Abstract
The equilibrium and stability properties of ideal compressible magnetohydrodynamic (MHD) flows are investigated. The domain is taken to be cylindrical with arbitrary cross-section. Variational principles for plasma equilibria with mass flow are formulated, where we associate the cylindrical MHD equilibrium states to critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross-helicity), the momentum and the magnetic helicity. Lyapunov stability conditions for compressible cylindrical ideal MHD flows with arbitrary cross-section are determined.
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