Hot plasma decoupling condition for long wavelength modes

The stability of layer modes is analyzed for z-pinch and bumpy cylinder models. These modes have long wavelength across the layer and are flute-like along the field line. The stability condition can be expressed in terms of the ratio of hot to core plasma density. It is shown that to achieve conditions close to the Lee-Van Dam, Nelson core beta limit, one needs a considerably smaller hot-to-core plasma density ratio than is required to achieve stability at zero core beta.