Non-linear analysis of the stability of the Screw Pinch.

Non-linear effects on the stability of the Screw Pinch in cylindrical system surrounded by a uniform pitch magnetic field in an incompressible pressureless plasma have been studied. A linear dispersion relation governing the stability of interface has been obtained with the help of normal mode analysis. Perturbation technique has been used to obtain the non-linear Schrödinger equation for the time variation of amplitudeA(t) which evolves according to $$\partial ^2 A/\partial t^2 = \lambda ^2 A + \alpha A^3 $$ . This can lead to non-linear stabilization, explosive instability or eventual decay, depending on the sign of α. The whole calculations have been made form=1, kink modes in a sharp boundary plasma pinch. Non-linear analysis for θ-pinch (μ→0) andz-pinch (μ→∞) have also been discussed in detail. It has been found that non-linear theory have a destabilizing influence on both θ- andz-pinches.