Hot plasma effects on electron resonant scattering by electromagnetic ion cyclotron waves

M. Fraz Bashir
Department of Earth Planetary and Space Sciences, Univ. of California Los Angeles, USA


Relativistic electron losses in the inner magnetosphere are mainly attributed to magnetopause shadowing due to outer radial diffusion and electron scattering into the atmosphere due to their resonant interaction with various electromagnetic waves. The most effective wave mode responsible for such scattering is electromagnetic ion cyclotron (EMIC) waves (Thorne and Kennel, 1971). Resonant energies of electrons interacting with EMIC waves are well determined by the cold plasma dispersion (Summers and Thorne, 2003) and for typical $H$- and $He$- band waves this energy is usually larger than 1 MeV. Therefore, multiple observations of EMIC wave scattering of sub-MeV electrons (Capannolo et al., 2019) pose questions for models of EMIC wave resonances with such electrons. A possible solution to this puzzle is the inclusion of hot plasma effects in the EMIC wave dispersion because EMIC waves are indeed often observed in association with energetic ion injections from the magnetotail (Jun et al. 2019) and such ion populations may significantly modify the EMIC dispersion. It has been reported, however, that hot plasma effects for observed EMIC waves only result in an increase in the energy of resonant electrons (Chen et al., 2019). But these estimates were focused on EMIC wave frequencies corresponding to the peak wave intensity, whereas low-intensity higher-frequency part of EMIC waves may be more promising to scatter sub-MeV electrons (Bashir et al., 2022a). This study aims to reveal and model the hot plasma effects for relativistic electron scattering by observed EMIC waves.

This paper provides a generic hot plasma model which agrees well with the exact numerical solution and highlights the importance of hot plasma effects on the relativistic electron scattering by EMIC waves for a wide range of plasma parameters.


We analyze the hot plasma effects on relativistic electron resonant scattering based on three EMIC events (see Figure 1) observed by the Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft (Angelopoulos et al., 2008) and develop a hot plasma model applicable to a wide range of plasma parameters in the Earth's magnetosphere.

Where η_hs=n_0hs/n_tot is the hot plasma density ratio of the density of hot species s and total ion density, A_hs=T_(⊥hs) 〖/T〗_(∥hs)-1 is the temperature anisotropy, x=〖ω/Ω〗_p is the normalized frequency, ϵ_hs=m_hs/m_p is the mass ratio and β_(∥hs)is the plasma beta.

Based on observed EMIC waves and plasma properties, the hot plasma effects on the EMIC wave dispersion are analyzed by numerically solving the dispersion relation for EMIC waves. An analytical hot plasma model is compared with numerical solutions. We show that the hot plasma model agrees very well (within 10-15% error) with numerical results of both the EMIC frequency (see magenta curve in Figure 2a) and growth rate (see red curves in Figure 2b) for a wide range of plasma parameters and thus can be used to estimate pitch angle diffusion rates in radiation belt diffusion models and test particle simulations. The wavenumber decrease (Emin increase) for the frequency of maximum wave power is the well-known effect of hot plasma However, our results demonstrate that hot plasma effects can lower Emin as close to the cold plasma result or even lower than the cold plasma (see Figure 2c). The pitch angle diffusion rates for the observed parameters are estimated which demonstrates that the presence of hot plasma significantly changes the scattering rates (see Bashir et al., 2022b).

Figure 1. Overview of three EMIC wave events captured by THEMIS. Each set of panels from top to bottom shows the fpe/fce, magnetic wave power, ellipticity, wave normal angle (WNA), ion omnidirectional flux and ion flux anisotropy.

Figure 2. Comparison of the numerical and analytical model for the observed EMIC wave events based on ion distribution fits from Fig. 1.


We have presented an analytical hot plasma model for EMIC wave dispersion relation and verified this model with numerical solutions based on observed EMIC wave parameters during three cases. Note that although we focused on proton-electron plasma, the model provided can be applied to multi-ion (including heavy ions) plasma. The main conclusions of our study are: 1. The presented analytical model of hot plasma effects for EMIC waves outputs the wavenumber (and growth rate) in excellent agreement with the numerical solutions (with a 10-15% error). This model can be used to evaluate more precisely the diffusion coefficients and nonlinear wave-particle interactions.

2. The hot plasma effects significantly increase the minimum energy of electrons resonating with the most intense EMIC waves (waves with frequencies corresponding to the maximum growth rate) but can decrease the minimum resonant energy for the higher-frequency part of EMIC spectra corresponding to smaller wave intensity (marginally stable waves). Therefore, a proper evaluation of the minimum energy of electrons that undergo resonant scattering by EMIC waves requires investigation of the entire unstable wave frequency range.

3. The estimated pitch angle scattering rate based on the hot plasma model, realistic plasma, and wave spectrum parameters shows that the hot plasma effects significantly change the scattering rates and expand the electron pitch angle range for the interaction between EMIC and relativistic electrons.


Bashir, M. F., Artemyev, A., Zhang, X.-J., and Angelopoulos, V. (2022a). Energetic electron precipitation driven by the combined effect of ulf, emic, and whistler waves. Journal of Geophysical Research: Space Physics, 127 (1), e2021JA029871. doi: https://doi.org/10.1029/2021JA029871

Bashir, M. F., Artemyev, A., Zhang, X.-J., and Angelopoulos, V. (2022b). Hot Plasma Effects on Electron Resonant Scattering by Electromagnetic Ion Cyclotron Waves, Geophys. Res. Lett., 49, e2022GL099229.

Chen, L., Zhu, H., and Zhang, X. (2019). Wavenumber Analysis of EMIC Waves Geophys. Res. Lett., 46 (11), 5689-5697. doi: 10.1029/2019GL082686

Capannolo, L., Li, W., Ma, Q., Chen, L., Shen, X. C., Spence, H. E., Redmon, R. J. (2019). Direct Observation of Sub-Relativistic Electron Precipitation Potentially Driven by EMIC Waves. Geophys. Res. Lett. doi:10.1029/2019GL084202

Summers, D., and Thorne, R. M. (2003). Relativistic electron pitch-angle scattering by electromagnetic ion cyclotron waves during geomagnetic storms. J. Geophys. Res., 108 , 1143. doi: 10.1029/2002JA009489352

Thorne, R. M., and Kennel, C. F. (1971). Relativistic electron precipitation during magnetic storm main phase. J. Geophys. Res., 76, 4446. doi: 10.1029/JA076i019p04446

Biographical Note

M. Fraz Bashir is an Assistant Researcher in the Department of Earth, Planetary, and Space Sciences at UCLA. His research focuses on gaining a better understanding of the complex electromagnetic phenomena in the Sub-Earth System, and their role in predicting/modeling the space weather event, and quantifying particle loss, acceleration, and transport mechanism.

Please send comments/suggestions to
Emmanuel Masongsong / emasongsong @ igpp.ucla.edu