On the Eigenvalues of Kinematic α effects Dynamos
Abstract
The kinematic alpha-effect dynamo problem is considered for both alpha-square and alpha-omega dynamos with boundary conditions corresponding to an external perfect conductor. By writing the equations in the form of integral equations and using the methods of Fredholm theory, it is shown that the close correspondences between the eigenvalues of stationary solutions in dipole and quadrupole modes for alpha-square dynamos, and between the eigenvalues for both stationary and oscillatory solutions of the dipole mode and quadrupole mode for alpha-omega dynamos, observed by Roberts (1972), are exact in this case. The adjointness property of the governing equations is elucidated by a variational principle for nonoscillating solutions.
- Publication:
-
Astronomische Nachrichten
- Pub Date:
- 1977
- DOI:
- 10.1002/asna.19772980104
- Bibcode:
- 1977AN....298...19P
- Keywords:
-
- Dynamo Theory;
- Eigenvalues;
- Electrodynamics;
- Kinematics;
- Magnetic Dipoles;
- Earth Core;
- Electromotive Forces;
- Fredholm Equations;
- Geomagnetism;
- Quadrupoles;
- Solar Magnetic Field;
- Astronomy