Reflectometry for density and fluctuation measurement on EAST

Transcription

1 Reflectometry for density and fluctuation measurement on EAST Tao Zhang*, Shoubiao Zhang, Fei Wen, Hao Qu, Yumin Wang, Xiang Han, Defeng Kong, Xiang Gao and EAST contributor Institute of Plasma Physics, Chinese Academy of Sciences, P.O. Box 116, Hefei, Anhui 30031, P.R. China * Abstract: By installing the X-mode polarized Q-band (3 GHz 56 GHz), V-band (48 GHz 76 GHz) and W-band (7 GHz 110 GHz) refelctometries at the mid-plane of low field side on EAST, the plasma density profiles from edge to core in most experiments can be measured. Voltage controlled oscillators (VCOs) are used as microwave sources to achieve fast sweeping of the probing wave frequency and the super-heterodyne detection is realized by using the single side-band modulators (SSBM). The line integrated densities deduced from density profiles measured by reflectometry are consistent with those directly measured by a horizontal interferometer. The density behaviors during and in-between ELM crashes have been analyzed. An X-mode polarized V band (50-75GHz) radial and poloidal correlation reflectometry is also developed for density fluctuation measurement. Two frequency synthesizers (1-19GHz) are used as sources. The low frequency waves from the sources are upconverted to V-band using active quadruplers and then coupled together for emission through one single pyramidal antenna. Two poloidally separated antennae are used to receive the reflected waves from plasma. This reflectometry system can be used for radial and poloidal correlation measurement of the density fluctuation. In EAST ohmic plasma, the radial correlation length is about 1.5 cm measured by the system. The poloidal correlation analysis provides a means to estimate the fluctuation velocity perpendicular to the main magnetic field (v ). In present analysis, the distance of the two poloidal probing points is calculated from ray-tracing analysis while the delay time was deduced from the slope of the cross-phase dφ/df. The result shows that the v in the core of EAST ohmic discharge is about from -1 km/s to -3 km/s. This fluctuation reflectometry has been also used to study the pedestal turbulence. 1. Introduction Reflectometry is based on a radar technique in which a microwave beam is directed into the plasma with the wave reflected from the cutoff layer being detected [1, ]. Since the phase of the reflected wave is determined by the optical distance, the electron density profile can be derived from the phase variation along the wave path [3]. Due to its simple instruments, the reflectometry has been widely applied to measure density profiles on present major fusion devices [4-11]. EAST has been equipped with reflectometry diagnostics for density and density fluctuation measurement. Fig. 1 shows the line-sights of the two reflectometries. The reflectometry to measure density profile is composed of three systems, i.e. Q-band (3 GHz 56 GHz), V-band (48 GHz 76 GHz) and W-band (7 GHz 110 GHz) with X-mode polarization and located at about 3 cm above the low field side (LFS) midplane of J port with a horizontal view line. In general, this reflectometry system can measure the density profile from the edge up to the core region at about half of the minor radius. A V-band two channel X-mode correlation reflectometry was also developed to measure the density fluctuation. This system locates at about 15 cm below 1

2 the low field side (LFS) midplane of K port with a 5 degree view line.this system has been used to analyze the poloidal correlation, radial correlation and the velocity perpendicular to the main magnetic field, i.e. v. The density reflectometry and fluctuation reflectometry will be described in section and 3 respectively and lastly we summarized in section 4.. Reflectometry for density profile measurement The Q-band, V-band and W-band density reflectometry used the similar circuit as shown in Fig.1. The sources are voltage controlled oscillators (VCOs). An arbitrary waveform generator (AWG) based on FPGA has been developed to output three independent waveforms synchronously, which are used to control the VCOs of the Q-, V- and W-band reflectometries. This ensures the synchronous measurement of the three independent reflectometries. The waveforms of VCO control voltages are acquired on bench test such that the output frequencies from the VCOs are linear with time [1]. For each system, the output wave of VCO is split into two portions, one for probing the plasma and the other for reference. To achieve superheterodyne detection, the probing wave frequency is modulated in a single sideband modulator (SSBM) by a quartz oscillator at 100 MHz. The wave frequency output from SSBM is upshift 100 MHz and then up-converted by using active quadruplers for Q- and V-band and sextupler for W-band. Two adjacent antennae are used for emission and reception respectively. The wave in the reference arm is also up-converted by quadrupler or sextupler and mixed with the reflected wave. The IF signal from the mixer is then amplified and passes through a bandpass filter. An I/Q detector is used to measure the in-phase (I) and quadrature signal (Q) to allow absolute phase and amplitude detection. Currently, the parameter settings of EAST reflectometry systems are as follows: The frequency range: Q-band is 3 GHz - 56 GHz, V-band 48 GHz - 76 GHz and W-band 7 GHz GHz. I/Q sampling frequency is 60 MHz. The period of probing frequency sweeping is 50 μs. For X-mode polarized reflectometry launched from low field side, the wave will be reflected from right-hand cutoff layer, i.e. X-mode cutoff frequency is fce fce f X = + f pe + 4

3 where f ce is electron cyclotron frequency, and f pe is electron oscillation frequency f pe 1 = π It is noted that the X-mode cutoff frequency is equal to the electron cyclotron frequency at zero density. This means that the entire edge density profile can be measured from zero density if the frequency of X-mode probing wave sweeps across the f ce. In experiment, this zero density layer was usually identified from the change of the IF signal amplitude [5, 13]. By installing the Q-band reflectometry, the zero density layer has been determined in the EAST normal operated plasma with toroidal magnetic field of 1.85 T at R ax =1.87 m. In EAST experiment, the reflectometry are triggered at 10 ms before the plasma in each discharge. In this 10 ms time window without plasma, the probing wave is reflected from the inner wall and the data has been used to acquire the time delay (τ) from plasma and then the inverted density profile [14]. Fig.3 (a) shows time-frequency spectra by applying the short time Fourier transformation (STFT) on the complex signal constructed from the I and Q signal before the plasma formation in discharge Here, the result for probing frequency larger than 50 GHz is not shown since those signals are usually very small and not used for analysis. In this time-frequency spectra, there are two clear frequency strips, in which the lower frequency strip is due to the wave directly reflected from the inner wall and the higher one is confirmed as multiple reflection. The beat frequency (f b ) of the reflected signal is not a constant value due to the system dispersion produced mainly by wave propagation in coaxial cable and waveguide. Fig.3 (b) shows the time-frequency spectra of signal at a time of plasma current flattop phase. From reflected signal in this spectrum, a sudden decrease of the beat frequency is clearly observed when probing frequency sweeps from 38 GHz to 40 GHz. When the probing frequency is lower than a certain frequency (f zero, cutoff frequency at zero density), the X-mode polarized wave pass through the plasma and reflects from the inner wall. This induces an even higher beat frequency than that without plasma. When the probing frequency is larger than the f zero, the wave is reflected from low field side edge plasma. As a result, the optical length of wave propagation is much shorter and thus the beat frequency is much lower. This f zero could be determined from the sudden decrease of the beat frequency in Fig.3 (b). However, the f zero determined in this way will have a large uncertainty due to a low time definition from the time-frequency analysis. Fig.3 (c) shows the I/Q signal amplitude w/o plasma (A vac ), with plasma (A plasma ) and the normalized amplitude A norm (A norm =A plasma /A vac ) from top to bottom. Here, the e ne ε m 0 e amplitude is calculated as A= I + Q. The use of the normalized amplitude can eliminate the effect of output power unflatness for different probing frequencies. The f zero is taken as the first frequency at which the A norm is larger than (A max -A min )*0.+A min, where A max (A min ) is the maximum (minimum) value of A norm. As shown in bottom plot of Fig.3 (c), the horizontal dashed line indicates the value of (A max -A min )*0.+A min and then the f zero is determined as 59.5 GHz according to the above argument. Presently, the time delay due to plasma is obtained from the beat frequency, which is calculated by using the time-frequency analysis [14]. Since the fast sweeping of the probing frequencies, each point from the time-frequency analysis represents an average for a specific range of probing frequencies. This could induce uncertainty of the time delay and thus the density profile. In order to consider this uncertainty, we have taken the width of beat frequency spectrum as the error of f b and this resulted in an estimation of the error of time delay (τ err ). Fig. 4 (a) shows 3

4 the beat frequency spectrum for probing frequency of 4 GHz in Fig. 3 (b). For a selected frequency range, the spectrum is fitted by a function with a form of a*exp[-(f b -f c ) /w f ]. The Fig.3 (a) and (b) show time-frequency spectra measured by Q-band reflectometry without and with plasma respectively. (c) shows the signal amplitude without plasma, with plasma and the normalized amplitude from up to down. In the bottom plot, the horizontal dashed line indicates the value of (A max -A min )*0.+A min and the vertical line indicates the f zero =39.5 GHz. beat frequency at this probing frequency is taken to be the value of f c while the spectrum width w f is taken as the error of beat frequency. Then the time delay (τ) and its error (τ err ) can be calculated by using the expressions of τ=f b /(df prob /dt) and τ err = w f /(df prob /dt) respectively, where df prob /dt is the sweeping rate of the probing wave frequency. Fig.4 (b) shows the time delay with error for the plasma in Fig.3. Here, only Q- and V-band reflectometry data are used for analysis since the reflected signal of W-band reflectometry in this plasma is very low. A Monte Carlo procedure is then applied to acquire the density profiles. For each data point in Fig.4 (b), it is assumed the time delay can take any value in the range of [τ-τ err, τ+τ err ] and a uniformly distributed random numbers are produced in this range. A program is then used to randomly select one value in these random numbers. By doing such random selection for every data point one time, a set of time delay profile is formed. We usually repeated this progress 0 times and so 0 possible time delay profiles can be formed, as shown in Fig.4 (c) where these possible τ profiles are plotted together. From each possible τ profile, one density profile can be inverted by using a modified X-mode inversion method [15]. As a result, 0 possible density profiles can be formed and has been plotted together in Fig.4 (d). From these possible profiles, the needed density profile could be acquired by fitting these data using a suitable function or by averaging these profiles. And simultaneously, the error of the density profile measured by reflectometry can be evaluated. The density measured by reflectometry has been compared with the POINT diagnostics on EAST, which is a multichannel far-infrared laser-based POLarimeter-INTerferometer system to measure the electron density and Faraday rotation angle [16]. The POINT presently has five horizontal channels, which are along Z=34 cm, 17 cm, 0 cm, -17 cm and -34 cm respectively. Fig.5 (a) shows the line-sights of the upper three channels of POINT and that of reflectometry. The interferometer measures the density integration along the path, i.e. dl n e. In order to do the comparison, the density profiles (e.g. Fig.4 (d)) measured by reflectometry are firstly fitted by some smooth functions, here the MTANH function [17] used. The fitted profile is shown as red dashed line in Fig.4 (d) and this profile is then mapped to the line-sights of the three channels of 4

5 Fig.4 (a) Beat frequency spectrum and fitting using function a*exp[-(f b -f c ) /w f ]. (b) time delay with error. (c) 0 possible time delay profiles from Monte Carlo procedure. The red data points with error-bar are same as that in (b). (d) 0 possible density profiles inverted from the τ profiles in (c). The dashed line is MTANH fitting curve and the vertical line indicates the sepratrix. POINT using equilibrium reconstruction of EFIT. Lastly, the mapped density profiles are integrated directly along their corresponding paths. This integrated densities from reflectometry are compared with the value measured by the upper three channels of POINT at several times for discharge as shown in Fig.5 (b). The result shows a good consistency of the two diagnostics. It should be noted here that due to the lack of the density measurement by reflectometry in the core region from R=1.87 m to R=.0 m, uncertainty could be produced by using the fitted profile in Fig.4 (d). We have checked how large of the uncertainty for two extreme cases: one is a very flat core density for which the density from R=1.87 m to R=.0 m is nearly at the same value of ~.5*10 19 m -3 and the other one is a more peaked profile for which the density increases linearly from ~.5*10 19 m -3 at R=.0 m to 4*10 19 m -3 at R=1.87 m. It was found that the results for both cases produced not more than 5% difference from the fitted profile in Fig.4 (d). Fig.5 (a) Line-sights of horizontal interferometer POINT and reflectometry on EAST, (b) Comparison of the line integrated density between reflectometry and POINT. The reflectometry has been used to measure the density pedestal crash due to ELMs. After the ELM crash, the density pedestal also crashes, which leads to the pedestal top density decrease but the pedestal bottom and SOL density increases (Fig.6) and thus the pedestal density gradient 5

6 decreases. The density pedestal takes about 10 ms to recover the value before ELM crash and then keeps no clear change up to next ELM crash. 3. Reflectometry for density fluctuation measurement The schematic of radial and poloidal correlation reflectometry is shown in Fig.7. The system is composed of two channels. For each channel, a synthesizer is used as source. The synthesizer can be tuned from GHz to 0 GHz while we only choose the frequency range from 1 GHz to 19 GHz in experiment. When the synthesizer works at sweeping mode, the phase locking time is less than 9 ms which is much smaller than the typical energy confinement time of 100 ms on EAST. The output wave of the synthesizer in each channel is divided into two portions, one of which is used as probing am and the other as reference arm. The wave from the probing arm is mixed with a 100 MHz signal generated by a crystal oscillator in a single side band modulator (SSBM). The upper sideband frequency from the SSBM is up-converted to the required V band frequency with an active quadrupler. The probing waves in the V band frequency range acquired from the two channels are coupled with a 3 db coupler and launched into the plasma through one antenna. Each reference arm is also divided into two portions. The two waves are extended to the V band frequency range using active quadruplers and mixed with the reflected waves received by two poloidally separated antennae respectively. The IF signals output from these mixers are detected by I/Q detectors from which the in-phase (I) and quadrature (Q) signals are acquired and allows absolute, which allows absolute detection of phase and amplitude of the reflected waves. This system has been used to do radial and poloidal correlation analysis. Fig.8 shows the radial correlation analysis in ohmically heated plasma at EAST, where γ is the cross correlation coefficient and Δr is the radial separation. The line averaged density is m -3 and the plasma current is 300 ka. In this discharge, the first synthesizer works at the frequency range from GHz to 17. GHz with 10 steps. The step duration of each frequency is 10 ms. Simultaneously, frequency of the second synthesizer was fixed at 16.5 GHz. The corresponding measurement position locates at r/a=0.56. The experimental results in Fig.8 is fitted with Gaussian function γ=aexp(-δr /w ) where a and w are two fitting parameters. It is seen in the figure that the experimental values of γ can be fitted 6

7 with this function very well. From this fitting, the radial correlation L r is determined at 1.5 ±0.3 cm. The other goal of the newly developed correlation reflectometry is to measure the velocity of electron density fluctuation perpendicular to the main magnetic field, v which can be calculated as v =d/τ where d is the distance between the centers of two reflecting spots at the cutoff layer corresponding to two receiving antennae and τ is the delay time that can be deduced from the poloidal coherence analysis. Fig.9 shows an example of poloidal coherence and cross phase spectra by applying the coherence analysis to the signals received by the two poloidally separated receiving antennae. The measurements are performed in ohmically heated plasma where the line averaged density is m -3 and the plasma current is 50 ka. It is noted that only the frequency components with 'significant coherence' can be used for the data analysis. Here, we define 'significant coherence' as that the coherence value is larger than two times the noise level. For the case in FIG.\ref{fig:poloidal correlation}, the noise level of coherence value is estimated at about 0. by considering the statistic error in doing the spectral analysis. So the frequency components with 'significant coherence', i.e those with coherence larger than 0.4, are from about -100 khz to 50 khz. It is observed that there is a nearly constant slope for this frequency range in the cross phase spectrum, indicating the propagation of the fluctuation between two reflecting spots. The propagation time of this structure between the two poloidal probing points is called delay time which can be calculated as τ=-(1/π)(dφ/df). The delay time for the case shown in this figure is about μs. Here, the negative value of delay time indicates the turbulence structure propagates in the electron diamagnetic drift direction. Presently, the antennae are far away from the plasma (about 1.8 m between separatrix and antennae) and the estimation of the poloidal distance (d) needs to consider the wave propagation in vacuum and plasma. For this purpose, we have developed a D X-mode ray tracing code based on the complex eikonal method [18-1]. Fig.10 (a) shows an example of ray-tracing calculation using the code for a 56 GHz X-mode wave propagation in the real experimental geometry. In this calculation, the incident wave is assumed to be Gaussian and 0 rays are used. The ray-tracing method enables the calculation of the coordinates of reflecting point and receiving point for each ray. Fig.10 (b) shows Z coordinates at receiving plane and Z coordinates at cutoff layer of the 0 rays in the tracing calculation. The relation of the two Z coordinates is nearly linear. Poloidal distance between two reflecting spots at the cutoff layer is calculated by mapping the Z coordinates of receiving antennae onto the cutoff layer using this relation. Since difference of R coordinates of reflecting points (ΔR) is much 7

8 smaller compared with the difference of Z coordinates (ΔZ), we use ΔZ at cutoff as an estimation of d. For the case shown in Fig.10, the ΔZ is about 0.5 cm while the vertical distance of two poloidally separated antennae in the receiving plane is as large as 5 cm. Fig.10 (a) example of ray-tracing of a 56 GHz X-mode Gaussian wave (b) mapping of Z from antennae plane to the cutoff plane using this ray-tracing calculation. After determination of the delay time τ and poloidal distance d using above mentioned methods, the propagation velocity of the density fluctuation structure can be calculated. The radial profile of v in ohmically heated plasma on EAST has been measured by tuning the probing frequencies step by step during the flattop of plasma current and density. The delay times (τ) and the ΔZ are shown in Fig.11(a) and (b) respectively. FIG.11(c) shows the profile of v. The v in core of this ohmically heated plasma is from -1 km/s to -3 km/s. Here the negative v means that the fluctuation rotates in the electron diamagnetic drift direction. Fig. 11 (a) delay time derived from the cross-phase, (b) distance of two receiving antennae mapped on the corresponding cutoff layer using 3D ray-tracing code, (c) estimated perpendicular velocity of turbulence. 4. Summary By combining the Q-, V- and W-band reflectometries, the density profile from edge to core can be provided in most of present EAST experiments. A Monte Carlo procedure was used to analyze the density profiles from the reflectometry measurement. A comparison of the line integrated density measured by reflectometry and horizontal interferometer shows a good consistency of both diagnostics. The density crash during ELM crash is clearly observed. A V-band X-mode polarized two channel correlation reflectometry is designed and installed in 014 campaign. The radial correlation length of the fluctuation measured by reflectometry is about 1.5±0.3 cm in ohmically heated plasma core. The turbulence perpendicular velocity (v ) has been estimated based on the knowledge of the poloidal distance and the propagation time where the poloidal distance is calculated using a D X-mode ray tracing code and the propagation time is directly estimated from the poloidal coherence analysis. It has been shown that the value of v is 8

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