  We present a model for quasi-phase matching (QPM) in high-order harmonic
generation (HHG). Using a one-dimensional description, we analyze the
time-dependent, ultrafast wave-vector balance to calculate the on-axis harmonic
output versus time, from which we obtain the output pulse energy. Considering,
as an example, periodically patterned argon gas, as may be provided with a grid
in a cluster jet, we calculate the harmonic output during different time
intervals within the drive laser pulse duration. We find that identifying a
suitable single spatial period is not straightforward due to the complex and
ultrafast plasma dynamics that underlies HHG at increased intensities. The
maximum on-axis harmonic pulse energy is obtained when choosing the QPM period
to phase match HHG at the leading edge of the drive laser pulse.
