  Electron acceleration mechanism at high Mach number collisionless shocks
propagating in a weakly magnetized medium is investigated by a self-consistent
two-dimensional particle-in-cell simulation. Simulation results show that
strong electrostatic waves are excited via the electron-ion electrostatic
two-stream instability at the leading edge of the shock transition region as in
the case of earlier one-dimensional simulations. We observe strong electron
acceleration that is associated with the turbulent electrostatic waves in the
shock transition region. The electron energy spectrum in the shock transition
region exhibits a clear power-law distribution with spectral index of $2.0 {\rm
-} 2.5$. By analyzing the trajectories of accelerated electrons, we find that
the acceleration mechanism is very similar to shock surfing acceleration of
ions. In contrast to the ion shock surfing, however, the energetic electrons
are reflected by electron-scale electrostatic fluctuations in the shock
transition region, but not by the ion-scale cross-shock electrostatic
potential. The reflected electrons are then accelerated by the convective
electric field in front of the shock. We conclude that the multidimensional
effects as well as the self-consistent shock structure are essential for the
strong electron acceleration at high Mach number shocks.
