The afterglow emission from gamma-ray bursts (GRBs) is usually interpreted as synchrotron radiation from electrons accelerated at the GRB external shock that propagates with relativistic velocities into the magnetized interstellar medium. By means of multi-dimensional particle-in-cell simulations, we investigate the acceleration performance of weakly magnetized relativistic shocks, in the magnetization range 0 ? 10?1. The pre-shock magnetic field is orthogonal to the flow, as generically expected for relativistic shocks. We find that relativistic perpendicular shocks propagating in electron-positron plasmas are efficient particle accelerators if the magnetization is ? 10?3. For electron-ion plasmas, the transition to efficient acceleration occurs for ? 3 ? 10?5. Here, the acceleration process proceeds similarly for the two species, since the electrons enter the shock nearly in equipartition with the ions, as a result of strong pre-heating in the self-generated upstream turbulence. In both electron-positron and electron-ion shocks, we find that the maximum energy of the accelerated particles scales in time as ?maxt 1/2. This scaling is shallower than the so-called (and commonly assumed) Bohm limit ?maxt, and it naturally results from the small-scale nature of the Weibel turbulence generated in the shock layer. In magnetized plasmas, the energy of the accelerated particles increases until it reaches a saturation value ?sat/?0 mic 2 ~ ??1/4, where ?0 mic 2 is the mean energy per particle in the upstream bulk flow. Further energization is prevented by the fact that the self-generated turbulence is confined within a finite region of thickness ??1/2 around the shock. Our results can provide physically grounded inputs for models of non-thermal emission from a variety of astrophysical sources, with particular relevance to GRB afterglows.

https://iopscience.iop.org/article/10.1088/0004-637X/771/1/54/pdf

The maximum energy of accelerated particles in relativistic collisionless shocks

Collisionless shocks, that is shocks mediated by electromagnetic processes, are customary in space physics and in astrophysics. They are to be found in a great variety of objects and environments: magnetospheric and heliospheric shocks, supernova remnants, pulsar winds and their nebulae, active galactic nuclei, gamma-ray bursts and clusters of galaxies shock waves. Collisionless shock microphysics enters at different stages of shock formation, shock dynamics and particle energization and/or acceleration. It turns out that the shock phenomenon is a multi-scale non-linear problem in time and space. It is complexified by the impact due to high-energy cosmic rays in astrophysical environments. This review adresses the physics of shock formation, shock dynamics and particle acceleration based on a close examination of available multi-wavelength or in situ observations, analytical and numerical developments. A particular emphasis is made on the different instabilities triggered during the shock formation and in association with particle acceleration processes with regards to the properties of the background upstream medium. It appears that among the most important parameters the background magnetic field through the magnetization and its obliquity is the dominant one. The shock velocity that can reach relativistic speeds has also a strong impact over the development of the micro-instabilities and the fate of particle acceleration. Recent developments of laboratory shock experiments has started to bring some new insights in the physics of space plasma and astrophysical shock waves. A special section is dedicated to new laser plasma experiments probing shock physics.

The microphysics of collisionless shock waves

On 30 August 2007 Voyager 2 began to cross the termination shock, a boundary produced by the inter-action of the Sun with the rest of the Galaxy, where the supersonic solar wind abruptly slows as it presses outward against the surrounding interstellar matter. Five Letters in this issue present the data that the probe sent back. The Voyager 2 crossings occurred about 1.5 billion kilometres closer to the Sun than those of Voyager 1, illustrating the asymmetry of the heliosphere. The results from the plasma experiment, low-energy particle, cosmic ray, magnetic field and plasma-wave detectors reveal a complex and dynamic shock, reforming itself in hours rather than days. The cover graphic of Voayer 2 on the brink of entering interstellar space is by Henry Kline of JPL. It may be decades before another probe crosses the termination shock but remote observations can now bridge the gap — as shown by Wang et al. who report measurements of energetic neutral atoms in the heliosheath from the STEREO A and B spacecraft that complement the Voyager in situ observations made at the same time. In News & Views, J R Jokipii puts the Voyager findings into context. For more on the on Voyager odyssey, see page 24, and the Author page, and go to the movie on http://www.nature.com/nature/videoarchive/voyager
 . A transition between the supersonic solar wind and the subsonic heliosheath happens at the 'termination shock'. This paper reports observations of the magnetic field structure and dynamics of the termination shock, made by Voyager 2 on 31 August–1 September 2007 at 83.7 au from the Sun. The data revealed a complex shock of moderate strength undergoing reformation on a scale of a few hours, rather than the expected days A transition between the supersonic solar wind and the subsonic heliosheath was observed by Voyager 1, but the expected termination shock was not seen owing to a gap in the telemetry1,2,3,4. Here we report observations of the magnetic field structure and dynamics of the termination shock, made by Voyager 2 on 31 August–1 September 2007 at a distance of 83.7 au from the Sun (1 au is the Earth–Sun distance). A single crossing of the shock was expected, with a boundary that was stable on a timescale of several days. But the data reveal a complex, rippled, quasi-perpendicular supercritical magnetohydrodynamic shock of moderate strength undergoing reformation on a scale of a few hours. The observed structure suggests the importance of ionized interstellar atoms (‘pickup protons’) at the shock.

Magnetic fields at the solar wind termination shock

Collisionless shocks, that is shocks mediated by electromagnetic processes, are customary in space physics and in astrophysics. They are to be found in a great variety of objects and environments: magnetospheric and heliospheric shocks, supernova remnants, pulsar winds and their nebulae, active galactic nuclei, gamma-ray bursts and clusters of galaxies shock waves. Collisionless shock microphysics enters at different stages of shock formation, shock dynamics and particle energization and/or acceleration. It turns out that the shock phenomenon is a multi-scale non-linear problem in time and space. It is complexified by the impact due to high-energy cosmic rays in astrophysical environments. This review adresses the physics of shock formation, shock dynamics and particle acceleration based on a close examination of available multi-wavelength or in-situ observations, analytical and numerical developments. A particular emphasize is made on the different instabilities triggered during the shock formation and in association with particle acceleration processes with regards to the properties of the background upstream medium. It appears that among the most important parameters the background magnetic field through the magnetization and its obliquity is the dominant one. The shock velocity that can reach relativistic speeds has also a strong impact over the development of the micro-instabilities and the fate of particle acceleration. Recent developments of laboratory shock experiments has started to bring some new insights in the physics of space plasma and astrophysical shock waves. A special section is dedicated to new laser plasma experiments probing shock physics

Solar flares--the most powerful explosions in the solar system--are also efficient particle accelerators, capable of energizing a large number of charged particles to relativistic speeds. A termination shock is often invoked in the standard model of solar flares as a possible driver for particle acceleration, yet its existence and role have remained controversial. We present observations of a solar flare termination shock and trace its morphology and dynamics using high-cadence radio imaging spectroscopy. We show that a disruption of the shock coincides with an abrupt reduction of the energetic electron population. The observed properties of the shock are well reproduced by simulations. These results strongly suggest that a termination shock is responsible, at least in part, for accelerating energetic electrons in solar flares.

https://science.sciencemag.org/content/sci/350/6265/1238.full.pdf

Particle acceleration by a solar flare termination shock.

. The overall structure of quasi-perpendicular, high Mach number collisionless shocks is controlled to a large extent by ion reflection at the shock ramp. Departure from a strictly one-dimensional structure is indicated by simulation results showing that the surface of such shocks is rippled, with variations in the density and all field components. We present a detailed analysis of these shock ripples, using results from a two-dimensional hybrid (particle ions, electron fluid) simulation. The process that generates the ripples is poorly understood, because the large gradients at the shock ramp make it difficult to identify instabilities. Our analysis reveals new features of the shock ripples, which suggest the presence of a surface wave mode dominating the shock normal magnetic field component of the ripples, as well as whistler waves excited by reflected ions. Key words. Space plasma physics (numerical simulation studies; shock waves; waves and instabilities)

https://angeo.copernicus.org/articles/21/671/2003/angeo-21-671-2003.pdf

The properties and causes of rippling in quasi-perpendicular collisionless shock fronts

Energetic electrons have been widely observed downstream of the Earth's bow shock, although the exact electron acceleration mechanism is not completely understood. Using a combination of hybrid shock simulation and electron test particles, we show how trapping by two dimensional structure in the form of ripples can cause electrons to be convected downstream with the magnetic field, despite having magnetic moments which suggest that they should be reflected upstream. These electrons undergo considerable Fermi acceleration during this shock transition and may explain the observed energetic downstream populations.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000GL000095

R. E. Lowe

Papers

The properties and causes of rippling in quasi-perpendicular collisionless shock fronts

Energetic electrons downstream of Earth's bow shock: Simulations of acceleration by shock structure