Observational Evidence for Stochastic Shock Drift Acceleration of Electrons at the Earth’s Bow Shock

Abstract

The first-order Fermi acceleration of electrons requires an injection of electrons into a mildly relativistic energy range. However, the mechanism of injection has remained a puzzle both in theory and observation. We present direct evidence for a novel stochastic shock drift acceleration theory for the injection obtained with Magnetospheric Multiscale (MMS) observations at Earth's bow shock. The theoretical model can explain electron acceleration to mildly relativistic energies at high-speed astrophysical shocks, which may provide a solution to the long-standing issue of electron injection.

Magnetic pumping model for energizing superthermal particles applied to observations of the Earth's bow shock

“…The agreement demonstrated above suggests that the model is capturing the anisotropic features of the observed distribution functions. While the inferred amount of scattering is too low for SSDA 10 to be effective, it is near optimal for magnetic pumping and the analysis can now be extended to address the energization of the electrons over many cycles. Following the blueprint of the quasilinear method, we then separate the distribution function into the slowly-varying, isotropic background distribution, f 0 , and the anisotropic portion of the distribution function, f found,…”

“…In this Letter we find that magnetic pumping in the fluctuations generated in the vicinity of Earth's bow shock can provide a seed population of pre-energized magnetized electrons. Thus, along with mechanisms such as stochastic shock drift acceleration (SSDA) [8][9][10] , magnetic pumping may help address the injection problem of DSA 11,12 .…”

Parallel velocity mixing yielding enhanced electron heating during magnetic pumping

“…The regime with is likely to be relevant to the solar wind for which a recent analysis of the Strahl electrons show that pitch angle scattering is mostly limited to the low level provided by Coulomb collisions between electrons and ions (Horaites, Boldyrev & Medvedev 2019). Meanwhile, for the MMS bow-shock encounter analysed in Lichko & Egedal (2020) we estimate that , whereas the analysis of a similar MMS bow-shock event (Amano et al 2020) infer much larger values of . In future studies of in situ spacecraft data, to help determine the relevant value of of a given dataset, we note that (5.1) and (5.8) can be fitted to electron data as provided by, for example, MMS (Burch et al 2016) and may prove useful for inferring directly from the observations.…”

“…Previous work on magnetic pumping (such as transit-time damping (Barnes 1966;Berger et al 1971;Stix 1992;Lichko et al 2017)), have largely concluded that pumping is not efficient for energizing superthermal electrons with v > ω/(k cos Θ). Meanwhile, the pumping models of Egedal et al (2018) and Lichko & Egedal (2020) include the effects of trapping and differs significantly from earlier results, as the trapping permits especially electrons with v ω/(k cos Θ) to become energized.…”

Bursty betatron acceleration of electrons at nonstationary quasi-perpendicular shocks

“…Recently, a new acceleration model, a stochastic shock drift acceleration (SSDA), combination of SDA and stochastic scattering by whistler waves in the shock transition region, has been proposed [7], and observed energy spectra is well explained by the SSDA [8]. Betatron acceleration [9] is also candidate to gain perpendicular energy, accompanied by a growing overshoot magnetic field during the shock reformation.…”