Computational Studies of Magnetohydrodynamic Stability for Reversed-Field Pinches and Tokamaks

Abstract: This work describes the ideal & resistive Magnetohydrodynamic (MHD) stability properties of Tokamak and Reversed-Field Pinch (RFP) plasmas. The first four papers are concerned with the cylindrical approximation of RFPs and tokamaks whereas the final two papers deal with a fully toroidal description.

It is found that in cylindrical geometry, the violation of the Suydam criterion does not have strong effects on the growth rates of resistive modes except for very low values of resistivity or when the Suydam index far exceeds the stability limit. A study of the effects of stability of modification to the current profile locally at the rational surface shows that this method can be used to suppress the disruptions in tokamaks.

A comparison is made between the often used zero-pressure .DELTA.' theory and cylindrical numerical analysis of resistive modes at finite pressure for RFP. At zero beta, the .DELTA.' theory gives a good approximation. For typical experimental cases (.beta._p ~ 0.1), it is essential to solve the finite pressure resistive MHD equations. These results also connect to those when the system is ideally unstable.

Studies of how the pressure profile affects the resistive m=0,1 modes reveal the sensitivity of these modes to the pressure gradient with typical experimental .beta._p values (~ 10%) in a RFP. Local flattening of the .mu. = .mu.₀ (JB / B²) profile at the reversal surface destabilize both the m=0 and high-nm=1 mode but greatly reduce the growth rate of m=1 externally resonant mode. If the .mu. profile is hollow, the spectrum of unstable mode and the unstable region in minor radius become much narrower. However, the effect of hollow .mu. profile on the internal mode is more complicated and depends on the depth of hollowness and the value of the pinch parameter ( .THETA. = B_.THETA.(a) / z> ).

In toroidal computations, poloidal variations of the instabilities has to be accounted for and this can be made either by using Fourier expansion or finite elements. In either case, significant difficulties arise in resolving MHD modes for equilibria with strong shaping or high edge q. The toroidal resistive-MHD stability code MARS uses Fourier expansion. The poloidal convergence can be improved by a judicious choice of normalization factors for the perturbation quantities and multipliers for the equations. Using this method, a new version of the code has been produced with significantly improved poloidal convergence. Several test cases are analyzed to establish a suitable choice of normalization factors and multipliers. The new MARS code has been used to evaluate the ideal-MHD limits to beta and bootstrap fraction for JET discharges with peaked pressure profiles and negative central shear. The results show that the limits to both beta and normalized beta are higher for high plasma current. A broad current profile is advantageous, in particular when wall stabilization is taken into account. Detailed results concerning the influence of the minimum q are given.