Mathematics
Scientific paper
Dec 1975
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1975ge%26ae..15.1054k&link_type=abstract
Geomagnetizm i Aeronomiia, vol. 15, Nov.-Dec. 1975, p. 1054-1061. In Russian.
Mathematics
Dynamo Theory, Earth Planetary Structure, Geomagnetism, Magnetic Dipoles, Kinematic Equations, Mathematical Models, Steady State
Scientific paper
In a previous paper (Kropachev and Gorshkov, 1975) it was shown that for steady-state kinematic dynamo models, it is sometimes convenient to solve the dynamo equations with respect to the velocities while defining the magnetic fields in the form of a definite analytical expression. Such an approach is illustrated in the present work on the example of the solution of a simple model for a spherical dynamo, generating as an external field a single axisymmetric dipole. The type of motions leading to excitation of a given magnetic field is found. A characteristic feature of the obtained solution is that not just one particular solution is found, but rather a whole class of solutions, in which the velocities and fields depend on an infinite set of undetermined coefficients.
Gorshkov S. N.
Kropachev Eh. P.
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