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Turbulence-dominated Shock Waves: 2D Hybrid Kinetic Simulations
Abstract We investigate the interaction of turbulence with shock waves by performing 2D hybrid kinetic simulations. We inject force-free magnetic fields upstream that are unstable to the tearing-mode instability. The magnetic fields evolve into turbulence and interact with a shock wave whose sonic Mach number is 2.4. Turbulence properties, the total and normalized residual energy and the normalized cross helicity, change across the shock wave. While the energy of velocity and magnetic fluctuations is mostly distributed equally upstream, the velocity fluctuations are amplified dominantly downstream of the shock wave. The amplitude of turbulence spectra for magnetic, velocity, and density fluctuations are also increased at the shock wave while their spectral index remains unchanged. We compare our results with the Zank et al. model of turbulence transmission across a shock, and find that it provides a reasonable explanation for the spectral change across the shock wave. We find that particles are efficiently accelerated at the shock front, and a power-law spectrum forms downstream. This can be explained by diffusive shock acceleration, in which particles gain energy by being scattered upstream and downstream of a shock wave. The trajectory of an accelerated particle suggests that upstream turbulence plays a role scattering of more »
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Publication Date:
NSF-PAR ID:
10316501
Journal Name:
The Astrophysical Journal
Volume:
926
Issue:
2
ISSN:
0004-637X
5. We have performed two-dimensional hybrid simulations of non-relativistic collisionless shocks in the presence of pre-existing energetic particles (‘seeds’); such a study applies, for instance, to the re-acceleration of galactic cosmic rays (CRs) in supernova remnant (SNR) shocks and solar wind energetic particles in heliospheric shocks. Energetic particles can be effectively reflected and accelerated regardless of shock inclination via a process that we call diffusive shock re-acceleration. We find that re-accelerated seeds can drive the streaming instability in the shock upstream and produce effective magnetic field amplification. This can eventually trigger the injection of thermal protons even at oblique shocks that ordinarily cannot inject thermal particles. We characterize the current in reflected seeds, finding that it tends to a universal value $J\simeq en_{\text{CR}}v_{\text{sh}}$ , where $en_{\text{CR}}$ is the seed charge density and $v_{\text{sh}}$ is the shock velocity. When applying our results to SNRs, we find that the re-acceleration of galactic CRs can excite the Bell instability to nonlinear levels in less than ${\sim}10~\text{yr}$ , thereby providing a minimum level of magnetic field amplification for any SNR shock. Finally, we discuss the relevance of diffusive shock re-acceleration also for other environments, such as heliospheric shocks, galactic superbubbles and clusters of galaxies.