Thermal Equilibrium and Stability of Tokamak Discharges

Steady-state temperature and magnetic field profiles are derived in cylindrical geometry, including classical electron-ion equilibration, Ohmic heating, and the classical ion thermal transport appropriate to tokamak geometry. To fit the experimental data, a direct electron heat loss must accompany any appreciable resistivity anomaly. The classical equilibrium can be thermally stable only if Ti/Te ≳ 2/3. Direct electron heat loss by radiation is further destabilizing; but for typical parameters, stability can be achieved by a moderate amount of anomalous electron thermal conduction. The growth time of thermal instabilities is generally limited by the resistive skin time. The presence of a runaway component of the current allows shorter growth times, and this may be related to the present high-density limit in tokamaks.