Transport description of the rise time of sawtooth oscillations in reversed-field pinches

Abstract

High-Θ (Θ≡Bϑ(a)/〈Bφ〉) toroidal reversed-field pinch discharges in the ZT-40M device are characterized by soft x-ray sawtooth oscillations. It is demonstrated that a one-dimensional transport description is sufficient to model the rise time of sawtooth oscillations, provided the resistivity profile has significant gradients. This result suggests that the toroidal magnetic flux generation (dynamo) observed in the reversed-field pinch (RFP) may be restricted to the m=1 tearing events associated with the sawtooth crash (decrease in the soft x-ray flux).

Experimental scaling of fluctuations and confinement with Lundquist number in the reversed-field pinch

“…In the past, the RFP sawtooth oscillation was modeled as a slow resistive decay of the current profile, followed by a rapid reconnection event ͑crash͒ that reset the current profile. 50,11 However, the resistivity profile that was required to model the decay phase of the oscillation was somewhat unphysical ͑or anomalous͒. We report an experimental measurement of the scaling of the sawtooth period that indicates a hybrid resistive-MHD character as opposed to a purely resistive character to the ''decay phase.''…”

Density effects on sawtooth oscillations for high-theta 120 kA discharges in ZT-40M

“…Moreover, the code does not model the RFP This profile causes the current to peak, on axis and destabilizes tearing modes that are responsible for the dynamo and the sawtooth crash. 6 If a dynamo were included in this simulation, © would be suppressed but the flux would be enhanced, thus the simulation would not converge to the experimental values. Figures 13a and 13b show the same comparison as Figs.…”

“…In the sawtoothing discharges, the strong effective resistivity profile rapidly diffuses current density into the plasma axis during the sawtooth rise phase destabilizing internal tearing modes, 6 ' 8 Before these modes have a chance to grow large enough to relax the plasma, the equilibrium has diffused considerably past the marginal stability limit and into a robustly unstable state. 6…”

“…5 Moreover, the plasma dynamics can be simulated by a 1-D transport code during the soft x-ray rise phase of the high 0 sawtooth oscillation without the inclusion of a dynamo. 6 These simulations indicate that the dynamo may only be present during the sawtooth drop when m=l activity is present. Other studies have indicated m=l tearing modes are a likely source of the dynamo.…”

“…7 " 12 However, in order for these 1-D simulations to match the experimental data during the sawtooth rise phase, strong gradients in the resistivity profile had to be assumed (see Fig.la). 6 If Z f^ is assumed to be constant as a function of radius, then the classical resistivity relation 13 leads to a strongly peaked temperature profile as shown in Fig. lb.…”