  Thermal electrons cannot directly participate in the process of diffusive
acceleration at electron-ion shocks because their Larmor radii are smaller than
the shock transition width: this is the well-known electron injection problem
of diffusive shock acceleration. Instead, an efficient pre-acceleration process
must exist that scatters electrons off of electromagnetic fluctuations on
scales much shorter than the ion gyro radius. The recently found
intermediate-scale instability provides a natural way to produce such
fluctuations in parallel shocks. The instability drives comoving (with the
upstream plasma) ion-cyclotron waves at the shock front and only operates when
the drift speed is smaller than half of the electron Alfven speed. Here, we
perform particle-in-cell simulations with the SHARP code to study the impact of
this instability on electron acceleration at parallel non-relativistic,
electron-ion shocks. To this end, we compare a shock simulation in which the
intermediate-scale instability is expected to grow to simulations where it is
suppressed. In particular, the simulation with an Alfvenic Mach number large
enough to quench the intermediate instability shows a great reduction (by two
orders of magnitude) of the electron acceleration efficiency. Moreover, the
simulation with a reduced ion-to-electron mass ratio (where the intermediate
instability is also suppressed) not only artificially precludes electron
acceleration but also results in erroneous electron and ion heating in the
downstream and shock transition regions. This finding opens up a promising
route for a plasma physical understanding of diffusive shock acceleration of
electrons, which necessarily requires realistic mass ratios in simulations of
collisionless electron-ion shocks.
