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Mean‐field dynamo with cubic non‐linearity
Author(s) -
Kleeorin N. I.,
Ruzmaikin A. A.
Publication year - 1984
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.2113050513
Subject(s) - dynamo , physics , dynamo theory , quadrupole , magnetic field , dipole , quantum electrodynamics , helicity , eigenvalues and eigenvectors , mathematical analysis , nonlinear system , magnetic dipole , classical mechanics , quantum mechanics , mathematics
The turbulent mean‐field dynamo of αω‐type with a mean helicity quadratically dependent on the magnetic field is investigated. A nonlinear system of ordinary differential equation is derived for the amplitudes of the magnetic field expansion over the eigenvectors of the linear problem. In a one‐mode approximation the non‐linear supercritical solution is stable when dγ/d D > 0, where γ is the growth rate of the linear solution and D is the dynamo number. Non‐linear interation between two modes of dipole and quadrupole symmetry is considered. The conditions are found for the synchronization and beats of these modes under the assumption that the quadrupole mode is weaker than the dipole one.