Empirical scaling of the n = 2 error field penetration threshold in tokamaks

Abstract

This paper presents a multi-machine, multi-parameter scaling law for the n = 2 core resonant error field threshold that leads to field penetration, locked modes, and disruptions. Here, n is the toroidal harmonic of the non-axisymmetric error field (EF). While density scalings have been reported by individual tokamaks in the past, this work performs a regression across a comprehensive range of densities, toroidal fields, and pressures accessible across three devices using a common metric to quantify the EF in each device. The metric used is the amount of overlap between an EF and the spectrum that drives the largest linear ideal MHD resonance, known as the "dominant mode overlap". This metric, which takes into account both the external field and plasma response, is scaled against experimental parameters known to be important for the inner layer physics. These scalings validate nonlinear MHD simulation scalings, which are used to elucidate the dominant inner layer physics. Both experiments and simulations show that core penetration thresholds for EFs with toroidal mode number n = 2 are of the same order as the n = 1 thresholds that are considered most dangerous on current devices. Both n = 1 and n = 2 thresholds scale to values within the ITER design tolerances, but data from additional devices with a range of sizes are needed in order to increase confidence in quantitative extrapolations of n = 2 thresholds to ITER.

MHD stability and disruptions in the SPARC tokamak

“…Despite the successes of the first principles single dominant external field formalism, a notable experiment on the JET tokamak in Buttery et al (2012) was unable to appreciably correct an intrinsic error with a set of midplane correction coils that were expected to couple well to the dominant external field. In addition to the dominant external field, recent studies suggest that the ideal plasma response in some cases can be multi-modal (Paz-Soldan et al 2015;Logan et al 2018;Wang et al 2019) and plasmas also exhibit sensitivity to n = 2 errors (Lanctot et al 2017;Logan et al 2020).…”

“…The guidance for the critical error field above which locked modes are expected in SPARC is taken from the ITPA empirical scalings based on the overlap criterion (Logan et al 2020), which gives the following critical overlap criterion:…”

“…However, unlike present low-field machines, SPARC will access high plasma pressures at low β N , reducing the ballooning nature of the ideal kink response that localizes it to the low-field side, and thereby reduces the dominance of this single mode. The coupling of the second least-stable (Logan et al 2020) for n = 1 and n = 2 fields during the flattop phase of the three main SPARC operating scenarios.…”

“…The guidance for the critical error field above which locked modes are expected in SPARC is taken from the ITPA empirical scalings based on the overlap criterion (Logan et al. 2020), which gives the following critical overlap criterion: Using the equilibrium parameters for SPARC V2 (see table 1), the full-field L-mode scenario is found to be the most sensitive, with a penetration threshold of , corresponding to a critical overlap field of G. This field sensitivity is more than 40 % larger than the most sensitive plasma scenario planned for ITER (Gribov et al. 2008).…”

Nonlinear modeling of the scaling law for the $m/n = 3/2$ error field penetration threshold

“…This is emphasized in theory as discussed in the following [4]. (iv) b r calculated from vacuum magnetic perturbations is used in the scaling in most of the experiments, while the plasma response is found to be important [23][24][25] and has not been taken into account except several recent studies [16,17,21,26]. These limitations for the empirical scaling enlarge the uncertainty to predict EF tolerance in ITER.…”