Impact of toroidal and poloidal mode spectra on the control of non-axisymmetric fields in tokamaks

Abstract

In several tokamaks, non-axisymmetric magnetic field studies show that applied magnetic fields with a toroidal harmonic n = 2 can lead to disruptive n = 1 locked modes. In Ohmic plasmas, n = 2 magnetic reconnection thresholds in otherwise stable discharges are readily accessed at edge safety factors q ∼ 3, low density, and low rotation. Similar to previous studies with n = 1 fields, the thresholds are correlated with the “overlap” field computed with the IPEC code. The overlap field quantifies the plasma-mediated coupling of the external field to the resonant field. Remarkably, the “critical overlap fields” at which magnetic islands form are similar for applied n = 1 and 2 fields. The critical overlap field increases with plasma density and edge safety factor but is independent of the toroidal field. Poloidal harmonics m > nq dominate the drive for resonant fields while m < nq harmonics have a negligible impact. This contrasts with previous results in H-mode discharges at high plasma pressure in which the toroidal angular momentum is sensitive to low poloidal harmonics. Together, these results highlight unique requirements for n > 1 field control including the need for multiple rows of coils to control selected plasma parameters for specific functions (e.g., rotation control or ELM suppression).

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

“…This feature is robust to alternative predictions of ITER scenarios, which include a 15MA H-mode scenario In this combined scaling, the line integrated density n e has units of 10 19 m −3 , the on axis toroidal field B T has units of Tesla and the major radius R 0 has units of meters. Note that the normalized pressure scaling connects low power and/or Ohmically heated discharges reported in previous published and ITPA work [13,40,44] and higher power H-mode data available on select machines. The negative exponent can be interpreted as the detrimental impact of higher plasma amplification in H-mode.…”

“…This report focuses on the low n EFs, which are commonly held to be the most dangerous for their association with locking and disruptions. Although early work concentrated only on the lowest n = 1 EFs [1][2][3][4][5][6][7][8][9][10][11][12], recent work showed that the n = 2 EF has a similar density scaling and even similar thresholds in current machines [13]. The choice of poloidal mode (m) spectrum for compensation is more complicated, since the poloidal modes are strongly coupled due to toroidicity and shaping in the poloidal plane.…”

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).…”

Nonambipolar Transport due to Electrons with 3D Resistive Response in the KSTAR Tokamak

“…This bifurcation is understood as the evolution of unstable magnetic islands to large size at low order rational surfaces due to the electromagnetic 3D torque against the viscous torque of rotating plasmas, dissipating toroidal momentum [27] until locked to the frame of the external 3D fields. The viscous torque and rotation at the rational surface are therefore stabilizing against the onset of LMs, enhancing the plasma tolerance against RMP, as has been validated in various devices [7,[28][29][30][31][32] as well as KSTAR [32]. The case #19115 had the lowest NBI power and torque injection, and therefore a much lower RMP tolerance was expected than the other two discharges.…”