  A long laser beam propagating through an underdense plasma produces a
positively charged ion channel by expelling plasma electrons in the transverse
direction. We consider the dynamics of a test electron in a resulting
two-dimensional channel under the action of the laser field and the transverse
electric field of the channel. A considerable enhancement of the axial momentum
can be achieved in this case via amplification of betatron oscillations. It is
shown that the oscillations can be parametrically amplified when the betatron
frequency, which increases with the wave amplitude, becomes comparable to the
frequency of its modulations. The modulations are caused by non-inertial
(accelerated/decelerated) relativistic axial motion induced by the wave
regardless of the angle between the laser electric field and the field of the
channel. We have performed a parameter scan for a wide range of wave amplitudes
and ion densities and we have found that, for a given density, there is a well
pronounced wave amplitude threshold above which the maximum electron energy is
considerably enhanced. We have also calculated a time-integrated electron
spectrum produced by an ensemble of electrons with a spread in the initial
transverse momentum. The numerical results show that the considerable energy
enhancement is accompanied by spectrum broadening. The presented mechanism of
energy enhancement is robust with respect to an axial increase of ion density,
because it relies on a threshold phenomenon rather than on a narrow linear
resonance.

Plasma Physics