Stability of a z‐pinch with rising current

A two‐dimensional resistive MHD code is used to examine the stability of a z‐pinch to m=0 perturbations under conditions of rising current. The current waveform is chosen to rise according to the one‐third power of time in order to keep the unperturbed radius of the pinch constant. One‐dimensional calculations show that regardless of the initial shape of the current density profile, the plasma column recovers the self‐similar profile dictated by this current rise. In two‐dimensions, initial perturbations corresponding to m=0 instability modes oscillate without growing or grow weakly at low values of the current in apparent contradiction to ideal MHD theory. At high current, the pinch is unstable with a growth rate predicted by ideal MHD. This is put forward as a possible explanation of experimental results which shown anomalously stable Z‐pinches. Enhanced stability is also seen for low values of the Lundquist number when the current is set to the Pease‐Braginskii value where the ohmic heating and radiati...