Bifurcated states of a rotating tokamak plasma in the presence of a static error-field

The bifurcated states of a rotating tokamak plasma in the presence of a static, resonant, error-field are strongly analogous to the bifurcated states of a conventional induction motor. The two plasma states are the “unreconnected” state, in which the plasma rotates and error-field-driven magnetic reconnection is suppressed, and the “fully reconnected” state, in which the plasma rotation at the rational surface is arrested and driven magnetic reconnection proceeds without hindrance. The response regime of a rotating tokamak plasma in the vicinity of the rational surface to a static, resonant, error-field is determined by three parameters: the normalized plasma viscosity, P, the normalized plasma rotation, Q0, and the normalized plasma resistivity, R. There are 11 distinguishable response regimes. The extents of these regimes are calculated in P–Q0–R space. In addition, an expression for the critical error-field amplitude required to trigger a bifurcation from the “unreconnected” to the “fully reconnected” state is obtained in each regime. The appropriate response regime for low-density, ohmically heated, tokamak plasmas is found to be the nonlinear constant-ψ regime for small tokamaks, and the linear constant-ψ regime for large tokamaks. The critical error-field amplitude required to trigger error-field-driven magnetic reconnection in such plasmas is a rapidly decreasing function of machine size, indicating that particular care may be needed to be taken to reduce resonant error-fields in a reactor-sized tokamak.