Local Topological Stability Bounds of Magentohydrodynamics

It is shown that an Aharonov-Bohm (AB) effect exists in magnetohydrodynamics (MHD). This effect is best described in terms of the MHD variational variables [1, 2]. If a MHD flow has a non trivial topology some of the functions appearing in the MHD Lagrangian are non-single valued. These functions have properties similar to the phases in the AB celebrated effect. While the manifestation of the quantum AB effect is in interference fringe patterns, the manifestation of the MHD Aharonov-Bohm effects are through new dynamical conservation laws which also serve as local stability bounds.