Observation of Long-Distance Radial Correlation in Toroidal Plasma Turbulence

This Letter presents the discovery of macroscale electron temperature fluctuations with a long radial correlation length comparable to the plasma minor radius in a toroidal plasma. Their spatiotemporal structure is characterized by a low frequency of $\sim 1–3\mathrm{kHz}$, ballistic radial propagation, a poloidal or toroidal mode number of $m/n=1/1$ (or $2/1$), and an amplitude of $\sim 2\%$ at maximum. Nonlinear coupling between the long-range fluctuations and the microscopic fluctuations is identified. A change of the amplitude of the long-range fluctuation is transmitted across the plasma radius at the velocity which is of the order of the drift velocity.

Figure 1

(a) Typical time evolution of $T_e$ and the line-averaged density. (b) Contour plot of the magnetic flux surfaces on equatorial midplane of LHD. Measurement locations of magnetic probes (MAG) used in this analysis are indicated by filled circles. The reflectometer (RM) antenna and the ECE antenna are located apart from each other by 72° in a toroidal direction. (c) Radial profiles of $T_e$ and $n_e$ at 2.8 sec. (d) Autopower spectrum of ${\tilde{T}}_{\mathrm{rad}}$ at $\rho =0.4$ and cross-power spectrum between two adjacent channels of ${\tilde{T}}_{\mathrm{rad}}$ at $\rho =0.4$ and 0.42. The time window for fast-Fourier transform (FFT) is 8 msec and 30 ensembles are averaged.

Figure 2

(a) Contour plot of the cross-correlation function of the low-frequency component (1.5–3.5 kHz) of ${\tilde{T}}_{\mathrm{rad}}$ from 28-ECE channels with that of the reference channel at $\rho =0.4$. (b) Radial profile of the amplitude of ${\tilde{T}}_{\mathrm{rad}}$ in the three characteristic frequency bands. (c) Cross phase between ${\tilde{T}}_{\mathrm{rad}}$ at $\rho =0.4$ and the toroidal magnetic probe array. The straight line gives the toroidal mode number $n=1$.

Figure 3

(a) Typical time evolution of high-pass filtered ($\ge 100\mathrm{kHz}$) reflectometer signal (black line) and its envelope (red line) during ECH phase. (b) Power spectrum density of the envelope of the reflectometer signal. (c) Contour plot of the squared coherence between the envelope of reflectometer signal and the 28-channel ECE signals in the space of frequency versus radial location of each ECE channel for 2.7–2.8 sec. The time window for FFT is 8 msec and 30 ensembles are averaged.

Figure 4

Contour plot of squared cross-bicoherence between $n_e$ and $T_{\mathrm{rad}}$ fluctuations for 2.6–2.8 sec. The time window for FFT is 8 msec and 360 ensembles are averaged.

Figure 5

Typical time evolution of $T_{\mathrm{rad}}$ fluctuation (red line) and low-pass filtered ($\le 3.5\mathrm{kHz}$) signal (black line) at abrupt change of fluctuation amplitude. The onsets of change of amplitude (blue circles) are evaluated from envelope of low-passed signal measured at each radius.