  The energy gain in laser wakefield acceleration (LWFA) is ultimately limited
by dephasing, occurring when accelerated electrons outrun the accelerating
phase of the wakefield. We apply quasi-phasematching, enabled by axially
modulated plasma channels, to overcome this limitation. By matching the
modulation period to the dephasing length, a relativistic electron can undergo
energy gain over several dephasing lengths. Theory and simulations are
presented showing that at a weakly relativistic laser intensity, ~10^17 W/cm2,
and millijoule level pulse energies, quasi-phasematched LWFA results in energy
gains of 50 MeV larger than standard LWFA.
