Mean-field dynamo with cubic non-linearity
Abstract
A turbulent mean-field alpha-omega dynamo model of magnetic-field generation in astrophysical objects is developed, assuming a quadratic dependence of the helicity on the magnetic field. The mean-field equation for cubic nonlinearity is reduced to a system of infinite equations with coefficients determined by the eigenfunctions and eigenvalues of the linear problem, and the one-mode and two-mode approximations are examined in detail. The supercritical solution in the one-mode approximation is found to be stable for d(gamma)/dD greater than zero, where gamma is the growth rate of the linear solution and D is the dynamo number. In the two-mode approximation, the nonlinear interaction of a dipole mode and a weaker quadrupole mode is used to derive the conditions for synchronization and beating.
- Publication:
-
Astronomische Nachrichten
- Pub Date:
- 1984
- DOI:
- 10.1002/asna.2113050513
- Bibcode:
- 1984AN....305..265K
- Keywords:
-
- Astrophysics;
- Dynamo Theory;
- Magnetic Fields;
- Approximation;
- Eigenvalues;
- Field Strength;
- Nonlinear Equations;
- Plasma Physics