Small amplitude solutions of the dynamo problem. I - The adjoint system and its solutions

As part of an investigation directed to find small amplitude solutions of the MHD dynamo problem, the adjoint eigenvalue system was derived for the kinematic dynamo problem including the alpha-effect. The adjoint system was deduced both for spherical dynamos and for dynamos operating in containers of general form. Results demonstrate the agreement between the eigenvalues of the two systems and between those reported in earlier integrations, as well as the closeness of the eigenvalues of the dipole and the quadrupole types for alpha-square dynamos.