Mach number dependence on the shock dynamics and non-thermal electron acceleration efficiency

The collisionless shock has been known as a natural particle accelerator in space. The standard diffusive shock acceleration (DSA) requires strong turbulence that allows the accelerated particles to be diffusively confined in the vicinity of the shock. Furthremore some form of wave-particle interactions have often been invoked as the solution to the injection problem for the particle acceleration below the threshold for the standard mechanism. Therefore, understanding kinetic instabilities for driving turbulence and resulting wave-particle interactions is crucial.

At moderate Mach numbers relevant to shocks in the heliosphere, the electron acceleration is regulated by electromagnetic waves on the whistler mode branch, which has been confirmed by MMS spacecraft observations. We show that the in-situ observation is well explained by a theory of stochastic shock drift acceleration (SSDA). In the simplest case where the wave is strong enough and particle momentum distribution is nearly isotropic, SSDA may be recognized as essentially an extension of DSA to a shock of finite thickness. The theory predicts that, as long as the simplifying assumptions above are adequate, the efficiency of particle acceleration becomes better at higher the Alfvenic Mach number in the Hoffmann-Teller frame.

While in-situ observations demonstrate the shocks are full of turbulence, the shock behaves even more violently at higher Mach numbers. This is because the Alfven-Ion-Cyclotron (AIC) instability at moderate Mach numbers transitions to the Weibel instability. Both of them are on the same dispersion branch and driven unstable by the effective anisotropy associated with the reflected ions. However, the dynamics in the Weibel regime is quite different in character. The magnetic field is substantially amplified to produce folded current sheets within the shock transition layer that eventually breaks up via spontaneous magnetic reconnection. In this process, the flow kinetic energy is once converted to magnetic energy and then finally dissipates. This suggests that there is a new energy conversion channel effective only in a very high Mach number regime. We have confirmed both in theory and numerical simulations that the process is a generic feature of high Mach number shocks relevant to young supernova remnants.