Accurate approximation of the dispersion differential equation of ideal magnetohydrodynamics: The diffuse linear pinch
Abstract
The ideal magnetohydrodynamic stability of the diffuse linear pinch is studied in the special case when the poloidal magnetic field component is small compared with the axial field component. A two-term approximation for growth rates is derived by straightforward asymptotic expansion in terms of a small parameter that is proportional to (Bϑ/rBz). Evaluation of the second term in the expansion requires only a trivial amount of additional computation after the leading-order eigenvalue and eigenfunction are determined. For small, but finite, values of the expansion parameter the second term is found to be non-negligible compared with the leading term. The approximate solution is compared with exact solutions and the range of validity of the approximation is investigated. Implications of these results to a wide class of problems involving weakly unstable near ϑ-pinch configurations are discussed.
- Publication:
-
Physics of Fluids
- Pub Date:
- April 1980
- DOI:
- 10.1063/1.863059
- Bibcode:
- 1980PhFl...23..783B
- Keywords:
-
- Approximation;
- Hydrodynamic Equations;
- Magnetic Field Configurations;
- Magnetohydrodynamic Stability;
- Plasma Diffusion;
- Theta Pinch;
- Differential Equations;
- Eigenvalues;
- Eigenvectors;
- Plasma Equilibrium;
- Plasma Physics