Inertial magnetohydrodynamics

A version of extended magnetohydrodynamics (MHD) that incorporates electron inertia is obtained by constructing an action principle. Unlike MHD which freezes in magnetic flux, the present theory freezes in an alternative flux related to the electron canonical momentum. The associated Hamiltonian formulation is derived and reduced models that have previously been used to describe collisionless reconnection are obtained. - Highlights: • A rare, and possibly novel, version of MHD presented, and similarities to MHD highlighted via an appropriate frozen flux constraint. • Hamiltonian and action principle formalisms for this model, inertial MHD, are presented. • Shown to reproduce the Ottaviani–Porcelli model of reconnection as a special case