Suprathermal electrons are a major heat source of ionospheric plasma. How the suprathermal electrons evolve during their bounces inside the plasmasphere is a fundamental question for the magnetosphere-ionosphere coupling. On the basis of Van Allen Probes observations and quasi-linear simulations, we present here the first quantitative study on the evolution of suprathermal electrons under the competition between Landau heating by whistler mode hiss waves and Coulomb collisional cooling by background plasma inside a plasmaspheric plume. We show that the Landau heating can prevail over the collisional cooling for >50 eV electrons and cause the field-aligned suprathermal electron fluxes to increase by up to 1 order of magnitude within 1.5 hr. Our results imply that the plasmaspheric plume hiss waves could mediate energy from the ring current electrons to the ionospheric plasma.
- The collisional cooling by background plasma counteracts largely the Landau heating by hiss waves for <50 eV electrons
- The Landau heating can increase the field-aligned fluxes of >50 eV electrons by 1 order of magnitude within 1.5 hr
- Plasmaspheric plume hiss could mediate energy from the ring current electrons through the suprathermal electrons to the ionospheric plasma
Plain Language Summary
The ionospheric plasma temperature variation can affect the Earth's atmospheric escape and the spacecraft orbit decay. A major heat source of the ionospheric plasma is the suprathermal (several eV to hundreds of eV) electrons, which can bounce along the magnetic field lines inside the plasmasphere. How these suprathermal electrons evolve during their bounces is a fundamental question for the magnetosphere-ionosphere coupling. In the past, the plasmaspheric suprathermal electrons were usually considered to gain energy from the ring current ions through Coulomb collisions and wave-particle interactions. Here we show that strong whistler mode hiss waves can grow from the instability of the ring current electrons in the plasmaspheric drainage plume, and their Landau heating can prevail over the collisional cooling by background plasma for >50 eV electrons. The enhanced field-aligned suprathermal electrons could eventually heat the ionospheric plasma. These results have significant implications for understanding the energy transfer process from the magnetosphere to the ionosphere.
The suprathermal (several eV to hundreds of eV) electrons can effectively heat the ionospheric plasma via both elastic and inelastic collisions (Lemaire & Gringauz, 1998). They are produced from the ionization of atmospheric neutral particles by solar extreme ultraviolet photons and by magnetospheric energetic particles (Schunk & Nagy, 2009). These suprathermal electrons can escape from the production region and bounce along the geomagnetic field lines in the plasmasphere (Hanson, 1964). How the plasmaspheric suprathermal electrons evolve is a fundamental question in the magnetosphere-ionosphere coupling (Khazanov & Liemohn, 1995; Khazanov et al., 1992).
During geomagnetically active times, the plasmaspheric suprathermal electrons are envisioned to conduct the heat flux from the ring current ions to the ionospheric thermal plasma (Brace et al., 1988; Foster et al., 1994; Green et al., 1986; Horwitz et al., 1986). Two leading physical processes have been proposed for such energy transfer. One is the classical Coulomb collisional scattering of the plasmaspheric suprathermal electrons by the ring current ions (e.g., Cole, 1965; Fok et al., 1991; Jordanova et al., 1996; Kozyra et al., 1987; Liemohn et al., 2000). The other is the Landau heating of the plasmaspheric suprathermal electrons by the electromagnetic ion cyclotron waves growing from instabilities of the ring current ions (e.g., Cornwall et al., 1971; Erlandson et al., 1993; Gurgiolo et al., 2005; Hasegawa & Mima, 1978; Horne & Thorne, 1993; Thorne & Horne, 1992; Yuan et al., 2014; Zhou et al., 2013). In contrast, little attention has been paid to the possible energy transfer between the ring current electrons and the plasmaspheric suprathermal electrons. Whistler mode hiss waves can be excited by the ring current electrons in the plasmasphere (Meredith et al., 2018; Omura et al., 2015; Summers et al., 2014; Su et al., 2018a, 2018b; Thorne et al., 1979), and these waves are expected to subsequently transfer part of their energy to the plasmaspheric suprathermal electrons through the Landau resonance (e.g., Bortnik et al., 2008; Chen et al., 2009). This expected process was seemly supported by an observation of the field-aligned suprathermal electron flux enhancement associated with the whistler-mode waves inside a remnant plasmaspheric plume (Woodroffe et al., 2017). Subsequently, a quasi-linear simulation (Li et al., 2019) roughly reproduced the field-aligned heating of suprathermal electrons by the Landau resonance with hiss waves in a plasmaspheric plume. However, an important cooling mechanism for suprathermal electrons (Khazanov & Liemohn, 1995), Coulomb collisions with the background plasma, has not been taken into account in the previous studies (Li et al., 2019; Woodroffe et al., 2017).
In this letter, we quantitatively investigate the competition between hiss-driven Landau heating and Coulomb collisional cooling in the evolution of plasmaspheric suprathermal electrons. Using Van Allen Probes observations and quasi-linear simulations, we determine the favored conditions for the transfer of energy from ring current electrons through field-aligned suprathermal electrons to ionospheric plasma. These results have significant implications for understanding the magnetosphere-ionosphere coupling.
2 Van Allen Probes Observations
On 30 January 2014, Van Allen Probe B passed a series of finger-like plasmaspheric plumes and observed the energy transfer among electrons of different energies (Figure 1). The Electric and Magnetic Field Instrument and Integrated Science (EMFISIS) suite (Kletzing et al., 2013) and the Energetic Particle, Composition, and Thermal Plasma (ECT) suite (Spence et al., 2013) provided data for our analysis. The Helium Oxygen Proton Electron (HOPE) Mass Spectrometer (Funsten et al., 2013) and the Magnetic Electron Ion Spectrometer (MagEIS) (Blake et al., 2013) of the ECT suite measured the electron differential flux j as a function of the local pitch angle α and the kinetic energy Ek. With the wave spectral matrix from the waveform receiver (WFR) of the EMFISIS Waves instrument, we can calculate the total magnetic power density PB, the normal angle ψB (Santolík et al., 2002, 2003), and the sign of field-aligned Poynting flux SB (Santolík et al., 2010). With the upper hybrid resonance frequency from the high frequency receiver (HFR) of the EMFISIS Waves instrument, we can derive the local cold electron density Ne (Kurth et al., 2014). The triaxial fluxgate magnetometer of the EMFISIS suite measured the local magnetic field Bo. Along a magnetic field line, we assume that the magnetic field strength scaled with the TS04 geomagnetic field model (Tsyganenko & Sitnov, 2005).
A moderate substorm occurred around 02:50 UT as identified by the increase of AE index. Approximately 40 min later, Van Allen Probe B encountered the substorm injection of electrons with energies up to 100 keV and received the strong whistler mode hiss waves with amplitudes up to 0.3 nT in the plasmaspheric plumes. These plume hiss waves propagated mainly in the anti-field-aligned direction away from the equator, consistent with previous observations (Shi et al., 2019; Su et al., 2018a; Woodroffe et al., 2017; Zhang et al., 2019). As discussed by Su et al. (2018a), these waves could be a result of the combined linear and nonlinear instabilities of the freshly injected ring current electrons (Omura et al., 2015; Summers et al., 2014; Thorne et al., 1979). Corresponding to the intense plume hiss waves (e.g., TR1 and TR2), there were significant enhancements in the field-aligned suprathermal electron fluxes at energies 50–300 eV. In contrast, no flux enhancements were observable in the absence of strong hiss waves near the plume boundary (TR0). These observations imply the link between plume hiss waves and the suprathermal electron heating. However, after 06:30 UT, Van Allen Probe B went into the plasmaspheric body but observed no enhancement of field-aligned suprathermal electron fluxes (TR3). Compared to plume hiss waves, the hiss waves in the plasmaspheric body had ∼5 times smaller amplitudes but much larger normal angles. The larger normal angles the waves have, the stronger damping the waves should experience. In addition, according to previous statistical studies (e.g., Agapitov et al., 2018; Li et al., 2015; Meredith et al., 2004; Summers et al., 2008; Tsurutani et al., 2015), the hiss waves in the plasmaspheric body should persist over a longer time than those in the plume. A question arises as to why the significant heating of suprathermal electrons tend to occur in the plasmaspheric plumes rather than in the plasmaspheric body.
3 Quasi-Linear Simulations
3.1 Numerical Model
Here F = j/p2 is the electron phase space density depending on the equatorial pitch angle αeq and the momentum p, and ⟨D⟩ and ⟨A⟩ are the diffusion and advection coefficients, with the subscripts representing the physical dimensions for transport and the superscripts “wp” and “cc” denoting wave-particle interactions and Coulomb collisions. The computational domain is set to αeq ∈ [0°, 90°] × Ek ∈ [1 eV, 1 keV]. At eV without resonances (Figure 2), the fixed boundary condition is applied. At keV, the fixed boundary condition is adopted to simulate the balance between the drift and the local resonances. At , the boundary condition is utilized to characterize the symmetry of the plasmaspheric electron distribution. At , the boundary condition is expediently used to allow the heating of the field-aligned suprathermal electrons. Considering that the ionosphere is a source of the suprathermal electrons, we artificially set inside the loss cone.
Following the work of Jordanova et al. (1996), we calculate the bounce-averaged diffusion and advection coefficients related to the Coulomb collisions with the background cold electrons. The Coulomb collisional transport related to the cold ions is negligible in comparison to that related to the cold electrons (Khazanov et al., 1996). In the calculation, the cold electron temperature is assumed to be eV, and the ambient cold electron density is specified as Equation 4. As shown in Figures 2q and 2r, the collisional transport rates and decrease steeply with the energy increasing. Below several tens of eV, the collisional transport rates are much larger than the wave-driven diffusion rates.
3.2 Model-to-Data Comparison
To allow the model-to-data comparison (Figure 3), the observed local pitch angle α is mapped to the equatorial pitch angle αeq through the conservation of magnetic moment, that is, . Along an arbitrary field line, the ratio Bo/Beq between the equatorial and local magnetic field magnitudes is determined by the TS04 geomagnetic model (Tsyganenko & Sitnov, 2005).
Figures 3b–3d clearly show the gradual wave heating of electrons from lower to higher energies along with time. For the Landau resonance with electrons below 300 eV (Figure 2), the momentum diffusion coefficients peak near and the pitch angle diffusion coefficients peak at the moderate pitch angles αeq ≈ 30°. The resulted heating effect is most significant at low pitch angles and declines with the pitch angle increasing. For >330 eV electrons, as the result of the weak momentum diffusion of the Landau resonance but the strong pitch angle diffusion of the cyclotron resonance, no heating effect is observable. At hr, the hiss-driven resonant diffusion alone has generally reproduced the flux enhancement of 264 eV electrons but overestimated the fluxes of 33–132 eV electrons by up to 10 times (Figure 3d). The addition of Coulomb collisions has caused the suprathermal electrons to deposit their energy partially in the cold plasmaspheric electrons and significantly improved the model-to-data agreement below 200 eV (Figures 3e–3h). Within 1.5 hr, the variations in the fluxes of 33 and 468 eV electrons are ignorable, and the field-aligned fluxes of 66–264 eV electrons increase by 1 order of magnitude or more. This modeling time duration of 1.5 hr is reasonable, as estimated from the available observations in Figure 1. The final sampling time was close to 05:10 UT, and a first-order estimation of the starting time of intense plume hiss waves was 03:30 UT around which Van Allen Probe B encountered the substorm injection front. There were extremely weak waves in the two finger-like plumes before 03:30 UT, and the subsequent measurements in the plumes indicated the emergence of intense hiss waves. As shown in Figure 3i, in contrast to the steadily increasing overestimation of the field-aligned fluxes over time by the model with resonant interactions alone, the addition of Coulomb collisions reduces the temporal growth rates of the field-aligned fluxes and causes these fluxes to saturate at lower levels. These simulations support the idea that the observed energy-dependent enhancement of field-aligned suprathermal electrons could result from the competition between the wave Landau heating and the Coulomb collisional cooling.
The collisional cooling rates are proportional to the background density Ne and steeply decrease with energy Ek increasing (Figure 2r). The Landau heating rates are proportional to the square of wave amplitude , and the Landau heating at higher energies is affected less by the collisional cooling. Figures 4a and 4b show the minimum Landau resonant energy ER (Summers et al., 2007) as a function of the equatorial ratio fpe/fce of plasma frequency to electron gyrofrequency, the normalized wave frequency f/fce, and the wave normal angle ψB. ER increases significantly with fpe/fce decreasing or f/fce increasing but depends less on ψB. In comparison to the plasmaspheric body, the plasmaspheric plume usually has a smaller Ne but larger Bt and f/fce (Shi et al., 2019; Su et al., 2018a). Hence, the Landau heating of plume hiss waves can prevail over the collisional cooling at relatively high energies, and the enhanced field-aligned suprathermal electrons may deposit their energy, more or less, to the ionospheric plasma.
We compare the field-aligned electron fluxes j among three representative periods in Figure 4c. As marked in Figure 1, TR1 and TR2 with intense hiss waves were inside the plasmaspheric plumes, and TR3 with moderate hiss waves was inside the plasmaspheric body. In the energy range 50 eV < Ek < 300 eV where is close to or above (Figure 4f), TR1 and TR2 had up to 1 order of magnitude larger electron fluxes than TR3. TR3 had the moderate-amplitude (Bt < 0.1 nT), low-frequency ( to 10−2) hiss waves but the dense ( ) background plasma (Figures 1b and 1c), during which the Landau heating effect centering at tens of eV could have been canceled out by the strong Coulomb collisional cooling effect. Because TR1 and TR2 had larger wave amplitudes ( –0.3 nT) and higher frequencies (f/fce > 10−2), the Laudau heating could prevail over the collisional cooling at relatively high energies. Probably because of a shorter duration of wave-particle interactions starting around 03:30 UT, TR2 had a weaker enhancement in the 50–300 eV electron fluxes than TR1.
Plasmaspheric suprathermal electrons have long been considered to conduct heat flux from the magnetosphere to the ionosphere. In contrast to previous numerous studies about the energy transfer from the ring current ions to the plasmaspheric field-aligned suprathermal electrons, we here examine whether the whistler mode hiss waves growing from the substorm-injected electron instability can heat the field-aligned suprathermal electrons. Because the plasmaspheric plume usually has a smaller plasma density but a larger hiss wave amplitude and a larger normalized wave frequency than the plasmaspheric body, the effective energy transfer from the ring current electrons through the plasmaspheric field-aligned suprathermal electrons to the ionospheric plasma is more likely to occur in the plasmaspheric plume. The quasi-linear simulation taking into account both Landau heating by the hiss waves and collisional cooling with the background plasma can well reproduce the observed energy-dependent enhancements of suprathermal electron fluxes. Below 50 eV, the collisional cooling counteracts largely the wave Landau heating. As the energy increases, the collisional cooling rates decrease steeply. Around 200 eV, the Landau heating causes the field-aligned suprathermal electron fluxes to increase by 1 order of magnitude or above on a time scale of 1.5 hr. Above 400 eV, the cyclotron resonance of hiss waves arises and contributes little to the electron enhancement. For the ionospheric electron heating rate driven by the measurable >14 eV suprathermal electrons, the enhancement of field-aligned >50 eV electrons resulting from the competition between plume hiss wave Landau heating and Coulomb collisional cooling may introduce a 30% additional contribution. Although this letter is limited to a case study, the enhancement of suprathermal electrons related to plume hiss waves appears to be not rare in the observations of Van Allen Probes (see also Li et al., 2019; Woodroffe et al., 2017). In Figures S2 and S3, we have shown two additional events to support the generality of the obtained results. Further work needs to be done to establish whether and then how the ionospheric plasma responds to the intense plume hiss waves excited by the substorm-injected energetic electrons in the magnetosphere.
We acknowledge EMFISIS and ECT teams for the use of Van Allen Probes data. This work was supported by the Strategic Priority Research Program of Chinese Academy of Sciences Grant XDB 41000000, the National Natural Science Foundation of China Grants 41774170 and 41631071, the Chinese Academy of Sciences Grants KZCX2-EW-QN510 and KZZD-EW-01-4, the CAS Key Research Program of Frontier Sciences Grant QYZDB-SSW-DQC015, the National Key Basic Research Special Foundation of China Grant 2011CB811403, the National Postdoctoral Program for Innovative Talents Grant BX20190310, the China Postdoctoral Science Foundation Grant 2019M662171, and the Fundamental Research Funds for the Central Universities WK2080000005.
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