Pedestal Stability and Transport on the Alcator C-Mod Tokamak: Experiments in Support of Developing Predictive Capability

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1 1 EX/P4-15 Pedestal Stability and Transport on the Alcator C-Mod Tokamak: Experiments in Support of Developing Predictive Capability J.W. Hughes 1, P.B. Snyder 2, X. Xu 3, J.R. Walk 1, E.M. Davis 1, R.M. Churchill 1, R.J. Groebner 2, A.E. Hubbard 1, B. Lipschultz 1, T. Osborne 2, S. Wolfe 1, D.G. Whyte 1 1 Massachusetts Institute of Technology, Plasma Science and Fusion Center, Cambridge, Massachusetts USA 2 General Atomics, San Diego, California 92186, USA 3 Lawrence Livermore National Laboratory, Livermore, California 94550, USA contact of main author: jwhughes@psfc.mit.edu Abstract. New experimental data on the Alcator C-Mod tokamak are used to benchmark predictive modeling of the edge pedestal in various high-confinement regimes, contributing to a greater confidence in projection of pedestal height and width in ITER and reactors. Measurements in conventional Type I ELMy H-mode have been used to test the theory of peeling-ballooning (PB) stability and pedestal structure predictions from the EPED model, which extends these theoretical comparisons to the highest pressure pedestals of any existing tokamak. Calculations with the ELITE code confirm that C-Mod ELMy H-modes operate near stability limits for ideal PB modes. Experimental C-Mod studies have provided supporting evidence for pedestal width (in ELMy H-mode) scaling as the square root of pol at the pedestal top. This is the dependence that would be expected from theory if KBMs were responsible for limiting the pedestal width. The EPED model has been tested across an extended set of ELMy H-modes on C-Mod, reproducing pedestal height and width reasonably well across the data set, and extending the tested range of EPED to within a factor of three of the absolute pedestal pressure targeted for ITER. In addition, C-Mod offers access to two regimes, enhanced D-alpha (EDA) H-mode and I-mode, that have high pedestals but in which large ELM activity is naturally suppressed and, instead, particle and impurity transport are regulated continuously. Significant progress has been made in both measuring and modeling pedestal fluctuations, transport and stability in these regimes. Pedestals of EDA H-mode and I-mode discharges are found to be ideal MHD stable, consistent with the general absence of ELM activity. Like ELITE, the BOUT++ code finds the EDA pedestal to be stable to ideal modes. However, it does identify finite growth rates for edge modes when realistic values of resistivity and diamagnetism are included. The result is consistent with the interpretation of the quasi-coherent mode (QCM), which is omnipresent in the EDA pedestal, as a resistive ballooning mode, which could act to regulate the pedestal pressure profile in the same manner that KBMs are predicted to regulate collisionless pedestals. Full non-linear dynamics in BOUT++ are being used to simulate edge potential and density fluctuations, and the transport they drive in the EDA pedestal. Similar investigations are being initiated for I-mode. 1. Introduction In order to achieve satisfactory energy confinement and fusion gain, burning plasma devices generally require operation in a high-confinement regime with an edge transport barrier. Such regimes are manifested by the appearance of a pedestal in the edge pressure profile, and usually in both the density and temperature profile. These edge pedestals provide critical boundary conditions determining core plasma confinement, and thus fusion performance. A longstanding challenge has been to construct believable models for the pedestal, which could provide a theory-based projection for the fusion performance expected on ITER, as well as guidance for its operation. ITER is projected to reach a fusion gain of Q=10 in DT based on confinement projections from a multi-machine parametric scaling law. However, ITER s ability to achieve this condition may be affected by the details of radial transport in the pedestal region, which can influence core fueling efficiency and impurity content, the onset

2 2 EX/P4-15 and magnitude of edge MHD instabilities, static and dynamic heat loads on divertor surfaces, and other items of concern. A joint research target, or JRT, was initiated in the US to advance the predictive capability of theoretical models for the pedestal, in order to support ITER and other future devices [1]. This JRT comprised several theory and modeling groups, and exploited experiments on the largest three US magnetic fusion devices: Alcator C-Mod, DIII-D and NSTX. Experiments on C- Mod explored three high confinement regimes with edge pedestals. The ELMy H-mode is the typical high-power operating regime on most tokamaks, and is so named because it is obtains high confinement with a pedestal that relaxes via discrete edge localized modes (ELMs). By contrast the enhanced D-alpha (EDA) H-mode [2] and I-mode [3,4] are regimes in which the pedestal gradients are limited by continuous relaxation mechanisms. The physics governing these benign relaxations is of interest because of the increasingly urgent need for ELM avoidance in ITER. 2. EDA and ELMy H-mode: experimental contrasts H-modes discussed in this paper were induced using auxiliary heating from ion cyclotron range of frequencies (ICRF) heating on the H minority in D plasmas. Pre-operations boronization was performed in order to supply a low-z coating for the Mo plasma facing components, thus reducing high-z impurity sources. Even with minimized sources, H-modes require a mechanism to flush impurities form the core and maintain suitable energy confinement. C-Mod often accomplishes this by operation in the EDA regime, which tends toward relatively high pedestal collisionality ( *~1 or greater). Radial particle transport in the pedestal region is regulated by a benign electromagnetic fluctuation called the quasi-coherent mode (QCM), which is typically centered at frequencies near 100kHz and has k of about 1.5cm -1. The mode has been shown experimentally to correlate with enhanced radial particle flux, and its presence is associated with reduced core impurity accumulation [2]. This allows the EDA H-mode to remain stationary for many energy confinement times without the need for an ELM to relax the pedestal and expel excess impurities. Reduced pedestal collisionality weakens the favorable qualities of the EDA H-mode [5]. However, ELMs may also occur at reduced *, assuming the role of pedestal regulation with regular, discrete perturbations [6]. The QCM may exist in time between ELMs in some cases, but generally disappears completely at *~ Access to ELMy and EDA H-mode The most common approach for obtaining discrete ELMs on C- Mod is to operate with an atypically shaped equilibrium, illustrated alongside a more typical equilibrium in Fig. 1(a). The ELMy H-mode discharge has relatively low elongation ( ~ ) and upper FIG. 1.Example LCFS contours and time traces from typical EDA H-mode (blue) and ELMy H-mode (red) at matched B T,I P.

3 3 EX/P4-15 triangularity ( u ~0.2) (i.e. a weakly shaped crown ) and a large lower triangularity ( l ~0.8), accompanied by a displacement of the outer strike point from the vertical plate divertor to the more closed flat plate on the divertor floor (the so-called slot divertor configuration). Stationary low-collisionality H-modes are possible with low fueling in this atypical shape, whereas reduced fueling in more typically shaped plasmas ( ~ , u,l ~ ) tends to result in ELM-free H-modes with rapidly quenched confinement due to high core radiation. Figure 1(b) shows the clear differences between EDA and ELMy H-modes obtained in plasmas with similar engineering parameters (I P = 0.9MA, B T =5.4T). The particle inventory is about a factor of two lower in ELMy H-mode than in EDA, and the edge temperature is markedly increased. EDA and ELMy H-mode are clearly distinguished using edge D-alpha time signatures. A number of recent experiments were performed to extend the range of parameters in which ELMy H-mode is obtained on C-Mod [7]. Maintaining the slot divertor configuration, ELMs were obtained in a range of I P from 0.45 to 1.05MA, and at B T ranging from 3.5 to 8.0T. In addition, elongation as high as 1.56 was found to be compatible with the existence of ELMs, which improved the ability of edge TS to resolve the pedestal profile at the plasma crown Pedestal characteristics FIG 2.Profiles of (a) electron density, temperature and pressure, and (b) parallel current in the pedestal region of EDA (blue) and ELMy (red) H-mode (last 20% of ELM cycle). Discharges are the same as in Fig. 1. Note the difference in radial scales between (a) and (b). Pedestal profiles in these characteristic EDA and ELMy discharges are contrasted in Fig. 2. In either case, profiles are obtained from multiple pulses of a Thomson scattering (TS) diagnostic that measures edge n e, T e with millimeter resolution. The profile from each time point is mapped onto normalized poloidal flux ( ) using EFIT, and the mapped profiles are combined and fitted with a standard modified tanh function. Because the EDA H-mode is quasi-stationary, all TS profiles within a particular steady time window are taken in the fit. In the ELMy H-mode, each TS pulse is marked by its distance between the previous and following ELM, and only pulses falling into a bin corresponding to 80 99% of the ELM cycle (i.e. just

4 4 EX/P4-15 prior to the ELM crash) are used to construct the profile fits. It is immediately apparent from Fig. 2 that the H-mode pedestal is wider in the ELMy H-mode case ( ~ 0.04 vs. ~0.02 for the EDA), and has a substantially more relaxed density gradient. Peak pressure gradients are slightly lower in ELMy H-mode, although the inflexion point of the pressure pedestal occurs much farther inboard of the separatrix, and the wider overall pedestal results in a still higher p e at =0.95 than in the EDA case. Figure 2(b) shows the modeled edge current, also important to pedestal stability, and which is calculated according to Sauter [8]. Note that the radial extent of the j peak is larger in the ELMy case, due to the enhancement in bootstrap current over the steep gradient region in the pedestal. The accuracy of the Sauter formula in the pedestal region has recently been tested against numerical calculations and has shown reasonable agreement [1] Pedestal scalings FIG. 3.Empirical pedestal width, =( n + T )/2 as a function of poloidal beta at the pedestal top In both EDA and ELMy H-modes the dominant factor in determining pedestal pressure is plasma current with p e,ped ~I P 2 in EDA [5] and p e,ped ~I P in ELMy H-mode [7]. While pedestal width in EDA H-mode generally shows weak variation across parameter scans [5], the width in ELMy H-mode trends with pol 1/2. This was reported initially from power and density scans in the baseline ELMy H-mode at 5.4T, 0.9MA [9], and then confirmed over the extended data set discussed in Sec. 2.1 [7]. The summary of this result is shown in Fig. 3. Here, the pedestal width is calculated as the mean of the density and temperature width in flux space. The mild width scaling with pol in ELMy H-mode reflects an influence of the plasma current on pedestal width, such that the gradient in pressure scales with I P 2. This scaling of grad-p is also observed in the EDA pedestal, an indicator that a ballooning-like pressure limit can play a role in setting profile structure between the two regimes. As discussed below, resistive ballooning modes are a candidate physics mechanism giving rise to pedestal regulation in the EDA pedestal. In less collisional ELMy H-mode, the kinetic ballooning mode (KBM) has been considered as a pressure limiting process, specifically in the EPED model [10]. The scaling of ~ pol 1/2, seen also in other experiments [9, 11], is consistent with the KBM playing such a role. 3. Calculated stability and implications for pedestal regulation In addition to the KBM, the peeling-ballooning mode is invoked in the EPED model a constraining mechanism for the pedestal height and width. We sought therefore to evaluate the stability of C-Mod pedestals to this class of modes. More general stability analysis is also desirable for potentially identifying various modes that may drive transport and provide continuous, as opposed to discrete, pedestal regulation mechanisms. To these ends, measured

5 5 EX/P4-15 kinetic profiles were used to constrain equilibrium reconstructions in a number of discharges, and the combined data were used to calculate the stability of the edge pedestal. 3.1 Peeling-ballooning stability The theory of peeling-ballooning modes has been highly successful at explaining the onset conditions for Type I ELMs on a number of tokamaks, particularly through its model implementation in the ELITE code [12]. ELITE was used previously to test the peelingballooning stability of several EDA H-mode discharges, some of which exhibited small, irregular ELMs in addition to the usual QCM [13]. In these cases, calculated stability to peeling-ballooning modes was indeed correlated with the absence of ELMs. More recent calculations take advantage of a technique to perturb the pressure gradient and current profile about the experimental reconstruction, and evaluate stability on a grid of (p,j ). This technique yields contours of max / eff, the maximum linear growth rate normalized to a stabilization rate. Figure 4(a) shows an example of a stability diagram generated using this technique, with ELITE inputs taken from the ELMy H-mode presented in Figs. 1 and 2. Here eff = A, the Alfven frequency, and max /( A /20)<1 (a) is chosen as the criterion for stability, a reasonable assumption in cases where diamagnetic stabilization of the peeling-ballooning mode is relatively weak. Within experimental uncertainties, the pedestal is at the calculated stability boundary, with the most unstable modes occurring at moderate n, and near the pressurelimited side of the stability contour. Analysis of multiple ELMy H-mode cases gives similar results, verifying the accuracy of a key assumption of EPED. (b) FIG. 4. Peeling-ballooning stability calculated with ELITE in (a) ELMy H-mode and (b) EDA H-mode, with experimental points marked by yellow cross-hairs. By contrast, EDA H-modes tend to exist farther in phase space from the contour of instability. This is illustrated in Fig. 4(b) for the EDA discharge presented in Figs. 1 and 2. Because diamagnetism is very strong in the EDA pedestal, the eff is one derived from calculations done with the BOUT++ code [14], which gave a quantitative description of diamagnetic stabilization of ideal peeling-ballooning modes at moderate to high n-number [10]. Here max /( eff /2)<1 is the criterion for stability. BOUT++ was also used independently to calculate ideal MHD stability for the experimental

6 6 EX/P4-15 operating point of the EDA H-mode, confirming the ELITE result. One may note that the stability of the EDA H-mode edge allows this regime to operate at considerably higher pedestal pressure gradient than that obtained in ELMy H- mode. However the significant narrowing of the pedestal width that occurs in the EDA case means that the total pedestal pressure, and thus total energy confinement, is very similar between the two regimes. (a) 3.2 Effects of resistivity and diamagnetism on stability BOUT++ is an initial value code capable of calculating non-linear fluid turbulence, and can be used to investigate the effects of plasma diamagnetism and resistivity on pedestal stability. An EDA discharge was analyzed using BOUT++, with a numerical scan of plasma resistivity implemented. For high Lundquist numbers (S>10 8 ), low linear growth rates were obtained, while values of S~10 6, more relevant to the EDA pedestal, yielded a more sizable instability. Figure 5(a) demonstrates that the systematic increase in / A for n=15 modes agrees well with an analytic scaling of ~ 1/3, shown by the dashed curve [15]. Also in agreement with theory, growth rates are found to increase as ~n 2/3, as in Fig. 5(b). The inclusion of diamagnetism in preliminary calculations was shown to provide significant stabilization to modes with n>30. This would result in lower n resistive modes being the dominant driver for pedestal relaxation. We are following up on this result with additional analysis. Resistive modes are a candidate driver for the QCM seen in experiment. Typical n-numbers for the QCM, inferred from magnetics, are in the range of That the QCM may be a manifestation of a resistive ballooning mode is consistent with prior conjecture, motivated by empirical observations [2, 5]. Among these is that QCM activity is favored by higher edge *, q and grad-p. The observed tendency to burn through the QCM at sufficiently high heating power and induce ELM activity would then represent a transition from resistive to ideal MHD within the H-mode pedestal. 3.3 I-mode (b) FIG. 5. (a) Linear growth rates of pedestal modes, indicating destabilization when resistivity is included. (b) Dependence of on toroidal mode number, for S=10 6 High confinement is accomplished in the I-mode regime through the attainment of a strong electron and ion temperature pedestal, simultaneous with L-mode-like particle/impurity

7 7 EX/P4-15 confinement. Like EDA H-mode, I- mode can be run in a stationary manner, and does not require ELMs to suppress core build-up impurities [4]. In fact, because of the absence of a sharp density pedestal in I- mode, there is substantial reduction in pressure gradient and bootstrap current drive, relative to H-mode, making I-modes quite stable to peeling-ballooning modes. For a typical I-mode, ELITE calculations find growth rates an order of magnitude or more below the instability criterion. Because I- modes of modest performance operate so far from the stability boundary, this boundary can be challenging to find with the perturbative technique outlined above. However, indications are that the boundary is very similar to that in an H-mode of similar pedestal pressure and thermal stored energy. Figure 6 shows a comparison of the I- mode and EDA H-mode operating points, and their relation to the EDA stability boundary. ELMs have been observed in some I-modes at especially large values, and examination of these cases is ongoing. 4. Implications for pedestal structure The EPED model is a leading candidate for predicting the pedestal in ITER and other future tokamaks. As shown above, experimental pedestal observations on C-Mod are consistent with the key assumptions of the model, i.e. that kinetic ballooning modes and peeling-ballooning modes work together to determine the pedestal height and width. In fact, the ELMy H-mode data from C-Mod have been used to successfully validate the EPED model to the highest absolute pedestal pressures of any existing tokamak, and to almost half of that expected in ITER [1, 10]. The agreement between the model prediction and experiment is illustrated in Fig. 7 for a sample of C-Mod and DIII-D pedestal data. In experiment, the ELM is presumed to be the experimental manifestation of the peelingballooning mode, which gives an ultimate limit on pedestal pressure for a given pedestal width. However, it remains to obtain either a direct experimental or numerical verification that the KBM is rendered unstable in the periods between ELMs, and that it drives the cross-field transport needed to regulate the pedestal. Work is FIG 7. EPED predicts pedestal pressure on C-Mod and DIII-D with good accuracy. FIG 6. I-mode (orange) and EDA H-mode (yellow) operating points, in relation to the boundary for peeling-ballooning stability ongoing to find the experimental signatures of KBMs in the pedestal

8 8 EX/P4-15 using advanced fluctuation diagnostics [16], and also to find dominant KBM instabilities using gyrokinetic codes [1]. The case is stronger for a ballooning-like mode regulating pedestal transport in the EDA H- mode. As seen above, calculations show that ideal peeling-ballooning modes are typically stable in these plasmas, while resistive modes may have finite growth rates. An interpretation of the result is that at higher collisionality, the RBM supplants the KBM as the dominant mode regulating pedestal gradient. We are attempting to clarify this by additional calculations with BOUT++, run in a non-linear mode, which will allow the determination of fluctuating n,, and the fluctuation-driven transport for which these modes are responsible. Similar simulations are anticipated for I-mode, using on the one hand gyro-landau-fluid extensions to BOUT++, and on the other hand advanced gyrokinic codes. Here the goal will be to understand the relationship between transport suppression and fluctuation changes which are prominent upon the formation of the temperature pedestal. As regimes with continuous pedestal relaxation are developed and projected to burning plasma devices, it will be desirable to develop models similar to EPED in which multiple physics mechanisms work to simultaneously limit the height and width of the pedestal. Comparisons of calculated fluctuation characteristics to experimental signatures will be an important step toward informing these models. Acknowledgment This work was supported by US. DoE Agreements DE-FC02-99ER54512, DE-FG03-95ER References [1] GROEBNER, R.J., et al., this conference EX/11-4. [2] GREENWALD, M., et al., Fusion Sci. Technol. 51 (2007) 266. [3] WHYTE, D.G., et al., Nucl. Fusion 50 (2010) [4] HUBBARD, A.E., et al., this conference EX/1-3. [5] HUGHES, J.W., et al., Fusion Sci. Technol. 51 (2007) 317. [6] TERRY, J.L., et al. J. Nucl. Mater (2007) 994. [7] WALK, J.R., et al., Nucl. Fusion 52 (2012) [8] SAUTER, O.., et al., Phys. Plasmas 6 (1999) [9] SNYDER, P.B., et al. Nucl. Fusion 49 (2009) [10] SNYDER, P.B., et al. Nucl. Fusion 51 (2011) [11] DIALLO, A. et. al. Nucl. Fusion 51 (2011) [12] WILSON, H.R., et al. Phys. Plasmas 9 (2002) [13] MOSSESSIAN, D.A., Phys. Plasmas 10 (2003) [14] DUDSON, B.D. et al. Comput. Phys. Commun. 180 (2009) [15] CARRERAS, B.A., et al. Phys. Fluids 30 (1987) [16] GREENWALD, M. et al. this conference OV/2-3.

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