  We examine a regime in which a linearly-polarized laser pulse with
relativistic intensity irradiates a sub-critical plasma for much longer than
the characteristic electron response time. A steady-state channel is formed in
the plasma in this case with quasi-static transverse and longitudinal electric
fields. These relatively weak fields significantly alter the electron dynamics.
The longitudinal electric field reduces the longitudinal dephasing between the
electron and the wave, leading to an enhancement of the electron energy gain
from the pulse. The energy gain in this regime is ultimately limited by the
superluminosity of the wave fronts induced by the plasma in the channel. The
transverse electric field alters the oscillations of the transverse electron
velocity, allowing it to remain anti-parallel to laser electric field and
leading to a significant energy gain. The energy enhancement is accompanied by
development of significant oscillations perpendicular to the plane of the
driven motion, making trajectories of energetic electrons three-dimensional.
Proper electron injection into the laser beam can further boost the electron
energy gain.
