Stability of Twisted Magnetic Fields in a Fluid of Finite Electrical Conductivity

Abstract

A formal solution is given for the problem of the stability of uniformly twisted magnetic fields in an incompressible inviscid fluid of finite scalar viscosity and electrical conductivity. The perturbed hydromagnetic equations in the conducting fluid can be reduced to a single 10th order differential equation which can be solved in terms of Bessel functions. The solution is formal in the sense that, when boundary conditions are applied, the problem is reduced to the solution of an extremely complicated transcendental dispersion relation. If there is no axial magnetic field and only axisymmetric perturbations are considered, the problem can be solved completely. If the magnetic field is twisted and perturbations other than axisymmetric perturbations are considered, there are always perturbation helices which exactly match the magnetic field helix. For the case of twisted magnetic fields and arbitrary perturbations, finite electric conductivity alone is considered. In the cases that can be solved completely, the growth rates for infinite and zero conductivity are the extreme values. In the cases considered it was found that, with a suitable the correlation coefficients in the relativistic case is discussed. (auth) normalization, the growth rate for a fluid of low conductivity is greater than that for amore » fluid of high conductivity. The results cannot be applied to a compressible plasma but can be applied to a liquid conductor such as mercury or liquid sodium. (B.O.G.)« less