Observation of Large-Scale Profile Change of Magnetic Field in a Low-Aspect Ratio Reversed Field Pinch

Abstract

Reversed field pinch (RFP) is a compact, high-beta magnetic confinement system. Recent theoretical studies have shown that a low-aspect ratio RFP may have several advantages such as simpler magnetic mode dynamics because mode resonant surfaces are less densely spaced in the core region than in conventional (i.e., highor mediumaspect ratio) RFP. In order to study these advantages experimentally, the properties of low-aspect ratio RFP plasmas are investigated in the RFP machine ‘‘RELAX’’ (major radius R0 1⁄4 0:508m, minor radius a 1⁄4 0:254m, aspect ratio A 1⁄4 2) by various methods. As one of these methods, a radial array of magnetic probes is used to measure inner magnetic fields. Several types of magnetic field profiles in RELAX plasmas have been obtained using the array. In this paper, we describe a large-scale change in magnetic field profile accompanying the loss and recovery of toroidal field reversal, which phenomenon is characteristic to the RELAX plasmas to date. The radial array of magnetic probes is inserted in a poloidal cross section of RELAX from the top port to about 100mm inside the plasma. The radial array consists of pickup coils at 13 locations spaced about 8mm apart. Three orthogonal components, Br (minor radial), B (poloidal), and B (toroidal), are measured at each location from the edge r=a 1⁄4 1 to r=a 0:6. Here, r indicates the minor radial coordinate of coils. The effects of imperfect orthogonality of the pick-up coils have been estimated as follows. The Br and B pick-up coils pick up the toroidal component, with an upper bound of 5%, whereas the B coils pick up a negligible fraction of the poloidal component. Figure 1 shows time traces of the radial, poloidal and toroidal magnetic fields measured using the radial array in a self-reversal RELAX discharge, where no external toroidal reversed field is applied. (No correction is made to the magnetic field signals because the amplitudes of all the three components are of the same order of magnitude in this series of self-reversal discharges, and therefore the effects of the imperfect orthogonality of the coils are negligible.) Each magnetic field profile shows a significant change (compared with typical RFP discharges in RELAX) and appears to oscillate at a frequency of approximately 10 kHz. In particular, the edge toroidal field reversal is lost for a while, and recovers again. In the same discharge, the edge toroidal magnetic fields in the frequency band between 5 and 15 kHz at various places also oscillate at large amplitudes ( 5mT), and a phase difference is observed at different locations. Therefore, it is expected that the magnetic field profiles also strongly oscillate at toroidal angles where the array is not inserted, and are toroidally and poloidally (up-down) asymmetric due to the large amplitude. We compare the magnetic field profiles observed using the radial array with those of a ‘‘Helical Ohmic Equilibrium Solution’’ (HOES). Here, HOES is a theoretical solution for an equilibrium of a cylindrical plasma having helical symmetry and a finite Ohmic current density. The magnetic field in HOES is decomposed into the toroidally (axially) and poloidally symmetric component Bð0;0Þ i ðrÞ such as RFP and the helically deformed (asymmetric) component biðr; ; zÞ 1⁄4 ~ biðrÞ cosðuþ iÞ (i 1⁄4 r; ; z). Here, u 1⁄4 m þ kz is the helical angle, m and k are the constants, z is the axial coordinate of the cylinder, and i is the initial phase (constant). and z are the same but differ from r by =2 (for the reason that r b 1⁄4 0). We assume that the measured magnetic fields in the frequency band under 2 kHz (nearly a time average value) are symmetric (Bð0;0Þ i ) and over 2 kHz (nearly variation from the time average value) are asymmetric (bi), because the large-scale oscillation has a frequency of approximately 10 kHz. As shown in Fig. 2, the experimental bi (over 2 kHz) appears to oscillate as ~ biðrÞ cosð t þ iÞ (i 1⁄4 r; ; ). Here, and i are constants in time t. and appear to be about the same but differ from r by about =2. These relations similar to the above model suggest that i includes the helical angle u. Figure 3 shows radial profiles of b ( ) and b (replaced by bz) ( ) at a time of 5.89ms when the toroidal and poloidal magnetic fields peak and a radial profile of br (+) at a time of 5.86ms when the radial magnetic field peaks (these times are showed by the vertical lines in Fig. 2). Figure 3 also shows radial profiles of ~ bi in HOES. 7) The measured profiles of bi are in good agreement with the theoretical profiles of ~ bi in the range of 0:6 < r=a < 1:0. Thus, it is possible that the magnetic configuration is helically deformed as shown by B i ðrÞ þ ~ biðrÞ cosðuþ iÞ of HOES. Moreover, the changes in profile with time in Fig. 1 or Fig. 2, particularly, the phase difference of about =2 between br and b or bz, are consistent with the fact that i is almost linear with time ( i 1⁄4 t þ ci, here, c cz cr =2), which corresponds to the rotation of the helical configuration. That is, if such magnetic fields are measured using the radial array where u is a constant, the measured magnetic fields become B i ðrÞ þ ~ biðrÞ cosð t þ iÞ [substitute i 1⁄4 t þ ci for Bð0;0Þ i ðrÞ þ ~ biðrÞ cosðuþ iÞ, and replace uþ ci with i]. As a result, the cause of the large-scale profile changes of the magnetic field shown in Fig. 1 may be the helical deformation of the magnetic configuration and the rotation of this helical configuration in the toroidal or poloidal direction. (The amplitude of the helical component ~ bzðaÞ is larger than E-mail: [email protected] Journal of the Physical Society of Japan Vol. 77, No. 7, July, 2008, 075005 #2008 The Physical Society of Japan