Path integrals for mean-field equations in nonlinear dynamos
arXiv:1802.02842 · doi:10.1017/S0022377818000521
Abstract
Mean-field dynamo equations are addressed with the aid of the path-integral method. The evolution of magnetic field is treated as a three-dimensional Wiener random process, and the mean magnetic-field equations are obtained with the Wiener integral over all the trajectories of fluid particle. The form of the equations is just the same as the conventional mean-field equations, but the present equations are derived with the velocity-field realization affected by the magnetic-field force. In this sense, the present ones are nonlinear dynamo equations.
6 pages, 0 figures; submitted to Journal of Plasma Physics