Instabilities in a Traveling Periodic Bumpy Theta Pinch

A $\beta =1\mathrm{}$ theta pinch which, according to Haas and Wesson, would be stabilized by a traveling wave is shown to be unstable. The plasma is described by the incompressible fluid model. It is shown that most of the modes, $m\gtrsim 1.75{\delta }^{-1\mathrm{}}$, are unstable where $\delta$ is the ratio of the amplitude of the radius modulation to the mean radius of the pinch.