Electric field effects during disruptions

Tokamak disruptions are associated with breaking magnetic surfaces, which makes magnetic field lines chaotic in large regions of the plasma. The enforcement of quasi-neutrality in a region of chaotic field lines requires an electric potential that has both short and long correlation distances across the magnetic field lines. The short correlation distances produce a Bohm-like diffusion coefficient $\sim T_e/eB$ and the long correlation distances $a_T$ produce a large scale flow $\sim T_e/eB a_T$. This cross-field diffusion and flow are important for sweeping impurities into the core of a disrupting tokamak. The analysis separates of the electric field in a plasma into the sum of a divergence-free, $\vec{E}_B$, and a curl-free, $\vec{E}_q$, part, a Helmholtz decomposition. The divergence-free part of $\vec{E}$ determines the evolution of the magnetic field. The curl-free part enforces quasi-neutrality, $\vec{E}_q=-\vec{\nabla}\Phi_q$. Magnetic helicity evolution gives the required boundary condition for a unique Helmholtz decomposition and an unfortunate constraint on steady-state tokamak maintenance.