Time-dependent parallel electron energy transport in a magnetized plasma of arbitrary collisionality

The analysis of Hazeltine [Phys. Plasmas 5, 3282 (1998)], which considers the transport of electron number density and energy parallel to the magnetic field in a magnetized plasma of arbitrary collisionality, is generalized by incorporating a model electron–ion collision operator, including a self-consistent calculation of the parallel electric field, and taking time dependence into account. The resulting enhanced model is used to investigate the transport of electron energy across a magnetic island chain in a tokamak plasma. A general expression for the critical island width above which the electron temperature profile is flattened inside the magnetic separatrix of the island chain is derived. This expression is valid at arbitrary electron collisionality and also allows for temporal oscillation of the radial temperature gradient across the island chain. The expression is shown to asymptote to much simpler expressions in the short mean-free-path and long mean-free-path limits. An expression for the appropriate value of the parallel electron thermal conductivity to use in extended magnetohydrodynamical simulation codes that represent parallel electron energy transport in terms of a diffusive operator is obtained.