Higher Harmonics in the Perturbative Transport Study in TJ-II ECH Plasma

Abstract

We analyzed the higher harmonics of temperature perturbation in the modulated electron cyclotron heating experiment on TJ-II plasma. The higher harmonics (e.g., 5th harmonic) exhibited significantly weaker decay in amplitude as they propagated in radius as compared with the prediction by diffusive model. The change in the time derivative of temperature at the onset (and turning-off) of the heating power propagates in radius with very little temporal smoothening. Recently, a new method for analyzing anomalous transport in magnetically confined plasmas was developed. This new method directly measures the gradient-flux relation by studying the temperature response with respect to modulations of the electron cyclotron heating (ECH) power. Using this method, hysteresis in the gradient-flux relation was observed in LHD plasmas [1,2]. Because heat flux is a multivalued function of gradient, the temperature perturbation dynamics are far from a simple diffusive response with constant diffusion coefficient. Therefore, higher harmonics can exhibit smaller or larger spatial damping rates in comparison with the diffusive response. To observe the violation of the simple diffusive relation q = −nχ∇T with homogeneous χ, measuring the higher harmonics of temperature perturbation in the heating modulation experiment was proposed [3]. In this rapid communication, we report the application of the abovementioned method to the modulated electron cyclotron heating (MECH) experiment on the TJ-II [4].The power modulation experiment with line-averaged values around 0.5 × 10 19 m −3 was performed on a lowdensity plasma using continuous on-axis heating with 250 kW and modulated 50 kW (square waveform, 50% duty cycle) microwave beams. The modulation frequency of ECH ( f mod ) is 180 Hz, mostly absorbed in the central core r/a ≤ 0.3 (plasma radius a = 0.2 m), as determined in previous heat wave propagation experiments [5]. The electron temperature profile was measured at ten points in the high-field side region of 0.0 < r/a < 0.9 using an ECE author's e-mail: inagaki@riam.kyushu-u.ac.jp heterodyne radiometer with a time resolution of 10 µs [6]. The comparison with the T e measured using a He beam indicates that ECE can measure T e even at the edge [7]. We applied the conditional averaging technique [1]. In this procedure, the ECH turn-on time (t on ) is detected in each period and temporal evolutions of the electron temperature for time intervals of −3 ms < t − t on < 3 ms were extracted; the extracted signals were averaged over 25 modulations. Post averaging, the noise level significantly decreased. Figure 1 illustrates the power spectrum of the conditionally averaged temperature perturbation and Fig. 1 Power spectrum of the conditionally averaged temperature perturbation (black solid line) and that calculated from the raw signal (red dashed line). Higher harmonics up to the 5th are presented. The black dashed line is for visual aid.

Test of the Telegraph Equation for Transport Dynamics in Plasma

“…1. For m > 1/ω 1 τ, the right-hand side of (7) only weakly depends on m. Compared with the standard diffusion model, this result is more consistent with observations on LHD and TJ-II [9,10]. In those observations, the radial decay rate of amplitudes, k i , for the 5th and 7th harmonics were barely enhanced, contrary to the predictions by the diffusion model.…”

Analysis of higher harmonics on bidirectional heat pulse propagation experiment in helical and tokamak plasmas

“…The hysteresis in the flux-gradient relation can be assessed by the perturbative heating experiment. In particular, the modulation ECH (MECH) is widely used to provide the perturbation in the electron temperature, since its modulation frequency, input power, and deposition can be precisely controlled [1,2,4,5,6,10,11,12,15,16,17]. See also a review [18].…”

“…See also a review [18]. By analyzing not only the fundamental MECH frequency but also its higher harmonics, i.e., the so-called higher harmonic method [14], the possible violation from the diffusive transport picture can be discussed [16,17]. The amplitude radial decay rate of the temperature perturbation is predicted to obey the square root of their frequencies in the case that the linear local theory is valid.…”

Approaches to Hysteresis of Transport Relations in Toroidal Plasmas

“…Using an advanced data analysis, such as conditional average, harmonics, such as the 7th, have been studied. This method was successfully applied to LHD and TJ-II [9,10]. Observations of higher harmonics in the temperature fluctuation are shown in Fig.…”

“…Radial profiles of the intensity of the fundamental, 2nd, 3rd, and 5th harmonics. Reproduced from Ref [10]…”