Appearance and Dynamics of Helical Flux Tubes under Electron Cyclotron Resonance Heating in the Core of KSTAR Plasmas

Dual (or sometimes multiple) flux tubes (DFTs) have been observed in the core of sawtoothing KSTAR tokamak plasmas with electron cyclotron resonance heating. The time evolution of the flux tubes visualized by a 2D electron cyclotron emission imaging diagnostic typically consists of four distinctive phases: (1) growth of one flux tube out of multiple small flux tubes during the initial buildup period following a sawtooth crash, resulting in a single dominant flux tube along the $m/n=1/1$ helical magnetic field lines, (2) sudden rapid growth of another flux tube via a fast heat transfer from the first one, resulting in approximately identical DFTs, (3) coalescence of the two flux tubes into a single $m/n=1/1$ flux tube resembling the internal kink mode in the normal sawteeth, which is explained by a model of two current-carrying wires confined on a flux surface, and (4) fast localized crash of the merged flux tube similar to the standard sawtooth crash. The dynamics of the DFTs implies that the internal kink mode is not a unique prerequisite to the sawtooth crash, providing a new insight on the control of the sawtooth.

Figure 1

(a) Visible camera image of a plasma with 110 GHz ECH (shot 3967). The inset images are the DFTs captured by the ECEI. The white arrow is the approximate ECH beam path, whose second harmonic resonance was on the magnetic axis ($R=1.8\mathrm{m}$). As indicated, the toroidal magnetic field ($B_{\mathrm{t}}$) and the plasma current ($I_{\mathrm{p}}$) were both out of the plane and the toroidal plasma rotation ($V_{\mathrm{tor}}$) was into the plane (i.e., countercurrent direction). (b) Time traces of $I_{\mathrm{p}}$, heating power, line-averaged electron density ($n_e$), and ECE intensity. The highlighted zoomed view shows the characteristic time trace of the DFTs.

Figure 2

(Top) Time trace of an ECEI channel (indicated by the cross mark in the frame 1 below) showing a typical sawtooth pattern with DFTs. (Bottom) ECEI images of the DFTs at the selected times. The flux tubes rotate counterclockwise as indicated by the dashed arrow. The short arrows indicate the sudden growth of the second flux tube. The dashed circles represent the approximate location of the $q=1$ surface inferred from the inversion radius of the crash phase image (frame 7).

Figure 3

Growth of the second flux tube. The dashed curve traces the sudden rapid growth of the second flux tube as indicated by the arrows coinciding with the diminishment of the first flux tube. This process is schematically illustrated by the flux tube models below. The thick (blue) curve is the ECEI signal and the thin (red) curve with small open circles is the corresponding ECE radiometer signal toroidally separated by $3/16$ of the circumference at the same radial location.

Figure 4

Coalescence of the dual helical flux tubes. Before merge, the second flux tube (orange in the model) catches the first flux tube (red in the model) as indicated by the shortening of the time separation between the two flux tubes. The merging ($4\to 6$) completes in $\sim 100\mu \mathrm{s}$.

Figure 5

Rotation velocities of the flux tubes. (a) Frequency transitions for a typical sawtooth pattern with DFTs, $\mathrm{\text{single}}\to \mathrm{\text{dual}}(\mathrm{\text{frequency doubling}})\to \mathrm{\text{single}}\to \mathrm{\text{crash}}$. The core rotation accelerated during the merge process as indicated by the arrow. (b) Another example of frequency transitions, $\mathrm{\text{dual}}\to \mathrm{\text{single}}\to \mathrm{\text{dual}}\to \mathrm{\text{crash}}$. The horizontal dashed lines are at 8.5, 3.7, and 7.4 kHz, respectively. (c) Comparison between the ECEI signal and a Mirnov coil [MC; $d{B}_z/dt$ (AU)] signal.