Phase Locking and Unlocking Associated with Transition to Quasi-Single Helicity State in the RELAX Reversed-Field Pinch

Abstract

In a reversed-field pinch configuration, many m 1⁄4 1 internally resonant tearing modes grow. The phase relationship among the modes is usually random, while there are cases where the phases tend to align each other. This phaselocking structure causes local enhancement of the heat flux to the wall. In the low-aspect-ratio reversed-field pinch (RFP) machine RELAX (major radius R 1⁄4 0:508m, minor radius a 1⁄4 0:250m, aspect ratio A 1⁄4 2:032), it has been observed that the phase-locking is released when a dominant mode grows to a large extent with suppression of the remaining modes, which state is often referred to as the quasi-single helicity (QSH) state. It has been found that the experimental phase behavior can be described as a probability distribution in ð min; NsÞ space, where min is the minimum of the phase dispersion, and Ns the spectral index. RFP is a relatively high-beta magnetic confinement configuration with much higher toroidal current than in Tokamaks with comparable size. Due to its high toroidal current, magnetic field lines skew in the poloidal direction and at the edge the direction of the toroidal field reverses. The safety factor (q) profile in RELAX is a monotonically decreasing function of radius with on-axis value of 0:3. Therefore, m 1⁄4 1 internally resonant tearing modes with toroidal mode numbers n satisfying 1=n . 1=3 can be simultaneously unstable in RELAX. The operational regime of the RELAX RFP is characterized by a wide range of field-reversal parameter F , which is the ratio of edge toroidal field Bta to the averaged toroidal field hBti. There are two characteristic regimes, possibly characteristic to low-A RFP. One is a shallow-reversal regime where F > 0:1, characterized by frequent transitions to QSH states, which may be attributable to larger separations between mode rational surfaces in the core region and power distribution of the m 1⁄4 1 modes to fewer toroidal mode numbers; some equilibrium analyses and numerical simulations predicted those effect of low aspect ratio on the RFP configuration. The helical structure coinciding with the magnetic island of the dominant mode in QSH state has been clearly observed in RELAX. The other is a deep-reversal regime where F 6) aspect-ratio RFPs. Although the reason of the attainment of the deep-reversal regime is not clear so far, this regime seems attractive in terms of optimization of the aspect ratio in the RFP since the tearing mode amplitudes are lowered in this regime. In a wide range of operational regimes of RELAX, phaselocking phenomena have been observed. Phase-locking structure called slinky mode tends to be locked to the wall due to electromagnetic interaction with error fields, and causes locally enhanced heat flux on the wall. In RFXmod, by an elaborate feed-back control of tearing modes’ dynamics with 192 saddle coils covering all over the wall, they have successfully released the wall-locking and, recently, higher plasma current operation of 2MA was performed. In the following, we show a spontaneous release of wall-locking and/or phase-locking due to transition to QSH state observed in RELAX. Figure 1(a) shows time evolution of spectral index Ns defined as