On heat conduction in a plasma with a magnetic island

The heat conductivity of a plasma is usually much higher along the magnetic field than across it, and, as a result, the presence of a magnetic island can significantly affect the temperature profile in its vicinity. Radiation energy losses, which depend sensitively on temperature, are thus strongly affected by magnetic islands. This phenomenon is explored in a simple mathematical setting, and it is shown that the presence of a magnetic island greatly enhances a plasma's capacity to radiate energy. In the limit of highly anisotropic heat conductivity, the steady-state heat conduction equation can be reduced to an ordinary differential equation. Although this equation operates in one dimension, the topology is not that of the real line, but corresponds to a rod with a cooling fin. As parameters such as the incoming heat flux or the radiation amplitude are varied, the radiation has a tendency to linger around the island, in particular in the region of the separatrix, and the total radiated energy is then significantly increased. The island acts as a ‘cooling fin’ to the plasma. Furthermore, the solutions exhibit bifurcations, where the location of the radiation zone suddenly changes.