2021 THEMIS SCIENCE NUGGETS

Beam-driven electron cyclotron harmonic waves in Earth’s magnetotail

by Xu Zhang
Department of Earth, Planetary, and Space Sciences, UCLA

Introduction

The diffuse aurora is a region of diffuse glow extending around the aurora oval, which constitutes more than 75% of the particle energy input into the ionosphere. The diffuse aurora is mainly caused by the precipitation from the plasma sheet and the Electron Cyclotron Harmonic (ECH) wave acts as one of the potential drivers to scatter electrons into the ionosphere through wave-particle interaction. An ECH wave is an electrostatic emission in the nfce (fce is the electron cyclotron frequency) to (n+1) fce frequency range with the strongest wave power between fce and 2fce. ECH waves in the magnetotail are often correlated with energetic particle injections (energetic particles injected from the magnetotail into the inner magnetosphere) and with dipolarization fronts (sharp fronts of dipolarizing magnetic flux populated by hot plasma and embedded within fast flows in the plasma sheet) [Zhang et al., 2014].

Previous theoretical work has demonstrated that ECH waves can be excited by the loss-cone instability, which is an instability driven by the positive phase space density gradient in the direction perpendicular to the magnetic field in a loss-cone distribution [Ashour-Abdalla and Kennel, 1978]. Electron cyclotron harmonic waves driven by such a loss-cone distribution are usually unstable at very large (around 88°- 89°) wave normal angles (the angle between the ambient magnetic field and the wave vector). Because of the lack of electron distribution function measurements of sufficient angular resolution to reveal the properties of the loss cone (usually less than 1° in the magnetotail) and of the cold electron population, however, such an excitation mechanism has never been proven by satellite observations directly.

Another excitation mechanism for electrostatic electron cyclotron waves was proposed by Menietti et al. [2002]. By solving the hot plasma dispersion relation, Menietti et al. [2002] demonstrated that electrostatic waves above the electron cyclotron frequency can be excited by a low-energy electron beam streaming in the direction parallel to the magnetic field in the absence of loss-cone anisotropy and be unstable at moderately oblique (about 70°) wave normal angles. This is of potential importance because it is an excitation mechanism for ECH waves that has rarely been considered before. Since ECH waves excited by loss-cone distributions are unstable at very large wave normal angles, it may be possible to distinguish between beam-driven and loss-cone driven waves observationally using the wave normal angle of ECH waves. To gather evidence of the excitation of ECH waves by electron beams, we perform a statistical survey of ECH waves using data from the Time History of Events and Macroscale Interactions during Substorms (THEMIS) mission in our work.

Figure 1. An example case to demonstrate ECH waves at moderately oblique wave normal angles. (a): Electric field waveform data in the field-aligned current (FAC) system and ZFAC points in the direction parallel to the ambient magnetic field; (b): Electric field power spectrum. The solid red line represents fce and the dashed red line represents fce; (c): Electric field power spectral density in the parallel direction; (d): Ratio of electric field power spectral density in the parallel direction to electric field power spectral density in the perpendicular direction. Only data points when total electric field power spectral density is greater than 10-4(mV/m)2/Hz are plotted; 2(e): Total electric field power spectral density (black line) and parallel electric field power spectral density (red line) as a function of frequency. The three dashed blue lines indicate lower frequency, central frequency, and upper frequency of ECH waves in its first harmonic band.

Results

An example case of ECH waves with a moderately oblique wave normal angle is shown in Figure 1 (moderately oblique wave normal angle refers to that the wave normal angle is much smaller than 88°- 89°). Considering that ECH waves are electrostatic waves with almost no magnetic field wave power, a large parallel wave electric field compared with total wave electric field shown in Figure 1(a) and 1(d) suggests that ECH waves propagated at moderately oblique WNA. We are able to derive the wave normal angle of ECH waves from the ratio between the parallel wave electric field amplitude and the total wave electric field amplitude. For this event, the value is around 73°. We then perform a statistical survey of wave normal angles of ECH waves near dipolarization fronts using the DF event list in Zhang et al. [2018]. We integrate the electric field power spectral density from fce to 2fce. When the integrated electric field power is larger than a certain threshold, that data sample is included in our ECH wave event database. We then calculated the wave normal angles of ECH waves when wave burst data are available. Our statistical results demonstrate that ECH waves with wave normal angles smaller than 80° account for 34.6% of the total ECH wave samples behind dipolarization fronts, a significant fraction (~one third) of the entire database.

Figure 2. Electron phase space density anisotropy as a function of energy and wave normal angle. Figure 2(a): Electron phase space density anisotropy is defined as f∥/f⊥ (f∥ is electron phase space density in the parallel direction, f⊥is electron phase space density in the perpendicular direction). Red color indicates parallel anisotropy and blue color indicates perpendicular anisotropy; Figure 2(b): Electron phase space density anisotropy as a function of normalized energy and wave normal angle. Energy is normalized to electron temperature.

To investigate the possible free energy sources for the moderately oblique ECH waves which account for one third of the total ECH wave samples behind DFs, we collected electron phase space density f in different directions and at energies from 50eV to 200keV when ECH waves were observed. Figure 2 shows the ratio between electron phase space density in the parallel direction and in the perpendicular direction as a function of energy and wave normal angle. Clear parallel electron flux enhancements in the subthermal energy range (around a few hundred eV) are correlated with these moderately oblique wave normal angle events, suggesting the presence of low-energy electron beams parallel to the magnetic field when moderately oblique wave normal angle ECH waves were observed. It is likely that moderately oblique wave normal angle ECH waves observed behind dipolarization fronts are generated by low-energy electron beams.

Figure 3. Dispersion surface for ECH waves. Background magnetic field strength is 50nT. Figure 3(a): Normalized wave frequency (f/fce) as a function of normalized wave number and wave normal angle. Wave number is normalized to the gyroradius of thermal electron population (electron component 1 in Table 1); Figure 3(b): wave growth rate as a function of normalized wave number and wave normal angle. Solid black line indicates the contour of zero growth rate.

Finally, we investigate generation of moderately oblique wave normal angle ECH waves by electron beams under plasma sheet conditions. Electron distributions listed in Table 1 are used as input parameters to solve the dispersion relation using Waves in Homogeneous Anisotropic Magnetized Plasma (WHAMP) [Ronnmark, 1982]. The dispersion surfaces are shown in Figure 3. The wave, which is electrostatic with no magnetic field power and has a frequency between fce and fce, is unstable at wave normal angles between 60° and 70° and most unstable at 66°, consistent with our observations.

Componentn (cm-3)T∥(keV)T∥/T⊥Vdrift/Vthermal
10.510.850
20.050.00110
30.0250.10.853
40.0250.10.85-3
Table 1. Electron distribution function

Conclusion

Using ten years (2007-2017) of THEMIS observational data, we established a database of ECH waves near dipolarization fronts. By analyzing periods when time-series fields data are available (wave-burst mode data collections), we found the surprising evidence that wave normal angles of ECH waves are sometimes much smaller than previously reported. As shown in Figure 5, field-aligned electron fluxes in the subthermal energy range are enhanced when ECH wave normal angles are moderately oblique, suggesting that these waves might be driven by cold electron beams. By solving the plasma dispersion relations using WHAMP, we found that ECH waves driven by low energy electron beams are most unstable at WNA~66° under conditions at the edge of the plasma sheet.

Electron cyclotron harmonic waves have long been thought to be driven by loss-cone instabilities. Even though what excites ECH waves is still an open question, there has been very little reconsideration of the free energy sources of ECH waves since the 1970s. Our work shows both observationally and theoretically that ECH waves can be driven by low-energy electron beams in the magnetotail. The loss-cone distribution is not the only free energy source for ECH waves in the plasma sheet: ECH waves at moderately oblique wave normal angles are most likely driven by low energy electron beams.

Reference

Ashour-Abdalla, M., and C. F. Kennel (1978), Nonconvective and convective electron cyclotron harmonic instabilities, J. Geophys. Res., 83(A4), 1531-1543. Menietti, J. D., O. Santolik, J. D. Scudder, J. S. Pickett, and D. A. Gurnett, Electrostatic electron cyclotron waves generated by low-energy electron beams, J. Geophys. Res., 107(A10), 1285, doi: 10.1029/2001JA009223, 2002

Ronnmark, K., WHAMP- Waves in Homogeneous Anisotropic Multicomponent Plasmas, Kiruna Geophys. Rep. 179, Kiruna Geophys. Inst., Kiruna, 1982.

Zhang, X.-J., V. Angelopoulos, B. Ni, R. M. Thorne, and R. B. Horne (2014), Extent of ECH wave emissions in the Earth's magnetotail, J. Geophys. Res. Space Physics, 119, 5561– 5574, doi:10.1002/2014JA019931.

Zhang, X., Angelopoulos, V., Artemyev, A. V., Liu, J. (2018). Whistler and electron firehose instability control of electron distributions in and around depolarizing flux bundles. Geophysical Research Letters, 45, 9380–9389. doi: /10.1029/2018GL079613

Zhang, X., Angelopoulos, V., Artemyev, A. V., Zhang, X.-J., Liu, J. (2021). Beam-driven electron cyclotron harmonic waves in Earth's magnetotail. Journal of Geophysical Research: Space Physics, 126, e2020JA028743. https://doi.org/10.1029/2020JA028743

Biographical Note

Xu Zhang is a post-doctoral researcher in the Department of Earth, Planetary, and Space Sciences at UCLA. His research focuses on various plasma waves and wave-particle interactions.

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