Dynamics of energetic particle driven modes and MHD modes in wall-stabilized high beta plasmas on JT-60U and DIII-D

Transcription

1 1 EX/5-1 Dynamics of energetic particle driven modes and MHD modes in wall-stabilized high beta plasmas on JT-60U and DIII-D G. Matsunaga 1), M. Okabayashi 2), N. Aiba 1), J. A. Boedo 3), J. R. Ferron 4), J. M. Hanson 5), G. Z. Hao 6), W. W. Heidbrink 7), C. T. Holcomb 8), Y. In 9), G. L. Jackson 4), Y. Q. Liu 10), T. C. Luce 4), G. R. McKee 11), T. H. Osborne 4), D. C. Pace 4), K. Shinohara 1), P. B. Snyder 4), W. M. Solomon 2), E. J. Strait 4), A. D. Turnbull 4), M. A. Van Zeeland 4), J. G. Watkins 12), L. Zeng 13), the DIII-D Team and the JT-60 Team 1) Japan Atomic Energy Agency, Naka, Japan 2) Princeton Plasma Physics Laboratory, Princeton, NJ, USA 3) Department of Aerospace and Mechanical Engineering, UCSD, San Diego, CA, USA 4) General Atomics, San Diego, CA, USA 5) Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA 6) Southwestern Institute of Physics, Chengdu, China 7) Department of Physics and Astronomy, UCI, Irvine, CA, USA 8) Lawrence Livermore National Laboratory, Livermore, CA, USA 9) FAR-TECH, Inc., Science Center Dr, Suite 150, San Diego, CA, USA 10) Euratom/CCFE Fusion Association, Culham Science Centre, Abingdon, UK 11) Department of Engineering Physics, University of Wisconsin at Madison, Madison, WI, USA 12) Sandia National Laboratories, Albuquerque, NM, USA 13) UCLA, Los Angeles, CA, USA Abstract. In the wall-stabilized high-β plasmas in JT-60U and DIII-D, interactions between energetic particle (EP) driven modes and edge localized modes (ELMs) have been observed. The ELM pacing by the EP driven modes (EPdMs) occurs when the repetition frequency of the EPdMs is higher than the natural ELM frequency. The EPdMs have strong waveform distortion that is composed of higher toroidal harmonics. In particular, EP behavior seems to be sensitive to the waveform distortion, thus, stronger waveform distortion correlates with an intense increase of EP transport to the edge. According to statistical analysis, the ELM triggering by the EPdMs infrequently occurs just after the ELM crash. Namely, the ELM triggering by the EPdMs needs finite level of waveform distortion and pedestal recovery. Transported EPs by the EPdMs are thought to contribute to change the edge stability. 1. Introduction To realize an economical fusion reactor with high fusion output, operations with β as high as possible is preferable. High-β operation above the no-wall β limit is realized by a conducting wall close to the plasma. In this wall-stabilized high-β regime, interactions between EP-driven modes (EPdMs) and MHD modes with marginal stability are expected due to a significant EP density in burning plasmas. In high-β N operation in JT-60U, we have observed interactions between the EPdM and ELM, the ELM triggering by the EPdM [1]. This ELM triggering behaves like the so-called ELM mitigation, where the ELM energy loss and the ELM repetition frequency become smaller and higher. Recently, the ELM triggering by the EPdM has been also observed on DIII-D. These observations in both devices imply a new common physics in high-β plasmas suggesting that the EPs are important even for edge stability toward DEMO. In this paper, we report the ELM triggering by the EPdMs based on experimental observations and MHD stability analyses on JT-60U and DIII-D.

2 2 EX/5-1 θ β α β β δ θ δ θ Fig. 1: High-β N discharges on (a) DIII-D and (b) JT-60U where ELM triggering by EPdMs: normalized β with no-wall β limits, Mirnov signals and D α emissions. Expanded waveforms of Mirnov and D α signals on (c) DIII-D and (d) JT-60U. 2. Observation of ELM triggering by EP driven modes Figure 1 indicates typical discharges where the ELM triggering by the EPdMs are observed with B t /I p = 1.7 T/1.0 MA on DIII-D and B t /I p = 1.5 T/0.9 MA on JT-60U. The EPdMs are Energetic particle driven Wall Mode (EWM) on JT-60U emphasizing the role of wall stabilization [2] and Off-axis Fishbone Mode (OFM) on DIII-D emphasizing the similarity to classical fishbone [3]. Hereafter in this paper, the names of EPdMs is used for both modes. These EPdMs appeared when β N exceeded no-wall β N limit. Here, β N is normalized β-value. In these discharges, the no-wall β N limits are roughly described as 3.5 l i on DIII-D and 3.0 l i on JT-60U by using the internal inductance l i, respectively. The expanded waveforms of the ELM triggering by the EPdMs are shown in Fig. 1(c) and (d). These show that ELMs are clearly triggered by these EPdMs. The ELM triggering by the EPdMs looks different in both devices as seen in Fig. 1(a) and (b). The EPdMs on JT-60U can almost robustly trigger ELMs. On the other hand, EPdM-triggered ELMs irregularly occurred on DIII-D. To compare both ELM triggering, repetition frequencies of ELM and EPdMs are shown in Figure 2 with statistical histograms. These histograms are obtained from typical high-β N discharges as shown in Fig. 1 (12 and α α Fig. 2: Statistical analysis of repetition frequencies of ELM and EPdMs on (a) DIII-D and (b) JT-60U. 5 shots on DIII-D and JT-60U, respectively). On DIII-D, the natural ELM frequency f ELM is about 200 Hz, that is twice higher than that of EPdM repetition frequency f EPdM 100 Hz. While on JT-60U, the ELM has two frequency peaks around 40 Hz and 140 Hz. The peak in the

3 3 EX/5-1 lower frequency corresponds to natural ELMs. The peak in the higher frequency corresponds to the EPdM-triggered ELMs, thus f ELM = f EPdM. This looks like ELM pacing by the EPdM. Namely, when f EPdM > f ELM, which is JT-60U case, the ELM pacing by the EPdM can occur. 3. EP-driven modes, waveform distortion and EP transport The impacts of EPdMs has been reported in JT-60U and DIII-D [2, 3]. The EPdMs can induce RWM onset despite enough plasma rotation on RWM stabilization. The main characteristics we already found are [1, 4, 5]: (i) Initial mode frequencies closer to precession frequency of trapped EPs injected by NBs, (ii) Toroidally n = 1, poloidally m 3 mode structures and larger amplitude at low field side (ballooning structure), (iii) Frequency chirping down as mode amplitude growing, (iv) Mode appearance above the no-wall βn -limit, (v) Enhancement of EP transport to edge, (vi) Strong waveform distortion, thus no sinusoidal oscillation. Poloidal angle Poloidal angle Poloidal angle Z[m] Z[m] Z[m] The waveform distortion of the EPdM is one of the distinct features. The EPdM waveforms are n = 1 sinusoidal oscillations with a small amplitude in the initial phase. However, the waveform deviates from n = 1 sinusoidal oscillation as the amplitude becomes larger. Moreover, the waveform distortion seems to strongly correlate with the EP transport as described below. Here, the waveform distortion is defined as components other than n = 1. These n 6= 1 components appear as higher harmonics in time, f = 2 f 0, 3 f 0,... in Fourier space where f 0 is the EPdM initial frequency. Therefore, we define the waveform distortion as higher- f components by using high pass filter in the range of f ( f f 0 )/2. (b) Figure 3(a) shows an exam- (a) δbθ π/2 δbθ:(n=1) + (n=2) 1.0 ple of the EPdM on DIII-D pat0.0 0 tern of integrated Mirnov signals δ Bθ in poloidal direction (z) and -1.0 π/2 time, fundamental (n = 1) and π/2 δb :n=1 δbθ:n=1 1.0 θ distortion components (n 6 = 1) Here, time evolution is equivalent to toroidal mode structure -1.0 π/2 because the mode is rigidly roπ/2 δb :n=2 δbθ:n θ tating in the toroidal direction The poloidal pattern of δ Bθ indicates that mode pitch (ratio be-1.0 π/ time[ms] tween poloidal and toroidal com0 π 2π 3π Toroidal angle 0 π 2π 3π ponents) is not uniform in the Toroidal angle poloidal direction as shown as Fig. 3: (a) Poloidal patterns of integrated Mirnov signals δ Bθ (top), dotted lines. Note that the EPdM fundamental (middle) and distortion (bottom). (b) Perturbation of on JT-60U waveform also has poloidal magnetic field patterns by MARS-F: (top) combination of n = 1 and n = 2, (middle) n = 1 and (bottom) n = 2 components. similar waveform distortion. In these high-βn plasmas, n = 1, 2 and 3 ideal kink ballooning modes (IKBMs) are unstable without an ideal-wall and stable with an ideal-wall. Thus, n = 1, 2 and 3 IKBMs have marginal stability with a wall. These EPdMs have been considered to be EP driven IKBM or RWM

4 4 EX/5-1 branches because the observed EPdMs have a global mode structure as is similar to IKBM and RWM. In Fig. 3(b) shows poloidal magnetic perturbation patterns of unstable RWMs calculated by MARS-F code. [6]. From the top, a combination of n = 1 and 2, n = 1 and n = 2 are described as poloidal and toroidal patterns. Here, the ratio of the amplitudes of n = 1 and n = 2, and their phase difference are experimentally determined. The dotted lines also indicate pitches between poloidal and toroidal space. The combination of n = 1 and n = 2 enables to reproduce the waveform distortion. Namely, the waveform distortion comes from n = 2, 3,... branches, that are thought to be destabilized in a synchronized manner with n = 1 component. The waveform distortion is not only observed in Mirnov signals but also other measurements such as electron density, electron temperature and EP diagnostics [5]. Figure 4 shows time derivatives of the line-integrated electron densities measured by CO 2 interferometers in comparison with Mirnov signal during the EPdM on DIII-D. The distorted parts are emphasized as propagating wave packets that look like a density snake. Since the density gradient ( n e ) at the edge is larger than other regions as seen in Fig. 4(c), observed fluctuations mainly come from the edge region. The amplitude of all interferometer chords (R0, V3 and V2) except for the one far away from the outboard edge (V1) grew rapidly. The poloidal pattern looks like a density snake. The waveform distortion of the EPdM seems to strongly affect EP transport. Figure 5 shows the relation between the fundamental and distortion components and beam emission spectroscopy (BES) amplitude. When the natural beams used for the BES measurement turned off, the BES signals are due to passive θ Fig. 4: (a) Time derivative of CO 2 interferometer signals vs time with vertical axis of z-location with Mirnov signal at z = 0 m. Dotted lines show wave packet propagates in the poloidal direction. (b) EFIT equilibrium of at t = s with CO 2 interferometer arrays (R0, V1, V2, V3). (c) Electron density and its gradient profiles. δ θ δ θ δ θ Fig. 5: Dependence of BES amplitude on fundamental (n = 1) and distortion (n = 1) components of EPdM on DIII-D. (a) Integrated Mirnov signal, (b) decomposed fundamental and distortion components and (c) BES signal at edge. (d) BES amplitudes vs fundamental and distortion components. fast ion D α emissions (FIDA) [5]. Namely, the passive BES provides the EP density fluctuation ñ EP at the edge region. An example of the BES signal during the EPdM without diagnostic

5 5 EX/5-1 NBs is shown Fig. 5(c). Large spikes corresponding to the intense increases of EP transport are synchronized with Mirnov signals. The EP density increases as the distortion component increases. Figure 5(d) indicates that the BES amplitude has a linear dependence of the waveform distortion. Beam ion loss detector (BILD) and floating potential Vf SOL in SOL also have similar dependences of the waveform distortion. From these, it is found that the waveform distortion is considered to rapidly increase EP transport to the edge region. 4. Conditions of ELM triggering by EP driven modes The ELM triggering by the EPdMs does not always occur. Since the waveform distortion strongly relates to the EP transport, the dependence of the waveform distortion on ELM triggering is evaluated. Figure 6 shows the ELM triggering dependence on fundamental and distortion components of the EPdMs on DIII-D and JT-60U. The EPdM waveform is distorted as the n = 1 fundamental amplitude is larger than δbθ n=1 10 G. Diamonds in this diagram correspond to the ELM triggering timings. The ELM triggering seems to need a sufficient level of the waveform distortion. However, no ELM triggering occurred in some cases with large fundamental and distortion amplitudes as shown in red dotted lines. This means that the amplitude of the EPdM is one of the necessary conditions, not sufficient one. In particular, the EPdM just after the ELM crash cannot trigger the ELM. To validate this, statistical approaches have been performed. Figure 7 shows histograms of the time delay of the EPdM on DIII-D with maximum amplitude between the last ELM crash t ELM and the EPdM amplitude at the ELM triggering. The definition of t ELM is schematically shown in Fig. 7(a). Figure 7(b) is a histogram of t ELM with and without the ELM triggering. As mentioned above, the average of the ELM repetition frequency is f ELM 200 Hz, thus its period is τ ELM 5 ms. Namely, the pedestal recovery takes 5 ms period. The EPdM cycle without ELM triggering is shorter than τ ELM 5 ms in contrast to those with ELM triggering. This is a possible cause that the ELM triggering infrequently occur just after the ELM crash in DIII-D. Namely, the pedestal recovery, thus marginal edge stability, is needed for the ELM triggering by the EPdM. As a matter of fact, the EPdMs without the ELM triggering shown in Fig. 6 have t ELM < 3.5 ms on DIII-D. Figure 7(c) is a histogram of the EPdM maximum amplitude with and without the ELM triggering. For both cases, the probabilities of EPdMs are broad with the peak of 30 G. In particular, the ELM triggering needs larger amplitude than 15 G. This leads to a conclusion that there exists a threshold of the EPdM amplitude for the δ θ δ θ δ θ δ θ Fig. 6: Amplitudes of fundamental (n = 1) and distortion (n = 1) components of EPdMs on DIII-D and JT-60U. Diamonds indicate ELM triggering. Red dotted lines are without ELM triggering cases.

6 6 EX/5-1 δ θ δ θ Fig. 7: Statistical analyses of time delay from last ELM and EPdM amplitude with and without ELM triggering. (a) definition of time delay t ELM, histograms of (b) t ELM and (c) EPdM amplitude. Dotted line in (b) is average ELM period. ELM triggering. Note that the histogram of t ELM shown in Fig. 7(b) is made by using only the data larger than 15 G amplitude shown in Fig. 7(c). 5. Discussion for ELM triggering by EP driven modes 5-1. Edge stability The edge stability can be explained by the peeling-ballooning model. Namely, the edge stability is bounded by kink/peeling and/or peeling/ballooning modes that are destabilized by current density j edge and pressure gradient p edge at the edge region, respectively. The schematic view is shown in Fig. 8(a). The edge stabilities in the high-β N discharges on DIII-D and JT- 60U are calculated by ELITE [7] or MARG2D [8], respectively. Figure 8(b) and (c) correspond to calculated results for DIII-D and JT-60U. Experimental points just before ELMs are described as yellow crosses. The pedestal condition on DIII-D is close to kink/peeling and peeling/ballooning stability boundaries. On the other hand, the one on JT-60U is close to peeling/ballooning stability boundary. In both cases, the increases of p edge can reach to the peeling/ballooning stability boundary. If the impact of transported EPs by the EPdMs are sufficient enough to reach these stability boundaries, the ELM can be triggered. Namely, if the edge pressure gradient δp EP is increased by the EPdM, the ELM triggering can occur. In this interpretation, not only δp EP but also closeness of the stability boundary are critical to trigger the ELM. This is qualitatively consistent with the observation that the ELM triggering infrequently α α α Fig. 8: MHD stability at edge region ( j-α) diagram. (a) Schematic diagram of pressure gradient (α) and edge current ( j edge ). Numerical results of edge stability on (b) DIII-D and (c) JT-60U.

7 7 EX/5-1 ξ γτ ρ β β Fig. 9: Analytical study of EP contribution on kink/ peeling modes. (a) Eigenfunctions and (b) growth rates vs ratio between EP and thermal β of m/n = 6/1, 12/2 and 18/3 modes. occurred before a pedestal recovery, and consequently the EPdMs without the ELM triggering occurred within typical ELM period as shown in Fig. 7(b) EP contribution to peeling mode We have carried out a systematic analytic investigation of the stability of the ideal peeling modes in the presence of the EPs and a resistive wall. Drift kinetic effects of EPs on the stability of the peeling mode using a formulation similar to the one developed for the RWM [10]. In this approximation, the low-n (n = 1, 2 and 3) peeling modes are considered with high poloidal mode numbers m = 6, 12 and 18. As shown in Fig. 9(a), the eigenfunctions (the normal plasma displacements; ξ r ) scale roughly as r m 1. Even though we still use the RWM dispersion relation for these modes, the influence of the wall decreases as the modes become more peeling-like. Here, the parameters, the minor and major radii a = 1 m and R = 3 m (the theory is developed in the large aspect ratio limit), and the toroidal magnetic field B t = 2.3 T and uniform safety factor with slightly above an integer number q = 6.1 are chosen. A resistive wall is placed at the minor radius of b = 1.20a, 1.10a and 1.05a for the cases of n = 1, 2 and 3 to suppress typical RWMs and only to excite EP driven low-n modes. We find that stable, ideal, low-n, high-m, peeling modes can be triggered by EPs as shown in Fig. 9(b). These peeling modes are stable in the fluid approximation (i.e. without the kinetic effects from EPs). By including EPs with a slowing down distribution in the particle energy space (the birth energy is assumed to be 85 kev) and δ-function distribution in the particle pitch angle, δ(λ λ 0 ), with λ 0 = 1.30, 1.40 and 1.45 these stable peeling modes are destabilized as the increase of the EPs pressure. The destabilization comes from the mode resonance with the toroidal precession of EPs. The critical β EP to unstable the peeling mode is sensitive to a stability margin. Therefore, the absolute value of the critical β EP can not be simply compared with the experimental value. According to this analytic investigation, it is possible that these modes are destabilized by EPs transported by EP driven modes Possible interpretation for ELM triggering by EP driven modes Figure 10 summarizes our interpretation of the ELM triggering by the EPdMs based on the results and discussions. Here, solid lines and dotted lines are observed and conjectured physics, respectively. The EPdMs such as EWM and OFM are thought to be marginal modes such as IKBM or RWM driven by trapped EPs. The waveform of the EPdMs is distorted as the fundamental component increases. This may be due to the modification of EP distribution func-

8 8 EX/5-1 α δf β β Fig. 10: Interpretation of ELM triggering by EP driven modes. Solid lines and dotted lines are observed and conjectured physics, respectively. tion by the fundamental one. The EP transport is rapidly increased by the waveform distortion and then it may change edge stability as discussed above. 6. Summary We have observed that the ELM can be triggered by the EP driven modes on JT-60U and DIII-D. Comparing with both observations, it is found that the ELM pacing occurs when f EPdM > f ELM. One of the distinctive features of the EPdMs is the waveform distortion. The waveform distortion is composed of higher harmonics n = 2, 3,... in a synchronized manner and this behaves like a density snake near the plasma edge. EP diagnostics indicate that strong correlation between the waveform distortion and the EP transport to edge. Moreover, the ELM triggering by the EPdMs infrequently occurs just after ELM crash. This means that pedestal recovery, thus marginal stability condition on edge, is necessary for the ELM triggering by the EPdMs. Based on these results, we discussed a possibility that the transported EPs by the EPdMs affect significantly destabilizing peeling modes. ACKNOWLEDGMENTS This work was supported in part by the US Department of Energy under DE- AC02-09CH11466, SC-G903402, DE-AC52-07NA27344, DE-FC02-04ER54698, DE-FG02-07ER54917, DE-AC04-94AL85000, and DE-FG02-08ER85195 and a Grant-in-Aid for Young Scientists (B) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan, No We are thankful to Drs. E. Fredrickson, N. Ferraro and J. de Grassie for stimulus discussions on mode distortion. References [1] G. Matsunaga et al., Nuclear Fusion 50, (2010). [2] G. Matsunaga et al., Phys. Rev. Lett. 103, (2009). [3] M. Okabayashi et al, Nuclear Fusion 49, (2009). [4] M. Okabayashi et al, Phys. Plasmas 18, (2011). [5] W. W. Heidbrink et al., Plasma Phys. Control. Fusion 53, (2011). [6] Y. Liu et al., Plasma Phys. Control. Fusion 52, (2010). [7] H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002). [8] N. Aiba et al., Comput. Phys. Commun. 175, (2006). [9] Y. Liu et al., Nuclear Fusion 50, (2010). [10] G. Z. Hao et al., Phys. Rev. Lett. 107, (2011).