1 EX/P4-22 Characterization of neo-classical tearing modes in high-performance I- mode plasmas with ICRF mode conversion flow drive on Alcator C-Mod Y. Lin, R.S. Granetz, A.E. Hubbard, M.L. Reinke, J.E. Rice, S.M. Wolfe, S.J. Wukitch, and the Alcator C-Mod Team Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA E-mail contact of main author: ylin@psfc.mit.edu Abstract Neo-classical tearing modes (NTMs) have been observed on Alcator C-Mod. The NTMs occur in high performance I-mode plasmas that are heated by a combination of ICRF D(H) minority heating at 80 MHz and D( 3 He) mode conversion (MC) heating at 50 MHz. I-mode plasmas have confinement as good as H-mode but lower collisionality. Due to the stabilizing effect by the energetic minority hydrogen ions, long sawtooth ( 40 ms) and large sawtooth crashes ( T e0 3 kev) are produced in these hot (T e 9 kev) plasmas. A typical case is that soon after the plasma enters I-mode, a (m = 4, n = 3) mode (f = 40-60 khz) appears following a large sawtooth crash, and then a (3, 2) mode (20-40 khz) appears later at slightly higher β N. The (3, 2) mode can also occur without a preceding (4, 3) mode. In some plasmas, a (2, 1) mode may appear simultaneously with the (3, 2) mode, and lead to disruption. The onset criterion of the (3, 2) NTMs approximately follows that obtained from DIII-D and ASDEX Upgrade. The onset parameters are β P ~ 0.4-0.7, β N ~ 1.0-1.4, β N /ρ i * ~ 200-350, ν NTM (q=3/2) ~ 0.04-0.25. The saturated magnetic island width of the (4, 3) mode is typically W sat ~ 0.4-0.6 cm, and the mode usually has an insignificant effect on confinement. For the (3, 2) mode, W sat ~ 0.8-1 cm, which is 3-4 times the ion banana width, and the mode can cause small confinement degradation ( β/β ~ a few percent). The NTMs have a strong effect on plasma rotation. MC flow drive generates large toroidal rotation above 100 km/sec in L-mode, and when the plasma enters I-mode, plasma rotation is expected to increase significantly due to the additional intrinsic rotation torque from the edge T e pedestal. However, the rotation almost always stops rising after the onset of the NTM(s). The appearance of the (3, 2) mode usually rapidly reduces the rotation speed, and the (2, 1) mode, if occurs, would completely halt the rotation. 1. Introduction Since its first observation on TFTR [1], neo-classical tearing modes (NTMs) have been observed in many major tokamaks [2,3,4,5,6]. Being non-ideal MHD modes, NTMs impose a soft limit on plasma performance, and they need to be controlled on ITER in order to achieve high performance. The basic mechanism for the onset of NTMs can be summarized as following: A magnetic island eliminates the radial pressure gradient inside the island, and this flattened pressure profile removes the local bootstrap current. And the removal of bootstrap current then further increases the magnetic island. The island would grow until the drive from the loss of bootstrap current is balanced by the equilibrium current gradient. The result saturated island often has a significant radial width and thus it affects plasma global energy and particle confinement. At small island width, NTMs are stable, thus a triggering mechanism is required to create a seed island with finite width before NTMs can grow. The triggers are usually provided by large sawtooth crashes and ELMs. Avoiding NTMs by tailoring sawtooth oscillations has been reported [7]. Controlling NTMs using electron cyclotron heating has been demonstrated in some tokamaks [e.g.,8,9,10], and this method will be utilized on ITER. Alcator C-Mod is a compact (R = 0.68 m, a = 0.22 m) high field (B < 8.1 T ) tokamak, and typically runs with relatively high density compared to other tokamaks. Since NTMs usually occur in higher β and lower collisionality plasmas, they have rarely been observed in the usual
2 EX/P4-22 plasma operation parameter space, i.e., L-mode and H-mode plasmas. Several cases have been reported as possible NTM candidates in some high performance Enhanced D α H-mode plasmas in a previous study [11]. In recent experimental campaigns, with the discovery and development of so-called I-mode plasmas [12,13,14], which typically have much lower collisionality (without density pedestal) than H-mode, but have similar energy confinement associated with a T e pedestal, we have started to observe NTMs more frequently on Alcator C- Mod. This paper presents the first systematic characterization of the NTMs observed in Alcator C- Mod. Most of the observations are from experiments that aim at driving large plasma rotations in I-mode. Previously, we have studied flow-drive effect using ICRF mode conversion (MC), and the result showed that the flow drive effect is strongest at low density L-mode plasmas [15,16,17]. I-mode plasmas were thought to be good targets for such flow drive studies, and large rotation was expected by combining the flow drive effect from ICRF and the large intrinsic rotation associated with I-mode (driven by edge T e pedestal [18]). Instead, the result I-mode plasmas frequently show evidence of NTM activities, and the observed plasma rotation is not as large as previously thought. The existence of NTMs in I-mode plasmas also suggests that we will need to find a way to avoid or control NTMs on Alcator C-Mod in order to further develop I-mode as a potential operation scenario of high confinement for future fusion devices. In Section 2, we describe the experimental setup, and in Section 3, we present the characteristics of the observed NTMs, their effects of NTMs on plasma performance and rotation, followed by Discussion (Section 4) and Summary (Section 5). 2. Experimental setup These I-mode experiments were carried out in reversed field (also reversed current) configuration and lower single null shape, that is, the direction of B B drift is toward the top of the machine and away from the divertor. This configuration has been found to favour triggering I-mode and has a wide window of heating power between the L-mode to I-mode transition threshold and the I-mode to H-mode transition threshold [14]. The original aim of the experiment was to study ICRF MC flow drive effect in I-mode plasmas. There are two sets of ICRF antennas on Alcator C-Mod, and each of them is capable of coupling ~3 MW power to the plasma [19,20]. One system is phase variable (+90 o, -90 o, or 180 o ), and also frequency tuneable (50, 70, or 78 MHz). The other system runs at a fixed frequency 80 MHz and fixed 180 o phasing. At +90 o phasing, the launched RF wave is preferentially in the same direction as the plasma current (co-i p ), while -90 o phasing is counter-i p and 180 o phasing (dipole) is toroidally symmetric. In these experiments, with the central magnetic field B t0 ~ 5.1 T, the 80 MHz ICRF was used for central heating via Hydrogen minority heating (with residual H in the plasma), and the antenna at 50 MHz was for 3 He mode conversion heating and flow drive with externally puffed 3 He. Plasma rotation was measured by an x-ray crystal system (HIREX). MHD modes were observed in magnetic coil signals, soft x-ray signals and also ECE T e signals. 3. Characterizing NTMs
3 EX/P4-22 A typical plasma in this experiment is shown in Fig. 1. Plasma parameters are I p = 1.0 MA, B t0 = 5.1 T, and n e0 = 1.3 10 20 m -3. In Fig. 1-(d), we show the trace of total ICRF power. We use 50 MHz RF power at 2.5 MW (t > 0.6 sec) to drive plasma central rotation via mode conversion heating to more than 100 km/s as shown in Fig. 1-(e). The plasma stays in L-mode until t = 1.0 sec when we add 2.5 MW RF power at 80 MHz for central heating. The addition of RF power pushes the heating power above the threshold for L-mode to I-mode transition, and the plasma enters the I-mode region, as noted in the strong increase in plasma β in Fig. 1-(c). Fig. 1-(b) shows the central electron temperature trace, which has large sawtooth crashes. Fig. 1-(a) shows MHD modes identified as m = 4, n = 3, and m = 3, n = 2. The modes appear after the rise of β, and also the large sawtooth crashes. The (4, 3) mode appears about 50 ms after the I- mode transition, and later, with the further increase of β, the (3, 2) mode appears. The toroidal rotation does not increase with the I- mode (albeit with doubled stored energy and edge T e pedestal as high as 1 kev), and it actually decreases after the onset of the MHD modes. In these plasmas, because of the high ICRF power and relatively low density, a large population of energetic particles are expected to be generated via the ICRF heating. These energetic particles help stabilize sawtooth oscillations and result in particularly long sawteeth and large crashes. These large sawtooth crashes act as triggers for seeding magnetic islands, from which NTMs can be destabilized and grow. In Fig. 2, we show a detailed view of such a case. A sawtooth crash at 1.12 sec lowered the central T e from 7 kev to 3 kev, and after the sawtooth, an NTM with frequency about 30 khz appears and is sustained for many sawtooth periods. FIG. 1. A typical plasma shot in the experiment. (a) Spectra of a magnetic signal; (b) Central T e ; (c) Toroial and poloidal β; (d)icrf power; (e)central plasma toroidal rotation. L-mode for t < 1.0 sec, and I-mode for t > 1.0 sec. FIG. 2. A large sawtooth crash triggers an NTM. (a) Spectra of a magnetic signal, (b) Data trace of central T e with large sawtooth crashes. The mode numbers are calculated from the magnetic signals from coils in various toroidal locations and poloidal locations. A cross-phase study of the magnetic signals shows the mode in Fig. 2 is best described as mode n = 2 (Fig. 3-(a)) and m = 3 (Fig. 3-(b)). The spatial location of the mode can also be determined from the several ECE channels that observe the mode. The result location, R ~ 0.82 m, is consistent with the location of q = 3/2 surface from
4 EX/P4-22 FIG. 3. Mode number calculation for the mode shown in FIG. 2. (a) Cross phase from coils at the same poloidal location but different toroidal locations; (b) Cross phase from coils at the same toroidal location. The best match from the phase from the signals and toroidal/poloidal locations is n = 2, and m = 3. the q profile from EFIT reconstruction. NTMs with other mode numbers can also be determined and verified in the same manner. A variety of modes have been observed, including (5,4), (4,3), (3,2), and (2,1). In some plasmas, (3, 2) mode would appear right away like that in the plasma of Fig. 2, and then possibly (2,1) appears later. In some plasmas, only (5,4) or (4,3) are present. In Fig. 4, we show a plasma that (5,4), (4,3), (3,2), and (2,1) modes all exist in the same shot. The effect to plasma confinement of the NTMs is estimate to be β/β 4(ρ s /a) 4 W sat /ρ s, where ρ s is the minor radius of the island and W sat is the saturated island width [21]. In Fig. 4-(e), the island width is estimated from the magnetic signals using a standard analysis technique [11]. For the (4, 3) mode, W sat ~ 0.4-0.6 cm, and this mode has weak effect. For the (3, 2) mode in these plasmas, W sat ~ 0.8-1 cm, and β/β ~ 4-5%. This island width of the (3, 2) mode is approximately 3-4 times the ion banana width, comparable to the observed result from other tokamaks [22]. FIG. 4. A plasma with a variety of NTMs, (a) Spectrl of a magnetic signal, with the mode number of NTMs labelled. (b) Central T e ; (c) Plasma β; (d) ICRF power trace; (e) Island width; (f) Central rotation. The existence of NTMs produces a torque that would slow down the plasma rotation. The torque is generated by the induced field interacting with the machine wall. During the island growing phase, the drag force is W 4 [23]. In Fig. 4-(f) the toroidal rotation is found to
5 EX/P4-22 decrease significantly after the NTM onset and along with the growing of the island width. Detailed modelling of torque and rotation will be left for future work. The NTM onset critical conditions have been studied extensively in other tokamaks. Generally, NTMs favour low collisionality and high β. In Fig. 5, we plot the plasma parameters at the time of NTM onset for all the (3, 2) modes, and compare the Alcator C-Mod result with the empirical scaling obtained from ASDEX Upgrade and DIII-D tokamaks [22]. The Alcator C-Mod data are in the range of β P ~ 0.4-0.7, β N ~ 1.0-1.4, β N /ρ i * ~ 200-350, ν NTM (q=3/2) = (ν ii /ε)/ω e * ~ 0.04-0.25. When β N /ρ i * is plotted vs. ν NTM (q=3/2), the onset critical β is slight lower than that of the other machines while the trend is very similar. In terms of other plasma parameters, e.g., B t, density, plasma rotation and the auxiliary heating source, the C-Mod data occupy a unique parameter space. Further analysis of these data may help clarify some on-going understanding of NTM physics, for example, the effect of plasma rotation on NTM onset critical criteria [24], and the interaction between fast particles and NTMs. FIG. 5. NTM onset criteria for (3,2) mode and compared with data from other machines. NTMs also appear in other I-mode plasmas where only ICRF D(H) minority heating is applied. Fig. 6 shows such a case. Plasma parameters are B t0 = 5.8 T, I p = 1.1 MA, and n e0 = 1.5 10 20 m -3. The onset condition is in a similar range as those with mode conversion flow drive. As shown in Fig. 6-(c), the store FIG. 6. NTMs in I-mode heated only with ICRF minority D(H) heating, (a) Spectra of a magnetic signal; (b) Central T e ; (c)plasma stored energy calculated by EFIT; (d) ICRF power at 80 MHz. energy of the plasma is no longer increasing after the onset of NTMs. Unfortunately, 5 MW is near the limit of the practically available ICRF power, and we are unable to verify whether and/or how effective the NTMs have clamped the plasma performance. 4. Discussion Characterizing the NTMs is only a start in terms of NTM study. We are carrying out experiments aiming at exploring a practical way of avoiding the NTMs in high performance I- mode by tailoring the sawtooth oscillations. Sawteeth can be controlled via ICRF antenna phasing and by carefully manage the relative distance of the q = 1 surface and the ICRF mode conversion surface. These experiments will also determine, if NTMs are avoided in I-mode, whether we can drive significantly more plasma rotation via ICRF mode conversion flow drive. Preliminary results of these experiments will be reported at the conference.
6 EX/P4-22 5. Summary NTMs have been observed on Alcator C-Mod in high performance I-mode plasmas. We have characterized the modes, onset criteria and also studied their effect on plasma confinement and rotation. We plan to find a way to avoid or control these modes on Alcator C-Mod in order to further improve plasma performance in I-mode plasmas. Acknowledgments The authors thank the Alcator C-Mod operation and ICRF groups. This work was supported at MIT by U.S. DoE Cooperative Agreement No. DE-FC02-99ER54512. References [1] Chang Z. et al 1995 Phys. Rev. Lett. 74 4663 [2] La Haye R. L. et al 1997 Nucl. Fusion 37 397 [3] Gates D.A. et al 1997 Nucl. Fusion 37 1539 [4] Zohm H. et al 1997 Nucl. Fusion 37 B237 [5] Buttery R.J. et al 1997 Phys. Rev. Lett. 88 125005 [6] Huysmans G.T.A. et al 1999 Nucl. Fusion. 39 1965 [7] Sauter O. et al 2002 Phys. Rev. Lett. 88 105001 [8] Maraschek G. et al 2005 Nucl. Fusion 45 1369 [9] La Haye R.J. et al 2002 Phys. Plasmas 9 2051 [10] La Haye R.J. 2006 Phys. Plasmas 13 055501 [11] Snipes J.A. et al 2002 Plasma Phys. Control. Fusion 44 381 [12] Whyte D.G. et al 2010 Nucl. Fusion 50 105005 [13] Hubbard A.E. et al 2011 Phys. Plasmas 18 056115 [14] Hubbard A.E. et al 2012 Presentation EX1-3, this conference. [15] Lin Y. et al 2008 Phys. Rev. Lett. 101 235002 [16] Lin Y. et al 2009 Phys. Plasmas 16 056102 [17] Lin Y. et al 2011 Nucl. Fusion 51 063002 [18] Rice J.E. et al 2011 Phys. Rev. Lett. 106 105001 [19] Bonoli A., et al 2007 Fusion Sci. Tech. 51 401 [20] Wukitch S. J., et al 2012 Presentation FTP 1-1, this conference [21] Chang Z., et al 1990 Nucl. Fusion 30 219 [22] La Haye R.J., et al 2000 Phys. Plasmas. 7 3349 [23] Nave M.F.F. et al 1990 Nucl. Fusion 30 2575 [24] Sen A. 2011 Fusion Sci. Tech. 59 526