|presen.pdf||2006-02-19 20:31:26||Ohsaki Shuichi|
Variational principle of Hall MHD
Author: Ohsaki Shuichi
Submitted: 2005-12-20 19:56:41
University of Texas at Austin, Institute for Fusio
1 University Station - C1500
Austin, TX 78712
The Hall MHD equations have three invariants (energy and two helicities). When we consider a variational problem that solves the minimum energy state with helicitis conservation, the problem is known to be a ill-posed problem. The resultant state gives the Taylor state, which means that the one of helicities conservation dose not affect at all the mimizing energy process. However if we take the variation of the plasma flow and the generalized magnetic field instead of the magnetic field, the variational problem becomes a well-posed problem and the resultant field is different from the Taylor state. In the limit of coincidence of the general magnetic field and the magnetic field, the both problem becomes equal to the conventional MHD case that leads the force free magnetic field and parallel flow. We study the difference of the two variational principles.