are reviewed in this paper. Specifically, we focus on the nonlinear wave particle interactions and the current understanding of the frequency chirping of rising tone chorus waves. Various other related topics, such as the optimal excitation condition of chorus, the formation of subpackets, and the non-adiabaticity of the nonlinear interaction are also discussed. We end this review paper with a short list of questions of chorus waves that are still under research and debate.

Responses of geostationary orbit energetic electron fluxes to chorus waves under different geomagnetic conditions

We investigate the flux evolution of geostationary orbit energetic electrons during a strong storm on 24 August 2005(event A,the storm index Dst<200 nT,the average substorm index AE=436 nT)and a weak storm on 28 October 2006(event B,Dst>50 nT,average AE=320 nT).Data collected by LANL and GOES-12 satellites show that energetic electron fluxes increase by a factor of 10 during the recovery phase compared to the prestorm level for both events A and B.As the substorm continued,the Cluster C4 satellite observed strong whistler-mode chorus waves(with spectral density approaching 10 5nT2/Hz).The wave amplitude correlates with the substorm AE index,but is less correlated with the storm Dst index.Using a Gaussian distribution fitting method,we solve the Fokker-Planck diffusion equation governing the wave-particle interaction.Numerical results demonstrate that chorus waves efficiently accelerate^1 MeV energetic electrons,particularly at high pitch angles.The calculated acceleration time scale and amplitude are comparable to observations.Our results provide new observational support for chorus-driven acceleration of radiation belt energetic electrons.

Effect of seed electron injection on chorus-driven acceleration of radiation belt electrons

Using the hybrid finite difference method, we solve the Fokker-Planck equation to study the effect of seed electron injection on acceleration of radiation belt electrons driven by chorus waves. Numerical results show that in the absence of injection chorus waves can accelerate electrons at large pitch angles （ae〉60°）, producing enhancements in the phase space density （PSD） of （1-2 MeV ） electrons by a factor of 100-1000 within 1-2 days. In the presence of injection, chorus waves yield increase in PSD of electrons by accelerating the injected seed electrons. Meanwhile, the PSD evolution increases as the pitch angle in- creases but decreases as electron energy increases. Moreover, the PSD evolution can extend to higher energies with a time scale of 1-2 days for 1-2 MeV energies. When the injection increases by a factor of 10 higher than the initial value and re- mains for about two days, maximum values of PSD for 1 or 2 MeV increase to 6 or 3 times respectively higher than those without injection in two days. The current results suggest that the injected seed electrons play an important role in the evolu- tion of the radiation belt electrons.

Observations and parametric study on the role of plasma density on extremely low-frequency chorus wave generation

Extremely low-frequency(ELF)chorus waves with frequencies below 0.1 fcecan cause the scattering losses of relativistic electrons.Previous studies have suggested that ELF chorus waves are excited by anisotropic electrons with energies up to a few hundred ke V.Here,we report an interesting event observed using the Van Allen Probes on November 1,2012,where distinct ELF chorus waves occurred exactly corresponding to the enhancement of the plasma density.Using the correlated data of particles and plasma environments,the continuous calculation of growth rates along the satellite trajectory was conducted.The linear analysis results display a similar pattern to the observation results.To further identify the impact of the plasma density on the frequency control of ELF chorus waves,the growth rates were then calculated by only changing the value of the plasma density.The calculation results show that the growth rates move to lower frequencies with plasma density enhancement during the event.These findings indicate that the increased plasma density has a considerable impact on the wave frequency.The current study can enrich our understanding of the possible role of plasma density on the generation of ELF chorus waves.

Magnetospheric chorus wave instability induced by relativistic Kappa-type distributions

We study the field-aligned propagating magnetospheric chorus wave instability using a fully relativistic wave growth formula,the previously developed relativistic Kappa-type(KT) distribution and the regular Kappa distribution of energetic electrons.We demonstrate that the peak growth rate using the nonrelativistic Kappa simulation is higher than that using either the relativistic KT or the Kappa simulation at/above 100 keV, because the significant relativistic effect yields a reduction in the relativistic anisotropy. The relativistic anisotropy Arel basically decreases as the thermal parameter θ2 increases, allowing the peak growth by relativistic KT or Kappa distribution to stay at the lower frequency region. The growth rates tend to increase with the loss-cone parameter l because the overall anisotropy increases. Moreover, at high energy ~1.0 MeV, both the growth rate and the upper cutoff frequency become smaller as l increases for the relativistic KT calculation because the significant relativistic effect reduces both the resonant anisotropy and the number of the hot electrons, which is in contrast to the relativistic and nonrelativistic Kappa distribution calculations because the less relativistic or non-relativistic effect enhances the resonant anisotropy as l increases. The above results can be applied to the whistler-mode wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons often exist.