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 . This can lead to non-linear stabilization, explosive instability or eventual decay, depending on the sign of . The whole calculations have been made form=1, kink modes in a sharp boundary plasma pinch. Non-linear analysis for -pinch (0) andz-pinch () have also been discussed in detail. It has been found that non-linear theory have a destabilizing influence on both - andz-pinches.