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Local acceleration of protons to 100 keV in a quasi-parallel bow shock

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 Publication date 2021
  fields Physics
and research's language is English




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Recent observations in the quasi-parallel bow shock by the MMS spacecraft show rapid heating and acceleration of ions up to an energy of about 100 keV. It is demonstrated that a prominent acceleration mechanism is the nonlinear interaction with a spectrum of waves produced by gradient driven instabilities, including the lower hybrid drift (LHD) instability, modified two-stream (MTS) instability and electron cyclotron drift (ECD) instability. Test-particle simulations show that the observed spectrum of waves can rapidly accelerate protons up to a few hundreds keV by the ExB mechanism. The ExB wave mechanism is related to the surfatron mechanism at shocks but through the coupling with the stochastic heating condition it produces significant acceleration on much shorter temporal and spatial scales by the interaction with bursts of waves within a cyclotron period. The results of this paper are built on the heritage of four-point measurement techniques developed for the Cluster mission and imply that the concepts of Fermi acceleration, diffusive shock acceleration, and shock drift acceleration are not needed to explain proton acceleration to hundreds keV at the Earths bow shock.



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Using Magnetospheric Multiscale (MMS) observations at the Earths quasi-parallel bow shock we demonstrate that electrons are heated by two different mechanisms: a quasi-adiabatic heating process during magnetic field compression, characterized by the isotropic temperature relation $T/B=(T_0/B_0)(B_0/B)^{alpha}$ with $alpha=2/3$ when the electron heating function $|chi_e|<1$, and a stochastic heating process when $|chi_e|>1$. Both processes are controlled by the value of the stochastic heating function $chi_j = m_j q_j^{-1} B^{-2}mathrm{div}(mathbf{E}_perp)$ for particles with mass $m_j$ and charge $q_j$ in the electric and magnetic fields $mathbf{E}$ and $mathbf{B}$. Test particle simulations are used to show that the stochastic electron heating and acceleration in the studied shock is accomplished by waves at frequencies (0.4 - 5) $f_{ce}$ (electron gyrofrequency) for bulk heating, and waves $f>5,f_{ce}$ for acceleration of the tail of the distribution function. Stochastic heating can give rise to flat-top electron distribution functions, frequently observed near shocks. It is also shown that obliquely polarized electric fields of electron cyclotron drift (ECD) and ion acoustic instabilities scatter the electrons into the parallel direction and keep the isotropy of the electron distribution. The results reported in this paper may be relevant to electron heating and acceleration at interplanetary shocks and other astrophysical shocks.
Based on Magnetospheric Multiscale (MMS) observations from the Earths bow shock, we have identified two plasma heating processes that operate at quasi-perpendicular shocks. Ions are subject to stochastic heating in a process controlled by the heating function $chi_j = m_j q_j^{-1} B^{-2}mathrm{div}(mathbf{E}_perp)$ for particles with mass $m_j$ and charge $q_j$ in the electric and magnetic fields $mathbf{E}$ and $mathbf{B}$. Test particle simulations are employed to identify the parameter ranges for bulk heating and stochastic acceleration of particles in the tail of the distribution function. The simulation results are used to show that ion heating and acceleration in the studied bow shock crossings is accomplished by waves at frequencies (1-10)$f_{cp}$ (proton gyrofrequency) for the bulk heating, and $f>10f_{cp}$ for the tail acceleration. When electrons are not in the stochastic heating regime, $|chi_e|<1$, they undergo a quasi-adiabatic heating process characterized by the isotropic temperature relation $T/B=(T_0/B_0)(B_0/B)^{1/3}$. This is obtained when the energy gain from the conservation of the magnetic moment is redistributed to the parallel energy component through the scattering by waves. The results reported in this paper may also be applicable to particle heating and acceleration at astrophysical shocks.
Low sonic Mach number shocks form in the intracluster medium (ICM) during the formation of the large-scale structure of the universe. Nonthermal cosmic-ray (CR) protons are expected to be accelerated via diffusive shock acceleration (DSA) in those ICM shocks, although observational evidence for the $gamma$-ray emission of hadronic origin from galaxy clusters has yet to be established. Considering the results obtained from recent plasma simulations, we improve the analytic test-particle DSA model for weak quasi-parallel ($Q_parallel$) shocks, previously suggested by citet{kang2010}. In the model CR spectrum, the transition from the postshock thermal to CR populations occurs at the injection momentum, $p_{rm inj}$, above which protons can undergo the full DSA process. As the shock energy is transferred to CR protons, the postshock gas temperature should decrease accordingly and the subshock strength weakens due to the dynamical feed of the CR pressure to the shock structure. This results in the reduction of the injection fraction, although the postshock CR pressure approaches an asymptotic value when the CR spectrum extends to the relativistic regime. Our new DSA model self-consistently accounts for such behaviors and adopts better estimations for $p_{rm inj}$. With our model DSA spectrum, the CR acceleration efficiency ranges $etasim10^{-3}-0.01$ for supercritical, $Q_parallel$-shocks with sonic Mach number $2.25lesssim M_{rm s}lesssim5$ in the ICM. Based on citet{ha2018b}, on the other hand, we argue that proton acceleration would be negligible in subcritical shocks with $M_{rm s}<2.25$.
Using multipoint Magnetospheric Multiscale (MMS) observations in an unusual string-of-pearls configuration, we examine in detail observations of the reformation of a fast magnetosonic shock observed on the upstream edge of a foreshock transient structure upstream of Earths bow shock. The four MMS spacecraft were separated by several hundred km, comparable to suprathermal ion gyro-radius scales or several ion inertial lengths. At least half of the shock reformation cycle was observed, with a new shock ramp rising up out of the foot region of the original shock ramp. Using the multipoint observations, we convert the observed time-series data into distance along the shock normal in the shocks rest frame. That conversion allows for a unique study of the relative spatial scales of the shocks various features, including the shocks growth rate, and how they evolve during the reformation cycle. Analysis indicates that: the growth rate increases during reformation, electron-scale physics play an important role in the shock reformation, and energy conversion processes also undergo the same cyclical periodicity as reformation. Strong, thin electron-kinetic-scale current sheets and large-amplitude electrostatic and electromagnetic waves are reported. Results highlight the critical cross-scale coupling between electron-kinetic- and ion-kinetic-scale processes and details of the nature of nonstationarity, shock-front reformation at collisionless, fast magnetosonic shocks.
89 - T. Amano , T. Katou , N. Kitamura 2020
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 Earths 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.
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