Hall Resistive Tearing Mode: A Variational Formulation

A unified linear tearing-mode formulation is given incorporating both resistivity and Hall effects. A variational method is used that appears to be best suited to deal with the difficulties peculiar to the {\it triple-deck} structure associated with the Hall resistive tearing mode but also to lead to a convenient analytical dispersion relation for the Hall resisitive tearing mode. This analytical dispersion relation - * recovers the Furth-Killeen-Rosenbluth[15] result for the resistive branch; * gives a growth rate for the Hall branch which appears to be consistent with the growth rate of the electron-inertia driven tearing mode given previously (Coppi [19]); * recovers the scaling relation for the transition from the resisitive regime to the Hall regime numerically established by Fitzpatrick[20] in a driven Hall resistive reconnection situation.