Ambit fields are a flexible class of tempo-spatial random fields that has been introduced less than 10 years ago by Barndorff Nielsen and Schmiegel for the purpose of modeling velocities in turbulent flows. An important subclass of null-spatial ambit fields are Levy semistationary processes. We present limit theorems for the power variation of these processes in the setting of infill asymptotics when the driving Levy process is a pure jump process. The asymptotic results turn out to heavily depend on the interplay between the the considered power, the Blumenthal-Getoor index of the driving Levy process and the behaviour of the kernel function at 0.