  Electrostatic behavior of a collisionless plasma in the foot region of high
Mach number perpendicular shocks is investigated through the two-dimensional
linear analysis and electrostatic particle-in-cell (PIC) simulation. The
simulations are double periodic and taken as a proxy for the situation in the
foot. The linear analysis for relatively cold unmagnetized plasmas with a
reflected proton beam shows that obliquely propagating Buneman instability is
strongly excited. We also found that when the electron temperature is much
higher than the proton temperature, the most unstable mode is the highly
obliquely propagating ion two-stream instability excited through the resonance
between ion plasma oscillations of the background protons and of the beam
protons, rather than the ion acoustic instability that is dominant for parallel
propagation. To investigate nonlinear behavior of the ion two-stream
instability, we have made PIC simulations for the shock foot region in which
the initial state satisfies the Buneman instability condition. In the first
phase, electrostatic waves grow two-dimensionally by the Buneman instability to
heat electrons. In the second phase, highly oblique ion two-stream instability
grows to heat mainly ions. This result is in contrast to previous studies based
on one-dimensional simulations, for which ion acoustic instability further
heats electrons. The present result implies that overheating problem of
electrons for shocks in supernova remnants is resolved by considering ion
two-stream instability propagating highly obliquely to the shock normal and
that multi-dimensional analysis is crucial to understand the particle heating
and acceleration processes in shocks.
