Error field assessment from driven rotation of stable external kinks at EXTRAP-T2R reversed field pinch

Abstract

A new non-disruptive error field (EF) assessment technique not restricted to low density and thus low beta was demonstrated at the EXTRAP-T2R reversed field pinch. Stable and marginally stable external kink modes of toroidal mode number n=10 and n=8, respectively, were generated, and their rotation sustained, by means of rotating magnetic perturbations of the same n. Due to finite EFs, and in spite of the applied perturbations rotating uniformly and having constant amplitude, the kink modes were observed to rotate non-uniformly and be modulated in amplitude. This behavior was used to precisely infer the amplitude and approximately estimate the toroidal phase of the EF. A subsequent scan permitted to optimize the toroidal phase. The technique was tested against deliberately applied as well as intrinsic error fields of n=8 and 10. Corrections equal and opposite to the estimated error fields were applied. The efficacy of the error compensation was indicated by the increased discharge duration and more uniform mode rotation in response to a uniformly rotating perturbation. The results are in good agreement with theory, and the extension to lower n, to tearing modes and to tokamaks, including ITER, is discussed.

Tearing mode dynamics and locking in the presence of external magnetic perturbations

“…Prior to the RMP application, the m ¼ 0 modes are either stationary or rotate in opposite direction to the central m ¼ 1 modes. Thus, if this interaction was strong, the m ¼ 1 modes would decelerate and the phase velocities of the (1,6) and (1, 7) mode would equate to produce a flat velocity profile. This is in contrast to the sheared velocity profiles observed experimentally (Figure 2(a)).…”

“…In Figure 3, the experimental TM velocity reduction (Figure 2(b)) is compared with the modeled plasma velocity reduction profile. Recall that, at r ¼ r m;n s , the modeled plasma and TM velocity are the same due to the no-slip condition (6). The behavior of the modeled plasma velocity to the inside (outside) of the n ¼ 6 surface is mainly determined by viscosity and the inside (outside) boundary condition ½dDv / ðr; tÞ=dr r¼0 ¼ 0 (Dv / ðr ¼ aÞ ¼ 0).…”

“…5 A non-disruptive method to detect the intrinsic error field makes use of rotating RMPs to find the phase of the error field. 6,7 In stellarators, RMPs have been used to stabilize detached/radiative divertor plasmas, thereby reducing divertor heat load by a factor of 3-10. 8 In reversed-field pinches (RFPs), RMP application has been used to, for example, induce slow rotation to reduce localized plasma wall interaction 9 and to control the orientation of 3D equilibria.…”

Simultaneous iterative learning control of mode entrainment and error field

“…This implies that the motion of MHD modes can be used as a tool to diagnose the EF. This has been accomplished for kink modes and tearing modes on EXTRAP-T2R [11,12], and for locked or nearly locked tearing modes on DIII-D [13,14].…”

Analytical compensation of axisymmetric equilibrium fluxes picked up by locked mode detectors in tokamaks

“…This is sometimes realized by vacuum subtraction, i.e., by taking separate measurements in the presence of the equilibrium fields but in the absence of the plasma itself, and then subtracting the results from those of the actual plasma measurement, as performed in EXTRAP-T2R. 3 More generally, the signals from a pair of saddle loops, which are installed opposite each other in the toroidal direction, are subtracted to deduct the axisymmetric components and leave the non-axisymmetric components with odd toroidal mode numbers (n = 1, 3, 5, . .…”