  In the cavitation regime of plasma-based accelerators, a population of
high-energy electrons tailing the driver can undergo betatron motion. The
motion results in X-ray emission, but the brilliance and photon energy are
limited by the electrons' initial transverse coordinate. To overcome this, we
exploit parametrically unstable betatron motion in a cavitated, axially
modulated plasma. Theory and simulations are presented showing that the
unstable oscillations increase both the total X-ray energy and average photon
energy.
