Microwave Reflectometry in TJ-II

Transcription

1 Microwave Reflectometry in TJ-II E. Blanco, T. Estrada, L. Cupido*, M.E. Manso*, V. Zhuravlev** and J. Sánchez Laboratorio Nacional de Fusión, Asociación Euratom-CIEMAT, Madrid, Spain Abstract *Associação Euratom-IST, CFN, Instituto Superior Técnico, Lisboa, Portugal ** Institute of Nuclear Fusion, RNC Kurchatov Institute, Moscow, Russia Reflectometry measurements have permitted the characterization of the perpendicular velocity shear layer that develops spontaneously above a critical plasma density value. These observations have been crosschecked with the results obtained using a twodimensional full-wave code that we have developed to help in the interpretation of the experimental data. Both experimental and numerical results demonstrate the capability of the reflectometer to measure the velocity shear layer with a high spatial resolution. The experiments also show modifications in the spectra linked to the presence of a low order rational surface in the rotational transform profile. This modification in the spectra is interpreted in terms of a localized increase in the perpendicular velocity of the density fluctuations. However, quantitative information on the rotation velocity is not available with the present experimental set-up. The last section of the paper is devoted to study the viability of the Doppler reflectometry technique to measure the rotation velocity in TJ-II using the 2D full-wave code. Introduction Microwave reflectometry has been applied to the measurement of density profiles since more than 15 years [1]. The determination of the density profile by microwave reflectometry requires the measurement of the time delay (phase delay) of a probing beam reflected by the plasma cut-off layer. Different techniques were developed to improve the measurement of the time delay, e.g. fast swept frequency modulated continuous wave (FM-CW), amplitude modulated (AM), two frequency differentialphase or pulse radar systems. An amplitude modulation reflectometer is in operation in the stellarator TJ-II working in the frequency range from 25 to 45 GHz with X-mode polarization, and covering densities from.3 to m -3. The reflectometer works routinely and it is capable of measuring even in conditions of high turbulence. A complete description of the system can be found in [2]. A second reflectometer for density fluctuation measurements is installed in TJ-II. The reflectometer is a broadband fast frequency hopping heterodyne system [3]. The system allows us to probe several plasma layers within a short time interval during the discharge. The reflectometer works in the frequency range from 33 to 5 GHz with X-mode polarization, and covers densities from.3 to m -3. This is almost the whole density range of the TJ-II plasmas heated by ECH. However, due to the flat density profiles (or even hollow) of the ECH plasmas and the low magnetic field gradient in TJ-II, the accessible radial range is limited to ρ The antennae arrangement was designed to view the plasma perpendicularly to the cut-off layer. However, a small misalignment may exist as it is seen in the measurements. This small misalignment in the antennae arrangement has allowed the characterization of perpendicular velocity shear layers in the plasma, and to study the modifications of the spectra in the reflectometer signals linked to the presence of low order rational surfaces in the plasma. We have also developed a twodimensional full-wave code to help in the interpretation of the reflectometer signals.

2 The code uses the Finite-Difference Time-Domain technique to solve the wave propagation in magnetised and turbulent plasmas. Realistic plasma shape, density profile, magnetic configuration, and antennae arrangement are included to reproduce as much as possible the experimental conditions in TJ-II. A complete description of the code can be found in [4]. 1.- Characterization of perpendicular velocity shear layers As it has been reported [5] a perpendicular velocity shear layer develops spontaneously at the plasma edge of TJ-II above a certain plasma density. This spontaneous shear flow appears close to the Last Closed Magnetic Surface (LCMS). In this region, Langmuir probes can be used to characterize it. This phenomenon has been studied modulating the plasma density around the critical value (which is around m -3 for the standard magnetic configuration). The reflectometer is tuned to a low and fixed frequency (34 GHz) to probe a layer close to the radial position of the Langmuir probes. The reversal in the perpendicular phase velocity observed by the Langmuir probes is also observed in <n e > (1 19 m -3 ) <n e > 1 a) <f> # t (ms) power (db) # ms b) ms -5 5 f (khz) Figure 1. a) average plasma density (solid line) and mean frequency of the complex amplitude ( Ae i! ) spectra of the reflectometer signal. b) power spectra in two different time intervals with densities below (17-18 ms) and above ( ms) the critical density. the reflectometer signals. Figure 1(a) shows the time evolution of the averaged density (solid line) and the mean frequency of the complex amplitude spectra (Ae iφ ) of the reflectometer signals (dotted line). Figure 1(b) shows the power spectra of the complex amplitude obtained in two different time intervals where the density is lower (17-18 ms) and higher ( ms) than the critical value. It can be seen that as the density increases from.4 to m -3, the mean frequency of the spectra changes its sign indicating a reversal in the perpendicular rotation velocity of the plasma. This behaviour agrees with the perpendicular phase velocity measured by Langmuir probes [6]. The behaviour of the turbulence rotation for inner radial locations where Langmuir probes measurements are no available has been studied changing the reflectometer frequency in a staircase mode during the discharge and changing the plasma density from shot to shot. Figure 2 summarized the results for three different average plasma densities. Figure 2(a) shows the temporal evolution of the averaged plasma density for three different discharges (shot #11294 with an average density above the critical value, shot #11291 close to the critical value, and #11289 below the critical value). It also shows the changes in the reflectometer frequency versus time. Figure 2(b) shows the mean frequency of the complex amplitude spectra measured in the previous discharges. A fourth shot with higher density (solid circles) is also shown. Figure 2(c) plots the

3 same data as a function of the cut-off radius. This figure shows that if the density is lower than the critical value ( m -3 ) all the mean frequencies are positive independently of the radial position. As the density increases up to the critical value, a shear layer develops close to the plasma <n e > (1 19 m -3 ).8.6 a) #11294 #11291 # t (ms) Figure 2. (a) time evolution of the average density in three different discharges (below, close and above the critical value. The staircase variation of the probing frequency is also shown. f RF (GHz) edge (zero crossing at ρ.8). Increasing further the density the shear layer moves to inner radial locations (ρ.75 for an average plasma density of m -3 and ρ.7 for an average density of m -3 ). Figure 2(c) also indicates that the radial separation between points with different sign of the mean frequencies is 1 cm approximately, comparable to the vacuum wavelength of the probing beam. These results indicate that the reflectometer is capable of measuring the inversion of the perpendicular rotation velocity in a very narrow region. The high spatial resolution of the system has been tested with the help of the two-dimensional full-wave code described before. For this study we simulate a velocity shear layer close to the plasma edge. We consider a constant perpendicular b) c) f (GHz) RF ! Figure 2:(b) Mean frequency of the complex amplitude spectra for the different probing frequencies. A four discharge with a higher average density (full circles) is also shown. (c) same data as a function of the cut-off radius velocity of 3 km/s at the plasma edge. This velocity is changed linearly in the shear layer region to a positive value of +3 km/s and it remains constant for inner radial locations. The width of the shear layer is 4 mm approximately. The reflectometer signals are simulated for different probing frequencies within the band 33-5 GHz. First numerical simulations indicate that asymmetric spectra as the ones obtained in the experiments are reproduced for a misalignment in the antennae arrangement as small as two degrees. Thus, we consider this tilt angle in the simulations. Figure 3 shows the spatial dependence of the perpendicular velocity (solid line) and the mean frequencies of the complex amplitude spectra (circles) obtained from the simulations. This figure shows the capability of the reflectometer to measure the velocity shear layer with a spatial resolution of about 1 cm (better than twice the probing wavelengths in vacuum). The complex amplitude spectra for probing frequencies 44, 43, 42, 39, 37 GHz are shown in figure 4. Figure 3 also indicates a notable difference in the mean frequency (absolute value) at the plasma edge and radially inwards. However, the rotation velocity has the same magnitude. This difference can be partially understood in terms of the different

4 curvature of the cut-off layers and the different turbulence amplitude when moving radially inwards. An estimation of the increase in the plasma curvature due to the! f (GHz) 44 v p (m/s) v p (m/s) R (m) Figure 3. Perpendicular velocity and mean frequency of the simulated spectra as a f unction of the major and normalised radius plasma shape of TJ-II gives that the effective tilt angle of the antenna can rise as much as two degrees when moving radially inwards. On the other hand, we consider a constant profile of the normalized density fluctuations ñ/n in these simulations. Therefore the density fluctuation level ñ increases when moving radially inwards and contribute to the asymmetry in the spectra. We have checked that reducing the rms value of the turbulence from 1 to 5 %, the mean frequency decreases in a factor of 2. These simulations show the high spatial resolution of the reflectometer to measure the velocity shear layer. However, the system is not designed as a Doppler reflectometer. Thus, quantitative about the rotation velocity cannot be obtained. Next section is devoted to show the modification in the spectra due to the presence of a low order rational surface and the results are interpreted as an increase in the perpendicular rotation velocity. spectra (a.u.) f (GHz) f(khz)! Figure 5: Spectra measured in a magnetic configuration with iota = 3/2 at!!.65 (in vacuum) spectra (a.u.) f (khz) 2.- Modification of the spectra linked to rational surfaces Modifications in the spectra have been observed in configurations with a low order rational surface at the radial range covered by the reflectometer. In the set of experiments presented in this section, the rational surface 3/2 is located close to ρ =.65. Figure 5 shows the complex amplitude spectra of the reflectometer signal for different radial locations (from ρ =.55 up to ρ =.77). The spectrum at the most internal radial location (ρ =.55) shows a coherent mode of about 1 khz and the spectra modifications appears for the adjacent probing frequencies. The results can Figure 4.- Simulated power spectra for probing frequencies (from top to bottom) 44, 43, 42, 39, 37 GHz

5 be interpreted as a localized increase in the perpendicular rotation velocity of the fluctuations. If we consider that the misalignment of the antennas is two degrees as it was justified before, and we take into account the relatively long probing wavelengths, we conclude that the perpendicular velocity should be as high as 15 2 km/s to reproduce the experimental data. The increase in the perpendicular velocity can be explained if we consider that the magnetic island produces an enhancement in the electron diffusion higher than ion diffusion. The plasma reacts creating a strong positive electric field to preserve the ambipolarity and such strong radial electric field increases the perpendicular rotation velocity of the plasma. A similar phenomenon has been measured using HIBP during the formation of e-itbs triggered by low order rationals [7]. However, as it was mentioned before, absolute values of the rotation velocity cannot be obtained with the present reflectometer. To properly measure the perpendicular rotation velocity of the plasma, a Doppler reflectometer with optimum beam width and beam curvature is needed. In the next section we use the two dimensional full-wave code to obtain the characteristics that a Doppler reflectometer must have to be able to measure the plasma rotation in TJ-II. 3.- Doppler reflectometry studies using the 2D full-wave code The Doopler reflectometry technique allows the determination of the perpendicular rotation velocity of the density fluctuations. An accurate optimisation of the Doppler reflectometer arrangement allows the separation of the different diffraction orders selecting preferentially the order 1 (Bragg backscattered wave in the vicinity of the turning point). The spectral resolution of the system determines its capability to separate the th and 1 st order and the achievement of quantitative values. The relevant parameters for optimisation of the spectral resolution are the antenna pattern (spot size and Figure 6. Complex amplitude spectrum for the standard gain horns intalled i n TJ-II. The tilt angle is 18 degrees and the frequency of the wave is 4 GHz beam curvature) and the antenna tilt angle. In this section, we summarize the simulations that we have done to study the viability of Doppler reflectometry in TJ-II. First numerical simulations indicated that standard gain horns as the ones used in the frequency hopping reflectometer will not work for Doppler reflectometry measurement in TJ-II. As an example, figure 6 shows the simulated spectra with such antenna type. The plasma rotates in the perpendicular direction at a velocity of 3 km/s. The probing frequency is 4 GHz and the antenna tilt angle is 18º with respect to the normal surface of the plasma. The expected Doppler frequency should be located at 25 khz. However, both diffraction orders ( th and 1 st ) are not separated. This is mainly due to a poor spectral resolution of the system consequence of the beam curvature. Simulations were done using gaussian antennas with different beam widths. The cut-off layer is located in the Rayleigh zone of the beam where nearly plane wavefronts exist. We have found from the simulations that the optimum spectral resolution is obtained for a beam waist close to 3 cm as it can be observed in the figure 7. Also it is shown the same results for slab plasma (typical of large machines). In the last case, large beam waist leads to better resolutions.

6 Figure 8 shows the simulated spectra of the complex amplitude for a gaussian beam with the optimum value for the beam waist ( 3 cm). The probing frequency is 4 GHz, the perpendicular velocity of the density fluctuations is 3 km/s and the antenna tilt angle is 18 degrees. According to these parameters, the expected doppler shift should be -25 khz. As it can be seen, the numerical results are in well agreement with the expected Figure 7. Spectral resolution for TJ-II plasmas and slab plasmas as a function of the gaussian beam waist Figure 8. Complex amplitude spectrum for A gaussian beam of 3 cm. The tilt angle is 18 degrees and the frequency of the wave is 4 GHz values and the spectral resolution horns.! f / f is better than that obtained with standard gain D References [1] H. Bottolier and G. Ichtchenko. Rev. Sci. Instrum. 72 (1987) 539 [2] T. Estrada, J. Sánchez, B. van Milligen, L. Cupido, A. Silva, M.E. Manso and V. Zhuravlev. Plasma Phys. Control. Fusion 43 (21) 1535 [3] L. Cupido, J. Sánchez and T. Estrada. Rev. Sci. Intrum. 75 (24) 3865 [4] E. Blanco, S. Heuraux, T. Estrada, J. Sánchez and L. Cupido. Rev. Sci. Intrum. 75 (24) 3822 [5] C. Hidalgo, M.A. Pedrosa, L. Garcia, and A. Ware. Phys. Rev. E 7 (24) 6742 [6] M.A. Pedrosa, C. Hidalgo, E. Calderón, T. Estrada et al. Plasma Phys. Control. Fusion 47 (25) 777 [7] T. Estrada, L. Krupnik, N. Dreval et al. Plasma Phys. Control. Fusion 46 (24) 277