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Thermal electrons cannot directly participate in the process of diffusiveacceleration at electron-ion shocks because their Larmor radii are smaller thanthe shock transition width: this is the well-known electron injection problemof diffusive shock acceleration. Instead, an efficient pre-acceleration processmust exist that scatters electrons off of electromagnetic fluctuations onscales much shorter than the ion gyro radius. The recently foundintermediate-scale instability provides a natural way to produce suchfluctuations in parallel shocks. The instability drives comoving (with theupstream plasma) ion-cyclotron waves at the shock front and only operates whenthe drift speed is smaller than half of the electron Alfven speed. Here, weperform particle-in-cell simulations with the SHARP code to study the impact ofthis instability on electron acceleration at parallel non-relativistic,electron-ion shocks. To this end, we compare a shock simulation in which theintermediate-scale instability is expected to grow to simulations where it issuppressed. In particular, the simulation with an Alfvenic Mach number largeenough to quench the intermediate instability shows a great reduction (by twoorders of magnitude) of the electron acceleration efficiency. Moreover, thesimulation with a reduced ion-to-electron mass ratio (where the intermediateinstability is also suppressed) not only artificially precludes electronacceleration but also results in erroneous electron and ion heating in thedownstream and shock transition regions. This finding opens up a promisingroute for a plasma physical understanding of diffusive shock acceleration ofelectrons, which necessarily requires realistic mass ratios in simulations ofcollisionless electron-ion shocks.

The mechanism of efficient electron acceleration at parallel non-relativistic shocks