On the Eigenvalues of Kinematic α effects Dynamos
Abstract
The kinematic alphaeffect dynamo problem is considered for both alphasquare and alphaomega 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 alphasquare dynamos, and between the eigenvalues for both stationary and oscillatory solutions of the dipole mode and quadrupole mode for alphaomega 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