Canonical Helicity of Plasma: Topology of Fluids

Magnetic helicity is a topological measure of twistedness and linkage of magnetic vector fields and is a useful constraint for determining the ultimate equilibrium state of magnetized plasma. For plasmas with non-negligible flow, the magnetic helicity needs to be generalized to the so-called canonical helicity to include the fluid vorticity. In this talk, a general scheme for finding equilibrium states is explained: minimization of a “fragile quantity” (e.g. enstropy) constrained by a less fragile quantity (e.g. helicity). Such formalism has a keen connection with a fluid version of Schrödinger equation. A simple form of the canonical helicity transport equation is also introduced based on the generalized “electric” field, 𝐄= −𝜕𝑷𝜕𝑡⁄−∇ℎ, where P is the canonical momentum and h is the enthalpy. As an important application, the rapid change of plasma flow during magnetic reconnection is interpreted as a transport between magnetic helicity and fluid vorticity.