  The oscillator representation is used for the non-perturbative description of
vacuum particle creation in a strong time-dependent electric field in the
framework of scalar QED. It is shown that the method can be more effective for
the derivation of the quantum kinetic equation (KE) in comparison with the
Bogoliubov method of time-dependent canonical transformations. This KE is used
for the investigation of vacuum creation in periodical linear and circular
polarized electric fields and also in the case of the presence of a constant
magnetic field, including the back reaction problem. In particular, these
examples are applied for a model illustration of some features of vacuum
creation of electron-positron plasma within the planned experiments on the
X-ray free electron lasers.
