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The motion of suprathermal electrons through the quasi-perpendicular, curved bow shock is considered, using a combined test-particle and hybrid-code approach. Whistler-wave generation and pitch-angle scattering of the derived distributions is studied with an implicit full-particle code. The results are compared to published ISEE observations at the Earth's bow shock.
Spacecraft observations at the Earth's bow shock and at interplanetary shocks have established that the largest fluxes of accelerated suprathermal electrons occur in so-called shock spike events immediately downstream of the shock ramp. Previous theoretical efforts have mainly focused on explaining upstream energetic electron beams. Here we investigate the general motion and acceleration of energetic electrons in a curved, nearly perpendicular shock by numerically integrating the orbits of solar wind halo electrons in shock fields generated by a hybrid simulation (core electron fluid and kinetic ions). Close to the angle Theta(sub Bn) = 90 degs between the upstream magnetic field and shock normal, the calculations result in a (perpendicular) temperature increase proportional to the magnetic field ratio and give the highest phase space densities in the overshoot. For a steep distribution, the temperature change can correspond to an enhancement of the distribution by several orders of magnitude. These results are in agreement with predictions from adiabatic mapping. With smaller angles Theta(sub Bn), the overshoot and downstream densities fall off quickly, because the adiabatic energy gain is less and fewer electrons transmit. The shock curvature also leads to an accumulation of electrons close to 90 degs. Without pitch angle scattering, energization is only significant within a few (approximately 5 to 10 degs) degrees of the point of tangency. However, shock spike events appear to be observed more easily and farther away from 90 degs. Given that over a region of several degrees around 90 degs the theory gives enhancements of up to approximately 4 orders of magnitude, such electrons could in principle account for the typically observed enhancements of 1 to 2 orders of magnitude, if they were distributed over Theta(sub Bn). To test the idea that scattering could efficiently redistribute the energetic electrons, we have conducted test particle simulations in which artificial pitch angle scattering is included. We find that such a process can indeed be very efficient and can explain observations of shock spike events far away from Theta(sub Bn) is approximately 90 degs. The scattering naturally leads to much higher phase space densities at smaller Theta(sub Bn) than what a local one-dimensional mapping would predict and thus can account for an observed discrepancy with adiabatic theory stated in the literature.
In September 1983 the International Sun Earth Explorer 3 (ISEE 3) International Cometary Explorer (ICE) spacecraft made a long traversal of the distant dawnside flank region of the Earth's magnetosphere and had many encounters with the low Mach number bow shock. These weak shocks excite plasma wave electric field turbulence with amplitudes comparable to those detected in the much stronger bow shock near the nose region. Downstream of quasi-perpendicular (quasi-parallel) shocks, the E field spectra exhibit a strong peak (plateau) at midfrequencies (1 - 3 kHz); the plateau shape is produced by a low-frequency (100 - 300 Hz) emission which is more intense behind downstream of two quasi-perpendicular shocks show that the low frequency signals are polarized parallel to the magnetic field, whereas the midfrequency emissions are unpolarized or only weakly polarized. A new high frequency (10 - 30 kHz) emission which is above the maximum Doppler shift exhibit a distinct peak at high frequencies; this peak is often blurred by the large amplitude fluctuations of the midfrequency waves. The high-frequency component is strongly polarized along the magnetic field and varies independently of the lower-frequency waves.
We present recent high time resolution observations from an oblique (43 deg) shock crossing from the Magnetospheric Multiscale mission. Short-duration bursts between 10 and 100 ms of ion acoustic waves are observed in this event alongside a persistent reflected ion population. High time resolution (150 ms) particle measurements show strongly varying ion distributions between successive measurements, implying that they are bursty and impulsive by nature. Such signatures are consistent with ion bursts that are impulsively reflected at various points within the shock. We find that, after instability analysis using a Fried-Conte dispersion solver, the insertion of dispersive ion bursts into an already stable ion distribution can lead to wave growth in the ion acoustic mode for short durations of time. We find that impulsively reflected ions are a plausible mechanism for ion acoustic wave growth in the terrestrial bow shock and, furthermore, suggest that wave growth can lead to a small but measurable momentum exchange between the solar wind ions and the reflected population.
This paper describes plasma wave electric field measurements in the region immediately downstream of several typical quasi-parallel and quasi-perpendicular flank skocks.
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Collisionless shock waves in supernova remnants and the solar wind heat electrons less effectively than they heat ions, as is predicted by kinetic simulations. However, the values of T e /T p inferred from the Hα profiles of supernova remnant shocks behave differently as a function of Mach number or Alfvén Mach number than what is measured in the solar wind or predicted by simulations. Here we determine T e /T p for supernova remnant shocks using Hα profiles, shock speeds from proper motions, and electron temperatures from X-ray spectra. We also improve the estimates of sound speed and Alfvén speed used to determine Mach numbers. We find that the Hα determinations are robust and that the discrepancies among supernova remnant shocks, solar wind shocks, and computer-simulated shocks remain. We discuss some possible contributing factors, including shock precursors, turbulence, and varying preshock conditions.
Collisionless shock waves in high beta plasmas and in cold plasmas
The adiabatic energy gain of electrons in the stationary electric and magnetic field structure of collisionless shock waves was examined analytically in reference to conditions of the earth's bow shock. The study was performed to characterize the behavior of electrons interacting with the cross-shock potential. A normal incidence frame (NIF) was adopted in order to calculate the reversible energy change across a time stationary shock, and comparisons were made with predictions made by the de Hoffman-Teller (HT) model (1950). The electron energy gain, about 20-50 eV, is demonstrated to be consistent with a 200-500 eV potential jump in the bow shock quasi-perpendicular geometry. The electrons lose energy working against the solar wind motional electric field. The reversible energy process is close to that modeled by HT, which predicts that the motional electric field vanishes and the electron energy gain from the electric potential is equated to the ion energy loss to the potential.
Collisionless magnetic slow shocks laminar wave train structure, using two-fluid hydromagnetics with ion cyclotron radius dispersion
Abstract Relativistic collisionless shocks are considered responsible for particle energization mechanisms leading to particle acceleration. While electron energization in shock front region of electron/ion collisionless shocks are the most studied, the mechanism of electron energization in interaction with self-generated magnetic vortices (MVs) in the upstream region is still unclear. We investigate electron energization mechanism in the upstream region of electron/ion relativistic collisionless shocks, using two dimensional particle-in-cell (PIC) simulations. We discuss mechanism of electron energization which takes place in the upstream region of the shock, where the counter stream particles interact with incoming flow. The energy gain of electrons happens during their interaction with evolving fields of self-generated magnetic vortices in this region. Three Fermi-like electron energization scenarios are discussed. Stochastic acceleration of electrons in interaction with fields of MV leads to anisotropic heating of fast electrons due to diffusion in the momentum space of electrons and, finally, synergetic effect of evolving fields of MVs leads to the formation of a power-law tail of supra-thermal particles.
The structure of interstellar shocks driven by supernova remnants and by expanding H II regions around early-type stars is discussed. Jump conditions are examined, along with shock fronts, post-shock relaxation layers, collisional shocks, collisionless shocks, nonradiative shocks, radiative atomic shocks, and shock models of observed nebulae. Effects of shock waves on interstellar molecules are examined, with reference to the chemistry behind shock fronts, infrared and vibrational-rotational cooling by molecules, and observations of shocked molecules. Some current problems and applications of the study of interstellar shocks are summarized, including the initiation of star formation by radiative shock waves, interstellar masers, the stability of shocks, particle acceleration in shocks, and shocks in galactic nuclei.
Context: Collisionless shock waves have long been considered to be among the most prolific particle accelerators in the universe. Shocks alter the plasma they propagate through, and often exhibit complex evolution across multiple scales. Interplanetary (IP) traveling shocks have been recorded in situ for over half a century and act as a natural laboratory for experimentally verifying various aspects of large-scale collisionless shocks. A fundamentally interesting problem in both heliophysics and astrophysics is the acceleration of electrons to relativistic energies (> 300 keV) by traveling shocks. Aims: The reason for an incomplete understanding of electron acceleration at IP shocks is due to scale-related challenges and a lack of instrumental capabilities. This Letter presents the first observations of field-aligned beams of relativistic electrons upstream of an IP shock, observed thanks to the instrumental capabilities of Solar Orbiter. This study presents the characteristics of the electron beams close to the source and contributes to the understanding of their acceleration mechanism. Methods: On 25 July 2022, Solar Orbiter encountered an IP shock at 0.98 AU. The shock was associated with an energetic storm particle event, which also featured upstream field-aligned relativistic electron beams observed 14 min prior to the actual shock crossing. The distance of the beam’s origin was investigated using a velocity dispersion analysis (VDA). Peak-intensity energy spectra were analyzed and compared with those obtained from a semi-analytical fast-Fermi acceleration model. Results: By leveraging Solar Orbiter’s high temporal resolution Energetic Particle Detector (EPD), we successfully showcase an IP shock’s ability to accelerate relativistic electron beams. Our proposed acceleration mechanism offers an explanation for the observed electron beam and its characteristics, while we also explore the potential contributions of more complex mechanisms.