2D electron cyclotron emission imaging at ASDEX Upgrade (invited)

Rev. Sci. Instrum. 81, 10D929 (2010); https://doi.org/10.1063/1.3483214 81, 10D929 © 2010 American Institute of Physics. 2D electron cyclotron emission imaging at ASDEX Upgrade (invited) Cite as: Rev. Sci. Instrum. 81, 10D929 (2010); https://doi.org/10.1063/1.3483214 Submitted: 14 May 2010 . Accepted: 19 July 2010 . Published Online: 28 October 2010 I. G. J. Classen, J. E. Boom, W. Suttrop, E. Schmid, B. Tobias, C. W. Domier, N. C. Luhmann, A. J. H. Donné, R. J. E. Jaspers, P. C. de Vries, H. K. Park, T. Munsat, M. García-Muñoz, and P. A. Schneider ARTICLES YOU MAY BE INTERESTED IN Commissioning of electron cyclotron emission imaging instrument on the DIII-D tokamak and first data Review of Scientific Instruments 81, 10D928 (2010); https://doi.org/10.1063/1.3460456 Development of KSTAR ECE imaging system for measurement of temperature fluctuations and edge density fluctuations Review of Scientific Instruments 81, 10D930 (2010); https://doi.org/10.1063/1.3483209 Quasi 3D ECE imaging system for study of MHD instabilities in KSTAR Review of Scientific Instruments 85, 11D820 (2014); https://doi.org/10.1063/1.4890401 2D electron cyclotron emission imaging at ASDEX Upgrade „invited…a… I. G. J. Classen,1,2,b兲J. E. Boom,2W. Suttrop,1E. Schmid,1B. Tobias,3C. W. Domier,3 N. C. Luhmann, Jr.,3A. J. H. Donné,2,4 R. J. E. Jaspers,4P. C. de Vries,2 H. K. Park,5T. Munsat,6M. García-Muñoz,1and P. A. Schneider1 1Max Planck Institut für Plasmaphysik, 85748 Garching, Germany 2FOM-Institute for Plasma Physics, Rijnhuizen, 3430 BE Nieuwegein, The Netherlands 3University of California at Davis, Davis, California 95616, USA 4Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands 5POSTECH, Pohang, Gyeongbuk, 790-784, South Korea 6University of Colorado, Boulder, Colorado 80309, USA 共Presented 18 May 2010; received 14 May 2010; accepted 19 July 2010; published online 28 October 2010兲 The newly installed electron cyclotron emission imaging diagnostic on ASDEX Upgrade provides measurements of the 2D electron temperature dynamics with high spatial and temporal resolution. An overview of the technical and experimental properties of the system is presented. These properties are illustrated by the measurements of the edge localized mode and the reversed shear Alfvén eigenmode, showing both the advantage of having a two-dimensional 共2D兲measurement, as well as some of the limitations of electron cyclotron emission measurements. Furthermore, the application of singular value decomposition as a powerful tool for analyzing and filtering 2D data is presented. © 2010 American Institute of Physics. 关doi:10.1063/1.3483214兴 I. INTRODUCTION Many processes and instabilities in tokamak plasmas exhibit two-dimensional 共2D兲dynamics, thereby making them difficult to diagnose by one-dimensional 共1D兲diagnostics. The strength of 2D electron cyclotron emission imaging 共ECEI兲was first demonstrated at the TEXTOR tokamak.1It provided valuable physics insight in the research of, among others, the sawtooth instability2,3and tearing modes.4,5An overview of the development of ECEI systems since the first TEXTOR diagnostic can be found in the literature.6 Recently an ECEI system has been installed at ASDEX Upgrade in order to investigate the 2D electron temperature dynamics of other reactor relevant instabilities, including edge localized modes 共ELMs兲and neoclassical tearing modes, not easily accessible at TEXTOR. This system images a plasma area of approximately 12 by 40 cm 共8by16 channels兲. An overview of the technical and experimental properties of this ASDEX Upgrade ECEI system is presented here. Apart from giving a description of the system 共Secs. II and III兲, this paper also covers an overview of the experimental ranges and limitations from the perspective of a user 共Sec. IV兲. These properties will be illustrated by the measurements of the ELM instability, showing both the advantage of having a 2D measurement, as well as some of the limitations of electron cyclotron emission 共ECE兲measurements 共Sec. V兲. Finally, a singular value decomposition 共SVD兲is used to overcome the limitations set by thermal noise, which allowed the visualization of Alfvén waves 共Sec. VI兲. II. THE PRINCIPLE OF ECEI A standard 1D ECE radiometer measures the electron temperature at different radial locations along a single line of sight, making use of the magnetic field dependence of the electron cyclotron frequency ␻ ec=eB/medue to the variation of the magnetic field with major radius B⬇B0R0/Ras is seen in Fig. 1共a兲. In the thermal equilibrium, the measured intensity at a given resonant frequency 共and corresponding radius兲 is given by the Rayleigh–Jeans limit of Planck’s law IBB共 ␻ 兲= ␻ 2kBTe/共8 ␲ 3c3兲, so the plasma behaves as a blackbody and the intensity is proportional to the electron temperature. Therefore, a frequency resolved measurement of the electron cyclotron emission intensity constitutes a radially resolved measurement of the electron temperature. The same principle is employed in a 2D ECEI diagnostic, except that multiple lines of sight are simultaneously quasioptically imaged onto a linear array of diode detectors 关see Fig. 1共b兲兴. Each of the lines of sight is treated as a 1D ECE radiometer. This gives a direct 2D measurement of the electron temperature; radially resolved due to the frequency resolved measurement of the ECE intensity along each line of sight, vertically resolved due to the multiple lines of sight corresponding to the detectors on the array. III. ASDEX UPGRADE ECEI In Fig. 2, a schematic representation of the various components of the ASDEX Upgrade ECEI system is given. ECEI uses the same 36 cm diameter quartz vacuum window as the 1D ECE radiometer 共“manhole” in sector 9兲, and also shares part of the 共newly designed兲optics with this diagnostic. The two systems are separated by a beamsplitter 共a thin dielectric foil兲that has an approximately 50/50% transmission/ reflection over the full range of frequencies, with the ECEI optical path in reflection. The ECEI optics actually consist of a兲Invited paper, published as part of the Proceedings of the 18th Topical Conference on High-Temperature Plasma Diagnostics, Wildwood, New Jersey, May 2010. b兲Author to whom correspondence should be addressed. Electronic mail: [email protected]. REVIEW OF SCIENTIFIC INSTRUMENTS 81, 10D929 共2010兲 0034-6748/2010/81共10兲/10D929/6/$30.00 © 2010 American Institute of Physics81, 10D929-1 two branches, the front side optics that images the plasma radiation on the detector array, and the LO side optics 共separated from the first one by a further beamsplitter兲that images the local oscillator BWO beam on the array. All ECEI components 共except the computers兲are positioned in the ASDEX Upgrade torus hall. The various components of the system are described in the following paragraphs. The ASDEX Upgrade ECEI system utilizes the detector array and intermediate frequency 共IF兲electronics of the previous TEXTOR ECEI system. The detector array employs 16 dual dipole antennas with an array of 16 miniature elliptical substrate lenses9共minilenses兲in front of them, yielding highly Gaussian, parallel field patterns. In Fig. 3, a schematic layout of the ECEI electronics of a single antenna is shown. The signal is downconverted two times. The first downconversion occurs at the array by mixing the plasma signal with the BWO signal 共tunable between 90 and 140 GHz兲. This is a single sideband downconversion; the lower sideband is rejected by using quasioptical high pass filters 共dichroic plates兲 in front of the array. The downconverted broadband signal of each of the 16 antennas is transmitted to the 16 IF electronic modules by microwave cables. In the IF modules, the signal is divided into eight portions, which are subsequently mixed with eight local oscillator signals 共voltage controlled oscillators at fLO=2.4, 3.2, 4.0, 4.8, 5.6, 6.4, 7.2, and 8.0 GHz兲in the second downconversion step. The frequency difference between these local oscillators determines the radial interchannel spacing of ECEI and is hence 800 MHz. This typically corresponds to 1.5 cm in the plasma, depending upon the gradient of B. The full radial coverage of ECEI is hence approximately 12 cm. The resulting signals are band pass filtered 共double sideband兲, with an intermediate frequency bandwidth BIF of 700 MHz. This determines the frequency bandwidth of the ECE radiation selected by each channel and, along with broadening effects, the radial resolution. After detection, the signals are low pass filtered 共with a tenth order filter兲with adjustable video bandwidth BV=25–400 kHz, determining the time resolution of ECEI. The sampling frequency is normally set to 共at least兲twice BV. Finally, the signals are converted to a digital signal by 12 bit digitizers, capable of storing 2 Msamples per channel at a maximum sampling rate of 2 Msamples/s. More technical details concerning the array and electronics can be found in the literature.7–9 The front side optics, shown in Fig. 4, consist of a set of high density polyethylene 共HDPE兲lenses, part of which is shared with a 60 channel 1D ECE radiometer. The line of sight of the 1D system is designed to coincide with the optical axis of ECEI, simultaneously providing in the same poloidal plasma cross section a measurement of the full 1D electron temperature profile as well as the detailed 2D coverage of a selected area of about 12 by 40 cm 共8by16 channels兲. This also makes cross calibration with the absolutely calibrated 1D system easier. ECEI lines of sight have adjustable 共although not independent兲foci. This is made possible by translating one of the lenses to shift the position of the focal plane to the desired radius 共Fig. 4兲. This makes it possible to always operate ECEI in focus 共unlike 1D ECE, which has a fixed focus兲. Also, the confocal parameter 共about 40 cm兲is larger than the radial coverage, ensuring all ECEI channels are in focus. The optics have been designed such that the location FIG. 3. Schematic representation of the electronics of a single detector for a typical ECEI system. FIG. 4. 共Color online兲Optics of the ASDEX Upgrade ECEI system. Part of the optics are shared with the 60 channel 1D ECE radiometer. The position of the focal plane can be shifted by translating one of the HDPE lenses. FIG. 1. Comparison between 共a兲a standard 1D ECE radiometer and 共b兲a 2D ECEI system. In an ECEI system, multiple lines of sight are imaged onto a 1D array of detectors. FIG. 2. 共Color online兲Diagram showing all major components of ECEI. 10D929-2 Classen et al. Rev. Sci. Instrum. 81, 10D929 共2010兲 along the beam path where all 16 beams from the detectors exactly overlap each other in space 共the Fourier plane of the optics兲lies close to the window aperture. In this way, all beams use as much of the aperture as possible, thereby optimizing the perpendicular spatial resolution. The window aperture is hence the limiting factor determining the 共diffraction limited兲Gaussian beam waist w0=2d␭/ ␲ D, where dis the distance from the window aperture 共1.8 m at the center of the plasma兲and D=0.36 m is the window aperture diameter 共see Fig. 4兲. This gives a smallest possible spot size of about w0=15 mm in the plasma, which is also achieved by the optics. The antenna pattern of each of the detectors 共including their associated minilens兲can be approximated by a Gaussian beam with a waist of 7 mm in the object plane 共at the detector兲, and the array of 16 detectors has a length of 20 cm. The optics images this object plane 共array兲onto the focal plane in the plasma. Note that the spot size and vertical coverage in the plasma cannot be independently imaged. Consequently, the ideal spot size of 15 mm in the plasma 共about a factor of 2 larger than the spot size at the array兲, also fixes the vertical coverage in the plasma, which is about 40 cm 共twice the size of the array兲. Therefore, with the current array, a smaller vertical coverage is not possible 共the beams would not fit through the window aperture兲, and a larger coverage would lead to a proportionally larger spot size. The local oscillator for the first downconversion step is a backward wave oscillator 共BWO兲. This is a tunable microwave source that typically delivers a 50 mW microwave beam at an adjustable frequency between 90 and 140 GHz 共F-band兲with a frequency stability of 0.02%. The BWO optics image the radiation quasioptically onto the detector array as an elongated Gaussian beam, in order to illuminate all 16 detectors. The BWO is enclosed ina1cmthick iron casing for stray magnetic field shielding. The available cutoff frequencies of the dichroic plates for the sideband rejection are currently 99.1, 105.0, 111.7, 115.6, and 120.2 GHz. The filter has to be chosen such that the lower sideband plasma light is blocked, while permitting both the upper sideband and BWO frequencies to pass. Therefore, in practice, the filter must have a cutoff frequency just below the BWO frequency, thereby limiting the number of useful BWO frequency settings to the available dichroic plates. The operation during 140 GHz electron cyclotron resonance heating 共ECRH兲is possible. In order to protect the array against stray ECRH power, three quasioptical notch filters with a 共combined兲60 dB rejection at 140 GHz 共3dB rejection at about 127 GHz兲are used. No notch filters are currently available for other ECRH frequencies at the ASDEX Upgrade. Operation with a dichroic plate cutoff frequency above the ECRH frequency is always possible. In other cases, the system will be shielded with a shutter. The ECEI diagnostic has been designed to be fully remotely controlled. The position of the focusing lens, the frequency and power of the BWO and the selection of the dichroic plates 共using a stepper motor controlled slide with five filters and a shutter兲are all remotely controlled. Also, the system can be switched on and off remotely. No entry to the Torus Hall is required at any stage during operation, greatly enhancing the flexibility of the system. IV. OPERATIONAL RANGE AND LIMITS The range of radii to which ECEI can be tuned to during experiment depends on the toroidal magnetic field and on the frequency range of the diagnostic. Figure 5provides a graphical representation of this operational range. The horizontal shaded area represents the accessible plasma region 共the second harmonic ECE radiation from the HFS is blocked by the third harmonic resonance at the low field side兲. The tilted shaded area represents the range ECEI can be tuned to as a function of B0, limited by the frequency range of the BWO. In reality, not all BWO frequency settings can be used, due to the limited number of available dichroic plates to reject the lower sideband. The dark shaded area gives the limitation set by the currently available dichroic plates. Therefore, currently the plasma center is accessible between B0=1.8 and 2.25 T and the low field side 共LFS兲 edge between 2.35 and 2.9 T. Another limitation is set by cutoff. For a second harmonic X-mode ECE diagnostic, the cutoff occurs at the right hand cutoff frequency10 ␻ R=1 2关 ␻ ec+共 ␻ ec 2+4 ␻ p 2兲1/2兴, where ␻ p=冑nee2/共␧0me兲is the density dependent plasma frequency. Figure 6gives the density above which the cutoff occurs as a function of radius and toroidal magnetic field. Note that measurements at high density generally require a high toroidal magnetic field. When in cutoff, the second harmonic X-mode radiation cannot reach the observer, so signal levels drop toward zero, although some second harmonic O-mode radiation is normally still visible due to the finite sensitivity to O-mode of any real diagnostic. Another related effect to be aware of is the bending of the 共mainly off-axis兲 lines of sight due to refraction. Close to cutoff, the index of refraction of the plasma becomes noticeably smaller than FIG. 5. Range of possible measurement positions ECEI can be tuned to as a function of the toroidal magnetic field B0. The darkest shaded area represents the 共current兲operational range. 10D929-3 Classen et al. Rev. Sci. Instrum. 81, 10D929 共2010兲 unity that refracts the lines of sight away from the plasma center. This effect rapidly becomes smaller when the plasma is further from cutoff. Two other properties of ECE measurements to be shortly addressed are the optical thickness and broadening effects. The optical thickness for the second harmonic X-mode radiation is 共for typical ASDEX Upgrade parameters B0 =2.5 T and Rresonance=2 m兲approximately given by ␶ X2 ⬇3.3⫻Te关keV兴⫻ne关1019兴共see Ref. 10 for the exact formula兲. If the optical thickness is too low 共comparable to or below unity兲, the plasma is partially transparent and the ECE measurements 共the radiation temperature TR兲can no longer be regarded as a direct electron temperature measurement 共also density plays a role兲. Neglecting wall reflections, the radiation temperature is given by10 TR=Te关1−exp共− ␶ 兲兴, where ␶ is a function of both temperature and density. For the normal ASDEX Upgrade H-mode plasmas, these only play a role at the foot of the pedestal 共see Sec. V兲. The frequency broadening of the ECE radiation due to relativistic effects10,11 ⌬ ␻ rel⬇n ␻ ec共vth/c兲2共where vth =冑2kBTe/me兲, and Doppler broadening10,12 ⌬ ␻ D⬇2vth/w0 共which for perpendicular observation can be regarded as an effect of the finite transit time of the emitting electrons through the Gaussian spot of size w0兲, result in an emitting layer with significant radial extent 共for ECEI at 1 keV about 3 cm full width at half maximum兲. However, in the optically thick case, most of the radiation of the broadened emission layer is reabsorbed before it reaches the observer, and only the last layer 共typically narrower than 1 cm兲, closest to the observer, contributes to the ECE signal, and determines the radial spatial resolution. In the optically thin plasma edge 共see Sec. V兲the full emission layer is observed. V. 2D DYNAMICS: EDGE LOCALIZED MODES One of the main motivations for installing ECEI at the ASDEX Upgrade was the study of ELMs, which is one of the most important and still not fully understood instabilities in fusion devices. The necessity for a 2D diagnostic is illustrated in Fig. 7, where the ECEI measurements of the LFS plasma edge during different phases of an ELM crash are presented. The data have been filtered 共using singular value decomposition, see Sec. VI兲to reduce the thermal noise. The observed pronounced 2D dynamics would not have been accessible with a conventional 1D ECE radiometer. Figures 7共b兲–7共d兲are taken during the early stages of the crash 关time indicated in Fig. 7共a兲兴where a clear deformation of the temperature profile due to 共precursor兲mode activity is visible, showing a rather complicated and partly incoherent poloidal mode structure. In Fig. 7,t 0共2.747 165 s兲is defined as the time of the first visible deviation from the 共precrash兲smooth temperature profile. Figures 7共e兲and 7共f兲show images during a later phase of the crash 关time indicated in Fig. 7共a兲兴, where poloidally localized structures 共thought to be related to the ELM filaments observed by many other diagnostics兲 are seen to rotate poloidally 共upward in the figure兲. To enhance these structures in the images, not the absolute 共radiation兲temperature, but TR-TR,av is shown, where TR,av is the average temperature 共calculated separately for each ECEI channel兲after the ELM crash 关shaded area in Fig. 7共a兲兴. These filaments have a radiation temperature of about 200 eV. Whether one can interpret the observed filaments as electron temperature fluctuations depends upon the optical thickness of these structures. Figure 8共c兲shows the optical thickness for typical electron density and temperature profiles 关shown in Figs. 8共a兲and 8共b兲兴at different phases during the ELM cycle. For both the pre-ELM and post-ELM cases, the optical thickness drops below unity at roughly the separatrix position, with rapidly rising values inside the separatrix. In the case where the electron temperature profile has been modified to include a filament 关inspired by the radiation temperatures seen in Figs. 7共e兲and 7共f兲兴but the electron density profile is left unchanged, it turns out that the optical thickness of this filament is roughly unity. The assumption of simultaneously increased density could drastically increase this number. Consequently, the optical thickness is marginal 共normally values above 2 to 3 are considered fully optically FIG. 6. 共Color online兲Cutoff density 共solid curve兲as a function of major radius Rfor various toroidal magnetic fields B0共labels兲. The dashed curve gives a typical example of a density profile. In this example, parts of the plasma would be in cutoff for B0⬍2.5 T. FIG. 7. 共Color online兲During an ELM crash, a pronounced 2D structure is observed at the plasma edge. The time traces in 共a兲show a full ELM cycle. Images 共b兲–共d兲show the “precursor” phase, and images 共e兲and 共f兲show the movement of a “filament.” The arrows indicate the poloidal movement of the structures. 10D929-4 Classen et al. Rev. Sci. Instrum. 81, 10D929 共2010兲 thick兲, but sufficiently large to assume the radiation temperature TRis still comparable to the electron temperature Te 共note that TRⱕTeso the actual temperature of the filaments might be higher兲. Figure 8共d兲shows the broadened emission profiles for the filament case. The solid line shows the cold resonance, and the dashed and dotted lines represent the 共95%兲boundaries of the broadened regions for ECEI and 1D ECE, respectively. At low values of optical thickness, the emission from the full broadened profile reaches the observer 共reabsorption does not play a role兲, possibly reducing the radial resolution. However, in the region where the optical thickness is low, the width of the emitting layer is seen to be about 1 cm. The radial resolution in these edge measurements is hence comparable to that of core measurements. It should be noted that the effect of shinethrough13 共an increased radiation temperature just outside the separatrix, thought to be a nonlocal effect caused by downshifted radiation from further inside the plasma兲, often observed by the 1D ECE radiometer, has so far not been observed with ECEI. Although not fully understood, the difference might be explained by the different spot sizes of the two diagnostics 共typically w0=15 mm for ECEI and 35 mm for 1D ECE兲, resulting in a 2.5 times larger Doppler broadening for ECEI, and hence different emission profiles 关see Fig. 8共d兲兴. VI. SINGULAR VALUE DECOMPOSITION The accuracy of the ECEI measurements is limited by thermal noise, inherent to all ECE diagnostics.14 The 共thermal兲noise level is determined by the bandwidths of the system, and for ECEI at full sampling rate this amounts to a relative noise level of around 3% 冑具dTR 2典/具TR典=冑2BV/BIF.共1兲 A distinctive advantage of a 2D system such as ECEI is the fact that it provides many closely spaced data channels that, in many applications, will show similar data. This high degree of redundancy can be taken advantage of by using SVD as a powerful tool for analyzing and filtering the 2D data. SVD is a well known mathematical technique to decompose two-dimensional matrices into pairs of eigenvectors. The mathematical details can be found in the literature,15 but the general idea becomes clear by looking at the application of SVD for filtering ECEI data. In principle, ECEI data are three-dimensional: there are two space dimensions, and a time dimension. However, for the SVD decomposition, we will regard ECEI data as having one time dimension 共of length m, typically m=1000兲, and only one spatial dimension 共of length n=128兲, treating the 16 by 8 two-dimensional space as a one-dimensional array of length 128. Therefore, the ECEI data are represented by a twodimensional m-by-nmatrix X. The SVD decomposition of the data can now be written as X=USVT,共2兲 where Uis an m-by-nmatrix whose 共length m兲columns uk represent time eigenvectors 共sometimes called “chronos”兲. VTis an n-by-nmatrix whose 共length n兲rows vk Trepresent spatial eigenvectors 共“topos”兲.Sis an n-by-nmatrix whose only nonzero elements are on the diagonal, so S =diag共s1,....,sk兲, where sk, the so called singular values, are the eigenvalues belonging to the topos-chronos pairs of eigenvectors. By convention, the vectors are ordered from large to small sk. Therefore, in the case of ECEI, the SVD results in 128 pairs of eigenvectors 共ukand vk T兲with corresponding decreasing eigenvalues sk. The filtered ECEI data Xlwould then be represented by Xl=兺 k=1 l ukskvk T,共3兲 where lis the number of 共most significant兲eigenvector pairs retained in the summation. The information contained in the eigenvector pairs with k⬎lis hence lost. Mathematically, Xl 共the truncated SVD兲is the closest rank lmatrix to the original matrix Xand is hence the best approximation to X, possible by only using leigenvector pairs. Note that SVD filter- FIG. 9. 共Color online兲SVD filtering to remove 共thermal兲noise. In 共a兲, the spectrogram of the data of a single ECEI channel 共channel 8-4, shot 25525兲 containing RSAEs is shown. 共b兲The same data after SVD filtering 共truncated after ten eigenvector pairs兲.共c兲The residue that has been removed in the filtering. FIG. 8. 共Color online兲Typical profiles 共based on measurements兲of 共a兲 electron density, 共b兲electron temperature, and 共c兲optical thickness just before and just after an ELM crash. Also the case with a simulated filament is shown 共filament only in temperature, not in density兲. The broadening of the second harmonic ECE resonance for the filament case is shown in 共d兲for both ECEI and 1D ECE. 10D929-5 Classen et al. Rev. Sci. Instrum. 81, 10D929 共2010兲 ing does not reduce the spatial or time resolution of the filtered data, as many other filtering methods 共such as Fourier filtering兲do. Coherent oscillations 共present on multiple channels with similar dynamics兲will result in much larger singular values than incoherent 共noise兲oscillations. Therefore, the strong and coherent oscillations are still present in Xl, whereas the residue X-Xlcontains almost exclusively incoherent oscillations. This is of course only true if lis chosen sufficiently large, so that the coherent part of the data can be described by a rank lmatrix. In practice, lis normally chosen to be between 10 and 20 in the analysis of ECEI data. For this purpose, the ECEI data are divided into data segments of typically 1000 time points. For each of these segments, the truncated SVD is calculated. The length of the segments is both determined by computational limits, and the requirement that the oscillations in the data do not show too large a time evolution 共in which case more eigenvector pairs would be needed兲. An example of SVD filtering is shown in Fig. 9. Shown are three spectrograms of the data from a single ECEI channel 共channel 8-4, shot 25525兲that contains Alfvén wave activity, so called reversed shear Alfvén eigenmodes 共RSAEs兲. These coherent oscillations have relative temperature fluctuation amplitudes of around 1%, and are hence below the thermal noise level. Figure 9共a兲shows the spectrogram of the raw data 共X兲. Figure 9共b兲shows the SVD filtered data 共Xl, where l=10兲, and Fig. 9共c兲shows the residue X-Xl. The color scaling for all three spectrograms is equal, so this clearly demonstrated that the SVD filtering significantly enhances the coherent information in the data, and the residue practically only contains noise. As in practice almost all oscillations of interest are at or below the thermal noise level, SVD filtering has proven to be almost essential for any direct plotting 共stills or movies兲of 2D ECEI data 共like also the images in Fig. 7兲. Figure 10 shows examples of the spatial structure of RSAEs as measured by ECEI. The Fourier amplitude in Fig. 10共b兲and mode structure 共or more accurately the real part of the complex Fourier amplitude兲in Fig. 10共c兲show a radially localized oscillation with a poloidal mode number of around m=8. An RSAE with a second radial harmonic is shown in Figs. 10共d兲and 10共e兲. This analysis made use of both SVD filtering to get rid of the majority of the noise, and subsequent Fourier frequency selection to pick out the separate modes. These first, local, 2D ECE measurements of the mode structure of Alfvén waves reveal more information than previous 1D measurements,16 and could contribute to the understanding of these modes and the associated fast particle transport. Similar results have in the mean time been achieved with another ECEI system on DIII-D.17 1H. K. Park, E. Mazzucato, T. Munsat, C. W. Domier, M. Johnson, N. C. Luhmann, Jr., J. Wang, I. G. J. Classen, A. J. H. Donné, and M. J. van de Pol, Rev. Sci. Instrum. 75, 3787 共2004兲. 2H. K. Park, N. C. Luhmann, A. J. H. 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Classen, and A. J. H. Donné, Appl. Opt. 49,E20共2010兲. 7B. Tobias, X. Kong, T. Liang, A. Spear, C. W. Domier, N. C. Luhmann, Jr., I. G. J. Clssen, J. E. Boom, M. J. van de Pol, R. Jaspers, A. J. H. Donné, H. K. Park, and T. Munsat, Rev. Sci. Instrum. 80, 093502 共2009兲. 8C. W. Domier, Z. G. Xia, P. Zhang, N. C. Luhmann, Jr., H. K. Park, E. Mazzucato, M. J. van de Pol, I. G. J. Classen, A. J. H. Donné, and R. Jaspers, Rev. Sci. Instrum. 77, 10E924 共2006兲. 9P. Zhang, C. W. Domier, T. Liang, X. Kong, B. Tobias, N. C. Luhmann, Jr., H. Park, I. G. J. Classen, M. J. van de Pol, A. J. H. Donné, and R. Jaspers, Rev. Sci. Instrum. 79, 10F103 共2008兲. 10 M. Bornatici, Plasma Phys. 24, 629 共1982兲. 11 I. H. Hutchinson, Principles of Plasma Diagnostics 共Cambridge University Press, Cambridge, 1987兲. 12 C. Watts, H. J. Hartfuss, and M. Häse, Rev. Sci. Instrum. 75, 3177 共2004兲. 13 W. Suttrop and A. G. Peeters, IPP Report No. 1/306, 1997. 14 G. Bekefi, Radiation Processes in Plasmas 共Wiley, New York, 1966兲. 15 G. Strang, Introduction to Linear Algebra 共Wellesley Cambridge, Wellesley, MA, 1998兲. 16 M. A. Van Zeeland, G. J. Kramer, M. E. Austin, R. L. Boivin, W. W. Heidbrink, M. A. Makowski, G. R. McKee, R. Nazikian, W. M. Solomon, and G. Wang, Phys. Rev. Lett. 97, 135001 共2006兲. 17 B. Tobias, C. W. Domier, T. Liang, X. Kong, L. Yu, G. S. Yun, H. K. Park, I. G. J Classen, J. E. Boom, A. J. H. Donné, T. Munsat, R. Nazikian, M. Van Zeeland, R. L. Boivin, and N.C. Luhmann, Jr. Rev. Sci. Instrum. 81, 10D928 共2010兲. FIG. 10. 共Color online兲共a兲Spectrogram of shot 25528 showing many RSAEs. In 共b兲and 共c兲, respectively, the amplitude and mode structure of one of the RSAEs is shown. An example of an RSAE with a higher radial harmonic is shown in 共d兲and 共e兲. 10D929-6 Classen et al. Rev. Sci. Instrum. 81, 10D929 共2010兲