Impulse Formulations of Hall Magnetohydrodynamic Equations

Impulse formulations of Hall magnetohydrodynamic (MHD) equations are developed. The Lagrange invariance of a generalized ion magnetic helicity is established for Hall MHD. The physical implications of this Lagrange invariant are discussed. The discussion is then extended to compressible Hall MHD. Compressibility effects are shown not to affect, as to be expected, the physical implications of the generalized ion magnetic helicity Lagrange invariant.