25 research outputs found
Minimum energy states of the plasma pinch in standard and Hall magnetohydrodynamics
Axisymmetric relaxed states of a cylindrical plasma column are found
analytically in both standard and Hall magnetohydrodynamics (MHD) by complete
minimization of energy with constraints imposed by invariants inherent in
corresponding models. It is shown that the relaxed state in Hall MHD is the
force-free magnetic field with uniform axial flow and/or rigid azimuthal
rotation. The relaxed states in standard MHD are more complex due to the
coupling between velocity and magnetic field. Application of these states for
reversed-field pinches (RFP) is discussed
Energy of eigen-modes in magnetohydrodynamic flows of ideal fluids
Analytical expression for energy of eigen-modes in magnetohydrodynamic flows
of ideal fluids is obtained. It is shown that the energy of unstable modes is
zero, while the energy of stable oscillatory modes (waves) can assume both
positive and negative values. Negative energy waves always correspond to
non-symmetric eigen-modes -- modes that have a component of wave-vector along
the equilibrium velocity. These results suggest that all non-symmetric
instabilities in ideal MHD systems with flows are associated with coupling of
positive and negative energy waves. As an example the energy of eigen-modes is
calculated for incompressible conducting fluid rotating in axial magnetic
field.Comment: 10 pages, 3 figure