Hydromagnetic Instabilities in the Dense Plasma Focus

Coaxial discharges of the Mather type owe their performance to the rapid collapse of a noncylindrical current sheath into a dense plasma focus. The lifetime of the resulting fountainlike pinch column appears to be governed by the formation of sausage instabilities; however, typical estimates of the buildup time for m = 0 hydromagnetic instabilities in cylindrical columns are at least 5–10 times shorter than the observed lifetimes (∼50 nsec). In order to study the effect of pinch curvature a hydromagnetic stability analysis is performed in terms of the Bernstein energy principle expressed in curvilinear coordinates. A necessary stability condition for curved pinches with no axial magnetic fields turns out to be the presence of a delta-function current singularity on the axis, in accordance with hard-core pinch measurements of Colgate. For noncylindrical, axisymmetric pinches of finite curvature and large aspect ratio the m = 0 instability is found to grow about 10 times slower than the corresponding cylindrical pinch case.