Canonical Vorticity Framework for Magnetic Reconnection

Canonical vorticity $\mathbf{Q}_{\sigma}=m_{\sigma}\nabla\times\mathbf{u}_{\sigma}+q_{\sigma}\mathbf{B}$, the curl of the canonical momentum $\mathbf{P}_{\sigma}=m_{\sigma}\mathbf{u}_{\sigma}\mathbf{+}q_{\sigma}\mathbf{A}$, is an important ideal plasma parameter because $\mathbf{Q}_{\sigma}$ is perfectly frozen into the species fluid if the pressure is both isotropic and barotropic. We present a framework for reconnection where $\mathbf{Q}_{\sigma}$ is the main variable instead of $\mathbf{B}$. This framework shows that canonical vorticity evolution, i.e., $\partial\mathbf{Q}_{\sigma}/\partial t$, is driven by just two terms: a convective term which describes the frozen-in property of canonical vorticity and a “canonical battery” term which describes effects from the pressure tensor being non-isotropic or non-barotropic. This framework is simpler than the traditional framework based on the generalized Ohm's law where a multitude of terms give $\partial\mathbf{B}/\partial t$. To demonstrate the power of the canonical vorticity viewpoint, the growth, stability, morphology, and saturation of the magnetic reconnection electron-diffusion region are explained using the electron canonical vorticity framework.