Abstract
Some hydromagnetic instabilities of a cylindrical ideally conducting fluid, which is confined by the pinch effect of an axial current, are considered. Kruskal and Schwarzschild have previously studied the instabilities of a fluid carrying a surface current. We consider a volume current distributed according to a power law, and some general stability criteria and values of maximum possible growth rates are obtained. The volume current is more stable than the surface current, and in particular an infinite instability at short wavelength is replaced by one of finite growth rate. Finally, viscosity is introduced into the plasma carrying a surface current; disturbances at very short wavelength are damped, and a first approximation is obtained to a wavelength of maximum instability.