Observation of Alfvén Eigenmodes Driven by Off-axis Neutral Beam Injection in the TCV Tokamak

OBSERVATION OF ALFV ´ EN EIGENMODES DRIVEN BY OFF-AXIS NEUTRAL BEAM INJECTION IN THE TCV TOKAMAK B. GEIGER1, A. N. KARPUSHOV2, P. LAUBER3, S. SHARAPOV4, M. DREVAL5, F.BAGNATO2, M. BAQUERO-RUIZ2, A. DAL MOLIN6, B.P. DUVAL2, M. GARCIA-MUNOZ 7, C. MARINI8, M. NOCENTE6, O. SAUTER2, L. STIPANI2, D. TESTA2, M. VALLAR2AND THE TCV9AND EUROFUSION MST110 TEAMS 1UW Madison, Wisconsin, USA 2Ecole Polytechnique F´ ed´ erale de Lausanne, Swiss Plasma Center, Lausanne, Switzerland 3Max-Planck-Institut f¨ ur Plasmaphysik, Boltzmannstr. 2, 85748 Garching, Germany 4Culham Science Centre, Abingdon OX14 3EB, United Kingdom 5Institute of Plasma Physics of the NSC KIPT, 61880 Kharkiv, Ukraine 6Universita’ di Milano-Bicocca, Piazza della Scienza 3, 20126, Milano, Italy 7Univeristy of Seville, Spain 8Oak Ridge Associated Universities, Tennessee, USA 9see the author list of ”S. Coda et al, Nucl. Fusion 59, 112023 (2019)” 10 see the author list of ”B. Labit et al, Nucl. Fusion 59, 086020 (2019)” Email of corresponding author: [email protected] Abstract Fast-particle driven Alfv´ en Eigenmodes (AEs) have been observed in low-collisionality discharges with off-axis neutral beam injection (NBI), electron cyclotron resonance heating (ECRH) and a reduced toroidal magnetic field. During NBI and ECRH, Toroidicity induced Alfv´ en Eigenmodes (TAEs) appear in frequency bands close to 200 kHz, and chirping modes are observed at about 40 kHz and 80 kHz that are likely Energetic-Particle-Induced Geodesic Acoustic Modes (EGAMs). When turning offECRH in the experiment, those beam-driven modes disappear which can be explained by a modification of the fast-ion slowing down distribution. In contrast, coherent fluctuations close to the frequency of the beam driven TAEs are present throughout the experiment. The modes have the same toroidal mode number as the beam-driven ones and are even observed during ohmic plasma conditions. This clearly demonstrates that they are not caused by fast particles and suggests an alternative drive, such as turbulence. The mode-induced fast-ion transport has been found to be weak and marginal in terms of the fast-ion diagnostic sensitivities. Measurements of the plasma stored energy, neutron rates, neutral particle fluxes and fast-ion D-alpha spectroscopy show good agreement with neoclassical modelling result from TRANSP. This is further supported by a similarly good agreement between measurement and modelling in cases with and without ECRH and therefore with and without the modes. Instead, a significant level of charge exchange losses are predicted and observed which generate a bump-on-tail fast-ion distribution function that can provide free energy to EGAMs. 1 Introduction Good fast-ion confinement is essential in fusion devices to ensure efficient alpha-particle heating and to protect the first wall from localized losses [1]. While neo-classical transport is typically negligible and below 0.1 m2/s[2], transport induced by MHD modes such as Alfv´ en Eigenmodes (AEs) has been observed under certain conditions to be well above 1 m2/s[3, 4]. Such strong fastion transport significantly impacts the fast-ion confinement and has to be avoided in future fusion devices. This in turn requires the development of reliable theoretical models that are validated in various regions of parameter space. At the ”Tokamak ` a Configuration Variable” (TCV) [5, 6] the fast-ion transport can be investigated in a unique parameter space with very large fast-ion fractions. Thanks to the combination of a powerful 1 MW (25 keV) neutral deuterium (D0) beam source [7] and a relatively small plasma volume of 1m3(TCV has minor and major radii of 0.25 and 0.88 m, respectively), fast-ion densities can even exceed 50% of the electron density [8]. In addition, TCV is equipped with state-of-the-art fast-ion diagnostic, including FIDA spectroscopy [9], neutral particle analyzers [10] and neutron counters [11], and is therefore well suited to test fast-ion models and codes. This paper presents first experiments on neutral-beam driven AEs at TCV. The experimental setup and a representative plasma discharge are introduced in section two, and section three describes the observation of AEs based on magnetic and soft X-ray fluctuation measurements, as well as modelling results based on the linear gyrokinetic code LIGKA[12]. In section four, fast-ion measurements are compared with TRANSP/NUBEAM [13] modelling, and section five provides a short discussion and outlook. 2 Experimental setup The experiments described here were performed with a plasma current of Ip=120 kA and a reduced toroidal magnetic field of Bt=1.3 T (compared to 1.43 T). A limiter configuration was chosen to maintain L-mode conditions throughout the experiment, and the plasma was shifted upwards (z0=+12 cm) for off-axis NBI. The neutral beam source injects tangentially in the z=0 plane (see figure 1a), and upwards-shifting yields a fast-ion deposition profile that is peaked at a normalized toroidal flux label (ρt) of 0.46 and, thus an off-axis peaked fast-ion distribution (see figure 1b). Time traces of a representative experiment are plotted in figure 2. Starting at 0.7 s, NBI heating is applied during four 120 ms long phases with 0.82 MW of power delivered into the TCV vacuum vessel. The small spikes on top of the neutral beam heating power are due to a diagnostic neutral -1.6 -0.8 0.0 0.8 1.6 -1.6 -0.8 0.0 0.8 1.6 Y [m] X [m] 0.0 1.0 2.0 3.0 4.0 5.0 0.6 0.8 1.0 1.2 -0.8 -0.4 0.0 0.4 0.8 fast-ion density [m -3] x1018 Z [m] R [m] NPA FIDA D-NBI NBI FIDA NBI a) b) Figure 1: Top-down (a) and poloidal (b) views on the TCV tokamak. Deposition positions of NBI markers from TRANSP are drawn with gray points and the FIDA and NPA viewing geometries are illustrated in red. The gray contours in (b) show the fast-ion density during off-axis NBI and contours of the flux-surfaces are given in blue. beam (DNB) [14] used for charge exchange recombination spectroscopy (CXRS). Between 0.5 s and 1.2 s, the plasma was additionally heated by two 82.7 GHz gyrotrons (X2) that deposit 0.4 MW of ECRH power on the high-field-side at a normalized toroidal flux label (ρt) of about 0.5. As displayed in figure 2b, the core-electron density was close to 4×1019/m3and increased to about 6× 1019/m3when ECRH was turned off. The effective charge (Zeff) profile is considered flat at a value of 1.2 which increases to 1.5 during ECRH. This behavior has been inferred from comparisons between predicted and measured levels of the loop voltage (see section on TRANSP modelling) and is expected, as ECRH provides an enhanced level of physical sputtering from the carbon walls. The central electron temperature, as plotted in figure 2d, reaches up to 1 keV and does not increase with the application of off-axis ECRH. In contrast, a clear increase of the electron temperature at ρt∼0.5 can be observed when ECRH is applied and slightly increased levels become apparent during NBI. Finally, the evolution of the ion temperature and rotation are depicted in figures 2d+f for ρt=0.5 and ρt=0.9. Here, it is interesting to note that the application of NBI has only a weak impact on the measured kinetic profiles, suggesting that the absorbed NBI power is low and or that the ion heat and momentum transport are strong. Figure 3 shows comparisons between measured and fitted (modified hyperbolic tangent function [15]) kinetic profiles for two time-points in discharge #62117. The experimental electron temperature and density profiles are measured by a vertically aligned Thomson scattering system which covers the whole plasma cross-section, even when shifting the plasma vertically up. In contrast, the impurity ion temperature and rotation is measured by CXRS using the diagnostic neutral beam (DNB). The latter is located in the z=0 plane and thereby limits the radial coverage of ion-temperature and rotation measurements to ρt>0.5. A third order polynomial is used to extrap- 0.0 0.5 1.0 MW #62117 NBI DNB ECRH 0 4 8 1019/m3 nert= 0.1 rt= 0.5 rt= 0.9 1.0 1.5 2.0 Zeff Zeff 0.0 0.5 1.0 keV Te 0.0 0.5 1.0 keV Ti 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 time [s] -1 0 1 105rad/s rotation Figure 2: Representative time-traces of discharge #62117. olate the data towards the plasma core which provides large uncertainties that need to be considered when analyzing modelling results. 3 Mode activity The experiments discussed here are rich in magneto-hydrodynamic mode (MHD) activity. This is in part explained by large fast-ion fractions (here, up to 20% of the electron density) and in part by the reduced magnetic field strength (B=1.3 T), which provides Alfv´ en velocities that are low enough for the excitation of TAEs through 25 keV fast-ions. By considering an ion-density ni of 1.8×1019m−3(this corresponds to the electron density at ρt=0.5, divided by Zeff=1.5) and Bt=1.3 T, the ratio of the fast-ion velocity, vNBI, to the Alfv´ en velocity, vA, reads: vNBI vA =√2E/mD B/√µ0mDni∼1.55 ×106m/s 4.72 ×106m/s&1 3(1) where Eis the fast-ion energy (25 keV), mDis the deuterium mass and µ0is the vacuum permeability. The resulting factor of 1/3 is a well known threshold above which TAEs can be driven by circulating fast-ions through side-band excitation [16]. An overview of the mode activity using three different measurements is given in figure 4. Figures 4a+b show poloidal and radial magnetic field fluctuations that are observed by high frequency LTCC-3D magnetic sensors [17], and figure 4c shows data from a core-channel of a soft X-ray 0.0 0.5 1.0 Te [keV] 0.0 1.0 Ti [keV] 0.0 0.2 0.4 0.6 0.8 1.0 r t 0 3 6 ne [1019/m3] 0.0 0.2 0.4 0.6 0.8 1.0 r t -1 1 vtor [105rad/s] #62117 0.80 s 1.35 s with ECRH w/o ECRH a) c) b) d) Figure 3: Kinetic profiles of #62117 at 0.8 s and 1.35 s. camera system [18]. Enhanced mode-activity is clearly observed during the first three NBI phases with coherent fluctuations in the 200 kHz and 40-100 kHz regions. 3.1 TAEs The modes present in the magnetic signals close to 200 kHz have been identified as TAEs. The analysis of data from an array of toroidally distributed magnetic pickup-coils shows that the modes have a toroidal mode number of n=3. In addition, calculations of the expected TAE frequencies compare best with the experimental data for poloidal mode numbers m=6 and m=5. The expected TAE frequencies, as plotted in white in figure 4a+b, have been determined according to equations given in [19]: fT AE[kHz] =va 4πqR0 2−q1.+3 42 g q1−1 42 g·10−3(2) with the major radius, R0, and gbeing related to the plasma elongation κvia: g=κ2−1 κ2+1(3) Finally, qis the local safety factor which is defined for TAE modes as [20]: q=(m+0.5)/n(4) According to equation 4, the q-value of a given TAE is defined by it’s toroidal and poloidal mode numbers. Based on this q-value, the radial mode position (as a function of ρt) is then determined -7.0 -6.0 -5.0 -4.0 -3.0 -2.0 0 50 100 150 200 250 300 NBI (6,3) TAE at q=2.2, rho=0.57 (5,3) TAE at q=1.8, rho=0.49 -7.0 -6.6 -6.2 -5.8 -5.4 -5.0 0 50 100 150 200 250 300 frequency [kHz] (6,3) TAE at q=2.2, rho=0.57 (5,3) TAE at q=1.8, rho=0.49 -5.0 -4.4 -3.8 -3.2 -2.6 -2.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 time [s] 0 10 20 30 40 50 60 70 n=0 GAM at q=2.0, rho=0.53 (6,3) TAE at q=2.2, rho=0.57 (5,3) TAE at q=1.8, rho=0.49 poloidal fluctuations radial fluctuations soft X-ray a) b) c) Figure 4: Spectrogram of poloidal (a) and radial (b) flucatations measured by magnetic pick-up coils, compared with the expected frequencies for n=3, m=5 and n=3, m=6 TAEs. c) Spectrogram of data from a soft X-ray channel, compared with the expected frequency of a GAM at the q=2 surface. using equilibrium information provided by TRANSP. Thus, the corresponding temperature, density and κvalues can be obtained, as required to calculate vAand the mode frequency fT AE. The calculated frequencies for m=5 and m=6 modes (n=3) agree very well with the observed frequencies. In particular during NBI, those modes are observed in the poloidal and radial fluctuation data. This observation also agrees with simulations from the linear gyrokinetic code LIGKA[12]. LIGKA has been supplied with kinetic profiles and the TRANSP-predicted equilibrium as inputs and calculates the Alfv´ en continuum [21] (blue crosses in figure 5), as well as the global TAE mode structure of the least damped mode in the TAE gap for the experimentally given toroidal mode number. The resulting mode-amplitude profiles for n=3 TAEs are given in figure 5 in red for different poloidal mode numbers. As can be seen, the strongest mode amplitudes appear at ρt∼0.5 where a band-gap is present in the Alfv´ en continuum in order to minimise continuum damping. Interestingly, coherent fluctuations at the expected TAE frequencies can be seen in the poloidal fluctuation data well before the application of NBI heating. The modes are already present during the ohmic plasma (until 0.5 s), become more intense during pure ECRH, and get even stronger when NBI is additionally switched on. This shows that the modes are driven more unstable by NBI but cannot be purely beam-driven ones. A similar observation has been made during ohmic plasmas at ASDEX Upgrade where the presence of TAEs could be attributed to plasma turbulence [20]. This 0 50 100 150 200 250 300 350 400 0 0.2 0.4 0.6 0.8 1 f [kHz] rho toroidal Figure 5: Predicted Alfv´ en continuum (blue crosses) and radial mode structure of n=3 TAEs from LIGKA as a function of ρt. situation might be similar at TCV where plasmas are typically affected by turbulent fluctuations that develop from unstable trapped electron modes (TEM) and electron temperature gradient (ETG) modes [22]. In addition, it should be noted that such an interaction between turbulence and TAEs has recently been observed and studied in non-linear gyrokinetic GENE simulations that suggest a reduction of the turbulence level via coupling to TAEs [23]. However, it should be noted that in contrast to the local GENE simulations, the observed mode numbers are low, e.g. the destabilised TAEs seem to be global. The observations from the poloidal and radial magnetic sensors are quite different. While the poloidal sensors pick-up the supposedly turbulence induced modes, the radial sensor only observes the beam-driven ones. This suggests different polarization directions of the modes and will serve as an important input for comparisons with theoretical and numerical results. 3.2 EGAMs Upwards chirping modes at about 40 kHz are observed during NBI by the soft X-ray system (called Duplex Multiwire Proportional soft X-ray counter, DMPX). Figure 4c shows data from one representative channel where modes can be identified shortly after turning on NBI. The data is compared with the expected frequencies of an n=0 Geodesic Acoustic Mode (GAM), located at the q=2 surface. The GAM frequency has been calculated using [19]: fGAM[kHz] =vA 2πR" 2+1 q2!2 κ2+1βs#2 ·10−3(5) with βs=c2 s v2 A (6) where csis the sound velocity. The good agreement between the predicted and observed frequency and the chirping character of the modes strongly suggests that these are energetic particle driven GAMs (EGAMs) [24, 25]. 0 5 10 15 20 25 30 energy [keV] -1.0 -0.5 0.0 0.5 1.0 pitch 0.0 0.2 0.5 0.7 0.9 1.2 fast-ion density [1017/keV/pitch] -0.10 m < Z < 0.10 m [email protected]+-0.01s Figure 6: Fast-ion distribution as a function of energy and pitch compared to the pitch-energy resonance line at which 40 kHz EGAMs might be driven. . In addition, EGAMs are expected to be driven by bump-on tail fast-ion distribution functions which are present in TCV due to strong charge-exchange losses (discussed later). Figure 6 displays a TRANSP-predicted fast-ion distribution function for #62117 as a function of energy, E, and pitch =v||/vtot with v|| being the velocity parallel to the magnetic field lines and the total velocity vtot. The fast-ion distribution function consists of mainly passing fast ions, peaks at the three injectionenergies (25 keV, 12.5 keV and 8.3 keV) and features positive gradients in E. This provides free energy to excite the n=0 EGAMs that cannot be driven through radial gradients. In addition, figure 6 shows the location of possible wave-particle interactions in black which are given by: p(E)=fEGAM2πR q vNBI(E)(7) By employing the observed frequency fEGAM =40 kHz, a resonance line (p(E)) is obtained that overlaps significantly with the fast-ion distribution function for E<15 keV where strong velocity space gradients are present. Finally is should be noted that the n=0 character of EGAMs cannot be addressed by the magnetic sensors since these appear to be insensitive to the fluctuations. This might be in part explained by broadband-noise in the magnetic data below 50 kHz and in part by rather localized radial Eigenfunctions of those modes. In contrast, there are n=0 modes observed in the LTCC-3D data at about 80 kHz (see figure 4). For these modes, however, it is not clear whether they are EGAMs, as the expected frequencies (equation 5) would only match for core-localized modes (near q=1) where strong damping is expected. Unfortunately, the modes are not seen in data from the soft X-ray system due to bandwidth-problems which restricts our analysis to about 70 kHz. 3.3 Absence of Alfv´ en modes without ECRH During the 4th NBI phase in discharge #62117 (1.28 s-1.4 s), ECRH was turned off. Interestingly this phase does not exhibit NBI-driven fluctuations, which might be explained by either increased damping (stability) or by a reduced drive of the modes. In particular for the TAEs, the damping seems not to be affected significantly since the coherent fluctuations from the possibly turbulencedriven modes are still present (see figure 4a). 0.0 0.2 0.4 0.6 0.8 1.0 r t 0.0 0.1 0.2 0.3 0.4 0.5 fast-ion density [10 19/m3] #62117 0.80s 1.38s with ECRH w/o ECRH a) 0 10 20 30 Energy [keV] 0 5.0·1016 1.0·1017 1.5·1017 2.0·1017 fast-ions [1/keV] TRANSP #62117 1.35s 0.80s with ECRH w/o ECRH b) Figure 7: TRANSP predicted radial fast-ion density profile with (black) and without (red) ECRH. b) TRANSP predicted energy distribution with (black) and without (red) ECRH. In contrast, the slowing down time is reduced when switching offECRH as the electron temperature decreases and the electron density peaking increases. This reduces the off-axis fast-ion density and the bump-on tail character. Figure 7 compares TRANSP-predicted fast-ion distribution functions as a function of ρtand energy for the cases with and without ECRH. 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