Formation of foreshock transients and associated secondary shocks

Upstream of shocks, the foreshock is filled with hot ions. When these ions are concentrated and thermalized around a discontinuity, a diamagnetic cavity bounded by compressional boundaries, referred to as a foreshock transient, forms. Sometimes, the upstream compressional boundary can further steepen into a secondary shock, which has been observed to accelerate particles and contribute to the primary shock acceleration. However, secondary shock formation conditions and processes are not fully understood. Using particle-in-cell simulations, we reveal how secondary shocks are formed. From 1D simulations, we show that electric fields play a critical role in shaping the shock's magnetic field structure, as well as in coupling the energy of hot ions to that of the shock. We demonstrate that larger thermal speed and concentration ratio of hot ions favors the formation of a secondary shock. From a more realistic 2D simulation, we examine how a discontinuity interacts with foreshock ions leading to the formation of a foreshock transient and a secondary shock. Our results imply that secondary shocks are more likely to occur at primary shocks with higher Mach number. With the secondary shock's previously proven ability to accelerate particles in cooperation with a planetary bow shock, it is even more appealing to consider them in particle acceleration of high Mach number astrophysical shocks.