  It is shown that ions can be accelerated to MeV energy range in the direction
perpendicular to the magnetic field by the ExB mechanism of electrostatic
waves. The acceleration occurs in discrete steps of duration being a small
fraction the gyroperiod and can explain observations of ion energization to 10
keV at quasi-perpendicular shocks and to 100-1000 keV at quasi-parallel shocks.
A general expression is provided for the maximum energy of ions accelerated in
shocks of arbitrary configuration. The waves involved in the acceleration are
related to three cross-field current-driven instabilities: the lower hybrid
drift (LHD) instability induced by the density gradients in shocks and
shocklets, followed by the modified two-stream (MTS) and electron cyclotron
drift (ECD) instabilities, induced by the ExB drift of electrons in the strong
LHD wave electric field. The ExB wave mechanism accelerates heavy ions to
energies proportional to the atomic mass number, which is consistent with
satellite observations upstream of the bow shock and also with observations of
post-shocks in supernovae remnants.
