Plasma relaxation and topological aspects in Hall magnetohydrodynamics

Parker Problem in Hall Magnetohydrodynamics

Parker problem in Hall magnetohydrodynamics (MHD) is considered. Poloidal shear into the toroidal flow generated by the Hall effect is incorporated. This is found to lead to a triple deck structure for the Parker problem in Hall MHD, with the magnetic field falling off in the intermediate Hall-resistive region more steeply (like 1/x) than that (like 1/x) in the outer ideal MHD region. ∗Permanen...

Topological solitons in magnetohydrodynamics

Solutions of physical equations which have non-trivial topological properties have been studied for already more than five years. As examples we may give the "monopole""2 and the ' ' in~tanton'~ in gauge field theories and the "pseudoparticle" in a two-dimensional isotropic f e r r ~ m a g n e t . ~ All these solutions a re characterized by some topological index: the magnetic charge of the mon...

Topological Soliton in Magnetohydrodynamics *

We use the Hopf mapping to construct a magnetic configuration consisting of closed field lines, each of which is linked with all the other ones. We obtain in this way a solution of the equations of magnetohydrodynamics of an ideal incompressible fluid with infinite conductivity, which describes a localized topological soliton.

Well-posedness for Hall-magnetohydrodynamics

We prove local existence of smooth solutions for large data and global smooth solutions for small data to the incompressible, resitive, viscous or inviscid Hall-MHD model. We also show a Liouville theorem for the stationary solutions. Acknowledgements: The first and third authors wish to thank the hospitality of the Institut de Mathématiques de Toulouse, France, where this research has been car...

Minimum energy states of the cylindrical plasma pinch in single-fluid and Hall magnetohydrodynamics