The interaction of a powerful non-symmetric laser pulse with
a plasma is studied. The non-symmetry is manifested in an abrupt cut-off of
the rear edge
of the laser pulse compared with its leading edge. At the same time, three
qualitatively different regions are distinguished: the leading edge,
the rear
edge and the region behind the pulse, where it leaves a wake in the form of
generated fields. An analytical solution has been found that defines the
longitudinal accelerating field at the end of the rear edge. The results of
numerical calculations confirm our physical point of view that the
non-symmetry of the laser pulse increases the duration of the ion
channel behind the
front, thereby enhancing the focusing and effective acceleration of
electron bunches.