Statistical analysis of m/n  =  2/1 locked and quasi-stationary modes with rotating precursors at DIII-D

Abstract

Abstract.A database has been developed to study the evolution, the nonlinear effects on equilibria, and the disruptivity of locked and quasi-stationary modes with poloidal and toroidal mode numbers m = 2 and n = 1 at DIII-D. The analysis of 22,500 discharges shows that more than 18% of disruptions are due to locked or quasistationary modes with rotating precursors (not including born locked modes). A parameter formulated by the plasma internal inductance l i divided by the safety factor at 95% of the poloidal flux, q 95 , is found to exhibit predictive capability over whether a locked mode will cause a disruption or not, and does so up to hundreds of milliseconds before the disruption. Within 20 ms of the disruption, the shortest distance between the island separatrix and the unperturbed last closed flux surface, referred to as d edge , performs comparably to l i /q 95 in its ability to discriminate disruptive locked modes. Out of all parameters considered, d edge also correlates best with the duration of the locked mode. Disruptivity following a m/n = 2/1 locked mode as a function of the normalized beta, β N , is observed to peak at an intermediate value, and decrease for high values. The decrease is attributed to the correlation between β N and q 95 in the DIII-D operational space. Within 50 ms of a locked mode disruption, average behavior includes exponential growth of the n = 1 perturbed field, which might be due to the 2/1 locked mode. Surprisingly, even assuming the aforementioned 2/1 growth, disruptivity following a locked mode shows little dependence on island width up to 20 ms before the disruption. Separately, greater deceleration of the rotating precursor is observed when the wall torque is large. At locking, modes are often observed to align at a particular phase, which is likely related to a residual error field. Timescales associated with the mode evolution are also studied and dictate the response times necessary for disruption avoidance and mitigation. Observations of the evolution of β N during a locked mode, the effects of poloidal beta on the saturated width, and the reduction in Shafranov shift during locking are also presented.

MHD stability and disruptions in the SPARC tokamak

“…This parameter is closely related to ( is the safety factor at the 95 % poloidal flux surface) that numerical and experimental works have related to the tearing mode classical stability index (Cheng, Furth & Boozer 1987; Sweeney et al. 2017). Additional margin to this boundary can be afforded by reducing the plasma current or broadening the current profile to reduce .…”

“…These tearing modes differ in their onset as classical tearing modes are linearly unstable, requiring only an infinitessimal perturbation to initiate mode growth, whereas neoclassical tearing modes are linearly stable and nonlinearly unstable, requiring a perturbation or 'seed island' of a minimum amplitude. Tearing modes are deleterious, leading to a reduction in energy confinement (Chang & Callen 1990) and a drag on the plasma due to resistive wall eddy currents that can brake the plasma and potentially cause locking (Nave & Wesson 1990) and disruptions (De Vries et al 2011;Sweeney et al 2017). The dynamics of macroscopic classical and neoclassical tearing modes are described by the modified Rutherford equation (La Haye 2006):…”

“…The highest disruptivity with a value between 0.01 and 0.1 s −1 results from a stability boundary on l i /q cyl , where = a/R is the inverse aspect ratio, a and R are the plasma minor and major radii, l i is the internal inductance, q cyl = 2π aB T /μ 0 I p , B T is the toroidal field at the magnetic axis and I p is the plasma current. This parameter is closely related to l i /q 95 (q 95 is the safety factor at the 95 % poloidal flux surface) that numerical and experimental works have related to the tearing mode classical stability index Δ (Cheng, Furth & Boozer 1987;Sweeney et al 2017). Additional margin to this boundary can be afforded by reducing the plasma current or broadening the current profile to reduce l i .…”

“…2011; Sweeney et al. 2017). The dynamics of macroscopic classical and neoclassical tearing modes are described by the modified Rutherford equation (La Haye 2006): where is the local resistive time, is the minor radius, is the island width, is the normalized classical stability index, is the local inverse aspect ratio, is the length scale of the safety factor profile, is the length scale of the pressure profile (note the minus sign), is the local beta poloidal, and are small island thresholds, is the poloidal harmonic, is the vacuum island width (due to externally imposed usually static resonant ‘error fields’) and is the phase difference between O-points on the outboard midplane of the vacuum island and driven island.…”

Progress in disruption prevention for ITER

“…To date, most real-time systems have used one or more single-parameter physics-based detectors (e.g., MHD mode amplitude, radiated power fraction, global energy confinement level, …) to trigger a disruption mitigation system when a specified threshold is passed, or (with a lower threshold) to initiate more benign preventive actions. Analysis of a multi-machine database [31] has provided a basis for normalizing the critical locked mode amplitude for disruption, independent of machine size, while analysis of a DIII-D database [32] shows that the proximity of the outer edge of the island to the plasma surface is a key factor in whether a locked mode leads to a disruption. Machine-learning approaches (discussed below) should be applicable to data analysis for optimization of these individual physics-based tests [33] and the control responses.…”