On the hydromagnetic stability of an axially-symmetric rotating plasma with finite pressure

In the framework of the ideal single-liquid magnetic hydrodynamics stability of a rotating plasma filament in a strong longitudinal magnetic field is studied. It is shown that for axially-symmetric distortions the boundary-value problem is self-conjugate. At a homogeneous initial radial profile of the plasma pressure and rotation frequencies the effect of the finite pressure on the system stability is studied. At small values of the rotation frequency Ω< or approximately asup(4)Ωsup(4)/Csub(A)sup(4), where a is the the plasma filament radius, β - the ratio of the plasma pressure and magnetic pressure Csub(A)-alfven velocity, Csub(s)-thermal velocity of ions. At Csub(s)>>aΩ the rotating plasma filament is stable. It is shown that rather hot rotating plasma is stable. This fact can explain the stability of THETA pinches in which plasma practically always rotates