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Register a new userQuasi-adiabatic and stochastic heating and particle acceleration at quasi-perpendicular shocks
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Added by
Krzysztof Stasiewicz
Publication date
2020
fields
Physics
and research's language is
English
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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.
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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.
Shock accelerated electrons are found in many astrophysical environments, and the mechanisms by which they are accelerated to high energies are still not completely clear. For relatively high Mach numbers, the shock is supercritical, and its front exhibit broadband fluctuations, or ripples. Shock surface fluctuations have been object of many observational and theoretical studies, and are known to be important for electron acceleration. We employ a combination of hybrid Particle-In-Cell and test-particle methods to study how shock surface fluctuations influence the acceleration of suprathermal electrons in fully three dimensional simulations, and we give a complete comparison for the 2D and 3D cases. A range of different quasi-perpendicular shocks in 2D and 3D is examined, over a range of parameters compatible with the ones observed in the solar wind. Initial electron velocity distributions are taken as kappa functions, consistent with solar wind emph{in-situ} measurements. Electron acceleration is found to be enhanced in the supercritical regime compared to subcritical. When the fully three-dimensional structure of the shock front is resolved, slightly larger energisation for the electrons is observed, and we suggest that this is due to the possibility for the electrons to interact with more than one surface fluctuation per interaction. In the supecritical regime, efficient electron energisation is found also at shock geometries departing from $theta_{Bn}$ very close to 90$^circ$. Two dimensional simulations show indications of unrealistic electron trapping, leading to slightly higher energisation in the subcritical cases.
The structure of whistler precursor in a quasi-perpendicular shock is studied within two-fluid approach in one-dimensional case. The complete set of equations is reduced to the KdV equation, if no dissipation is included. With a phenomenological resistive dissipation the structure is described with the KdV-Burgers equation. The shock profile is intrinsically time dependent. For sufficiently strong dissipation, temporal evolution of a steepening profile results in generation of a stationary decaying whistler ahead of the shock front. With the decrease of the dissipation parameter whistler wavetrains begin to detach and propagate toward upstream and the ramp is weakly time dependent. In the weakly dissipative regime the shock front experiences reformation.
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.
The acceleration of suprathermal electrons in the solar wind is mainly associated with shocks driven by interplanetary coronal mass ejections (ICMEs). It is well known that the acceleration of electrons is much more efficient at quasi-perpendicular shocks than at quasi-parallel ones. Yang et al. (2018, ApJ, 853, 89) (hereafter YEA2018) studied the acceleration of suprathermal electrons at a quasi-perpendicular ICME-driven shock event to claim the important role of shock drift acceleration (SDA). Here, we perform test-particle simulations to study the acceleration of electrons in this event, by calculating the downstream electron intensity distribution for all energy channels assuming an initial distribution based on the averaged upstream intensities. We obtain simulation results similar to the observations from YEA2018 as follows. It is shown that the ratio of downstream to upstream intensities peaks at about 90$^circ$ pitch angle. In addition, in each pitch angle direction the downstream electron energy spectral index is much larger than the theoretical index of diffusive shock acceleration. Furthermore, considering SDA, the estimated drift length is proportional to the electron energy but the drift time is almost energy independent. Finally, we use a theoretical model based on SDA to describe the drift length and time, especially, to explain their energy dependence. These results indicate the importance of SDA in the acceleration of electrons by quasi-perpendicular shocks.
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