  We prove a central limit theorem for the momentum distribution of a particle
undergoing an unbiased spatially periodic random forcing at exponentially
distributed times without friction. The start is a linear Boltzmann equation
for the phase space density, where the average energy of the particle grows
linearly in time. Rescaling time, the momentum converges to a Brownian motion,
and the position is its time-integral showing superdiffusive scaling with time
$t^{3/2}$. The analysis has two parts: (1) to show that the particle spends
most of its time at high energy, where the spatial environment is practically
invisible; (2) to treat the low energy incursions where the motion is dominated
by the deterministic force, with potential drift but where symmetry arguments
cancel the ballistic behavior.
