Non-linear analysis of the stability of the Screw Pinch.
Abstract
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 topartial ^2 A/partial t^2 = λ ^2 A + α 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.
- Publication:
-
Astrophysics and Space Science
- Pub Date:
- August 1982
- DOI:
- 10.1007/BF00651831
- Bibcode:
- 1982Ap&SS..86...71S
- Keywords:
-
- Incompressible Fluids;
- Magnetic Field Configurations;
- Magnetohydrodynamic Stability;
- Screw Pinch;
- Linear Equations;
- Nonlinear Equations;
- Nonlinearity;
- Numerical Analysis;
- Plasma Physics;
- Schroedinger Equation;
- Temporal Distribution;
- Theta Pinch;
- Zeta Pinch;
- Plasma Physics;
- Magnetohydrodynamics:Plasma