Discovery of stationary operation of quiescent H-mode plasmas with Net-Zero NBI

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1 Discovery of stationary operation of quiescent H-mode plasmas with Net-Zero NBI torque and high energy confinement on DIII-D K.H. Burrell 1, K. Barada 2, X. Chen 1, A.M. Garofalo 1, R.J. Groebner 1, C.M. Muscatello 1, T.H. Osborne 1, C.C. Petty 1, T.L. Rhodes 2, P.B. Snyder 1, W.M. Solomon 3, Z. Yan 4, L. Zeng 2 1 General Atomics, P.O. Box 85608, San Diego, California , USA 2 University of California-Los Angeles, Los Angeles, California Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA 4 University of Wisconsin-Madison, Madison, Wisconsin Abstract Recent experiments in DIII-D [J. L. Luxon et al., Plasma Physics and Controlled Nuclear Fusion Research 1996 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] have led to the discovery of a means of modifying edge turbulence to achieve stationary, high confinement operation without Edge Localized Mode (ELM) instabilities and with no net external torque input. Eliminating the ELM-induced heat bursts and controlling plasma stability at low rotation represent two of the great challenges for fusion energy. By exploiting edge turbulence in a novel manner, we achieved excellent tokamak performance, well above the H 98y2 international tokamak energy confinement scaling (H 98y2 =1.25), thus meeting an additional confinement challenge that is usually difficult at low torque. The new regime is triggered in double null plasmas by ramping 1

2 the injected torque to zero and then maintaining it there. This lowers ExB rotation shear in the plasma edge, allowing low-k, broadband, electromagnetic turbulence to increase. In the H-mode edge, a narrow transport barrier usually grows until MHD instability (a peeling ballooning mode) leads to the ELM heat burst. However, the increased turbulence reduces the pressure gradient, allowing the development of a broader and thus higher transport barrier. A 60% increase in pedestal pressure and 40% increase in energy confinement result. An increase in the ExB shearing rate inside of the edge pedestal is a key factor in the confinement increase. Strong double-null plasma shaping raises the threshold for the ELM instability, allowing the plasma to reach a transport-limited state near but below the explosive ELM stability boundary. The resulting plasmas have burning-plasma-relevant β N = and run without the need for extra torque from 3D magnetic fields. To date, stationary conditions have been produced for 2 s or 12 energy confinement times, limited only by external hardware constraints. Stationary operation with improved pedestal conditions is highly significant for future burning plasma devices, since operation without ELMs at low rotation and good confinement is key for fusion energy production. 2

3 I. INTRODUCTION Recent experiments in DIII-D [1] have led to the discovery of a technique for improved operation of quiescent H-mode [1-2] (QH-mode) plasmas, which results in increased edge pedestal pressure and excellent energy confinement time while operating with no net external input torque. H-mode is the preferred operating mode for present-day tokamaks and for future tokamak fusion reactors because of superior energy confinement due to the existence of the edge pedestal and the associated steep gradients of density and temperature. However, in the usual H-mode plasmas, these steep gradients lead to periodic edge instabilities, edge localized modes (ELM), which result in substantial transient particle and heat pulses. In future devices, these transients could produce unacceptable damage to divertor components. As is illustrated in Fig. 1, QH modes operate without ELMs but with constant density and radiated power. The absence of ELMs means there are no pulsed divertor particle and heat loads, which is quite important for next step devices. QH-modes have the standard H-mode edge pedestal and exhibit H-mode levels of confinement; typical International Experimental Thermonuclear Reactor (ITER) H 89 confinement enhancement factors [3] are around 2 and H 98y2 is 1. In addition, even though they have no ELMs, the edge particle transport is rapid enough to provide particle exhaust in future devices [1,4,5]. QH mode was originally discovered on DIII-D [6,7] and was subsequently investigated on ASDEX-Upgrade [8,9], JT-60U [10,11] and JET [8]. QH modes in DIII-D have been run for long duration, a bit longer than 4 s, which is about 30 energy confinement times, 3

4 τ E, or about 2 current relaxation times τ R [1]. The maximum duration to date has been limited by neutral beam pulse length. Once sufficient power is supplied to create QH mode (typically 3 to 4 MW), the plasmas remain quiescent even at the input powers needed to reach the global beta limit (typically, 15 MW). Although the initial QH-mode plasmas were run with neutral beam injection (NBI) in the opposite direction to the plasma current, counter-ip, later experiments demonstrated QH-mode operation with a whole range of NBI torque from counter-ip through zero to co-ip [2,12-16]. The previous work with zero net NBI torque was done using electromagnetic torque from externally applied, 3D magnetic fields. The present work shows that zero net NBI torque operation is also possible without these fields. QH-mode plasmas operate near but below the peeling ballooning mode stability boundary that sets the ELM limit [2, 14, 17]. The additional transport that allows a transport equilibrium at conditions just below the peeling boundary is usually provided by a coherent edge electromagnetic mode, the edge harmonic oscillation (EHO). The enhanced particle transport associated with this increase is illustrated in Fig. 1 by the increase in the divertor D α emission when the EHO turns on around 1150 ms. Under conditions discussed later in this paper, the EHO is replaced by broadband MHD which also provides enhanced edge transport. The new discovery discussed in the present paper was made during experiments designed to test the effects of edge rotation on the EHO in QH-mode discharges. The present theory of the EHO posits that it is a saturated kink-peeling mode, which is destabilized by 4

5 rotational shear when the edge operating conditions are just below the peeling stability boundary [18,19]. Theory suggests and initial analysis [12,15] supports the idea that shear in the angular rotation associated with the ExB drift ω E = E r /RB θ is the important quantity. Here, E r is the radial electric field, R is the major radius and B θ is the poloidal field. However, as is illustrated in Fig. 2, when the NBI torque input to the plasma is reduced sufficiently in balanced double null plasmas, a rapid increase occurs in the width and height of the edge pedestal. This increase is maintained as the torque is lowered further; the wide pedestal only switches back to the more usual, narrower form when the torque is increased again. In general, the transition to the wide pedestal results in a 60% increase in pedestal electron pressure, a 50% increase in electron pedestal width and a 40% increase in thermal confinement factor. Over the data set we have to date, we have found the wide pedestal state at reactor-relevant parameters of normalized β, β N = , thermal energy confinement factor H 98y2 = and pedestal collisionality ν* e = To date, stationary conditions have been produced for 2 s or 12 energy confinement times, limited only by external hardware constraints. Transport calculations of the theoretical current diffusion time in the pedestal region indicate that the edge current density is also constant for about 12 edge current diffusion times. II. Spontaneous transition to improved pedestal conditions The creation of the wide pedestal state in QH-mode discharges is the result of changes in the plasma rotation and ω E. Altering NBI torque is the actuator used to access the improved, wide pedestal conditions. DIII-D is equipped with neutral beams which inject 5

6 in both the co-ip and counter-ip directions. By modulating the various beams and adjusting the fraction of co-ip and counter-ip beams used, torque ramps such as the one shown in Fig. 2 can be achieved. This allows independent variation of the input power and torque; the torque variation changes the plasma rotation, as illustrated in Fig. 2(c), and, hence, ω E. In discharges like the one in Fig. 2, we deliberately reduced the input power slightly as we lowered the input torque in order to maintain β N more constant. Otherwise, given the increase in energy confinement, β N would have risen. As can be seen in Fig. 3, the edge profiles change substantially across the wide pedestal transition. For the electron quantities, the steep gradient region moves away from the separatrix at ρ = 1, the maximum gradients decrease somewhat and the pedestal values increase. Note that there is improvement in both the pedestal electron density and temperature although the temperature increase is somewhat weaker. As is seen in Fig. 3(d), the magnitude of toroidal rotation speed associated with the E x B drift decreases due to the input torque, showing that ω E decreases. The ExB shearing rate ω ExB = [(RB θ ) 2 /B]dω E /dψ [20] changes in a complex fashion, decreasing for ρ 0.91 and increasing inside of that. The significance of this pattern in the change of ω ExB will be discussed further in Section IV. To date, the wide pedestal transition has only been seen in balanced double null discharges with cross section shape shown in Fig. 4(a). When the shape is altered slightly to the single null shape shown in Fig. 4(b), the wide pedestal transition is not seen. Instead, as the torque decreases, ELMs return. We speculate that the excellent 6

7 peeling-ballooning mode stability of the balanced double null shape [21] plays an important role in the creation of wide pedestal QH-mode. By reducing the NBI torque to zero and then holding it there for the rest of the discharge, stationary QH-mode plasmas with the wide pedestal have been created. An example of one of these is shown in Fig. 5. These discharges are stationary for about 2 s or about 12 global energy confinement times. Note that these stationary shots operate without ELMs and with net zero NBI torque. Unlike previous QH-mode discharges with low NBI torque [12,13,15,16], the present zero-torque plasmas did not require the use of external 3D magnetic fields to provide electromagnetic torque. Since stationary operation at low or zero injected torque is an essential feature for future devices, this demonstration of stationary operation is a key result for use of the wide pedestal plasmas in those machines. There are substantial changes in the magnetic and edge density fluctuations that take place when the wide pedestal forms. These are illustrated in Figs. 6 and 7. The poloidal magnetic field fluctuations shown in Figs. 6 and 7 have the common feature that the broadband MHD increases at the time of the wide pedestal transition and that the coherent EHO ceases at that time. As can be seen in Fig. 6, there are cases where the coherent EHO comes back for a period of time; however, this return does not affect the pedestal width. Accordingly, the onset of the broadband MHD is an essential characteristic of the wide pedestal state. As can be seen in Fig. 7(a), the density fluctuations in the steep gradient region of the edge pedestal also increase after the 7

8 transition although close examination of the time behavior shows a delay of 5 to 10 ms. This is discussed further in Section IV. The magnetic probe data in Figs. 6 and 7 also provides some information on why these shots achieved sustained operation at zero NBI torque without the need for electromagnetic torque from externally imposed 3D magnetic fields. Operation at zero NBI torque and, hence, very low toroidal rotation is often plagued by the onset of locked modes. Mode locking often occurs when a coherent MHD mode, such as the coherent n=1 EHO, locks to the wall owing to magnetic interaction. Since there are no coherent modes present during the low rotation phase of shots like that in Fig. 6, this mechanism is absent. This may help to explain why these discharges are able to operate at zero net NBI torque without the external 3D magnetic fields. Measurements by another magnetic probe system confirm the lack of detectable coherent modes at frequencies up to 500 khz anywhere in the plasma. In these discovery experiments, there was little time for parameter space exploration. A power scan was performed to investigate its effect. As is shown in Fig. 8, increasing the NBI power by about 35% ultimately led to the return of ELMs although the shot shown survives for roughly one second at the higher power level. Cases with greater power increase had ELMs even earlier. The increased line averaged and pedestal electron densities seen in Fig. 8(a) and (d) are probably due to increased NBI fueling while the increase in β N and pedestal electron pressure in Fig. 8(e) and (j) are probably due to the increased power input. Somewhat unexpected is the increase in H 98y2 confinement factor 8

9 and the pedestal width in Fig. 8(c) and (i). All of these changes indicate that the edge plasma conditions are not fixed by hard, MHD limits but are most likely transport limited through a balance of gradient-driven transport and input power and particle flux. 9

10 III. Peeling-ballooning mode stability and increased pedestal width The theory of the effects of coupled kink/peeling and ballooning modes on the stability of the H-mode edge plasma has been quite successful in explaining many features of the edge plasma. The drivers of edge instability are the edge current density and the edge pressure gradient. As embodied in the ELITE code [21-23], this physics has been extensively compared with results from QH-mode plasmas with the EHO [1,2,14-19,24-28]. The results show that the QH-mode plasmas operate very close to the peeling stability boundary where the most unstable modes are low-n modes, similar to the low n EHOs illustrated in Figs. 6 and 7. As is shown in Fig. 9, ELITE analysis demonstrates that pedestal conditions in the present experiment also agree with the stability prediction in that all of the operating points are on or below the stability boundary. A more important observation is that the analyses for times without the wide pedestal in Fig. 9(a) and (b) show that the operating points are on the peeling stability boundary within experimental error while for the times in the shot with the wide pedestal in Fig. 9(c) and (d), the operating points are significantly below the peeling boundary. Finding the operating point below the stability boundary is unprecedented; all the previous analyses for a number of different QH-mode shots show operation essentially on the stability boundary. Although the edge behavior in QH-mode is consistent with the basic peeling-ballooning stability, the wide pedestal condition indicates that there is additional physics occurring beyond that included in the EPED model [29]. The EPED model has successfully 10

11 predicted the pedestal height and width for a number of ELMing H-mode as well as QHmode discharges with the EHO. The EPED model couples the peeling-ballooning stability physics with the local effects of kinetic ballooning modes to produce a prediction for the pedestal height and width in cases where these two physics effects are dominant. In developing the first version of the EPED model, it was noted PED experimentally that the pedestal width w e could be related to the electron pedestal PED poloidal beta β pe by an equation of the form w e = C(2βpe ) 1/2 where C is a constant and PED w e is the width measured using the poloidal flux function ψ as a radial coordinate [29]. Fitting the constant to the results from a number of tokamak discharges gives C=0.089 [29]. Using this relation, the pedestal width in the wide pedestal QH-mode cases can be compared to the widths for standard ELMing H-mode; this comparison for two discharges is seen in Fig. 10. The fact that the pedestal width in the wide pedestal cases is 50% larger than in standard ELMing H-mode suggests that there is an additional physics effect in the present plasmas beyond the kinetic ballooning mode physics incorporated in the EPED model. The increased pedestal pressure and width in the wide pedestal QH-modes can be understood by considering in more detail the physics analysis that leads to the EPED predictions. As is shown in Fig. 11, the stability boundaries for the critical pressure for peeling-ballooning modes and the kinetic ballooning modes vary differently with pedestal width. The EPED model uses the intersection point of these two curves to give a unique prediction for the pedestal pressure and width. However, if there is an additional transport process in the plasma edge which increases the pedestal width for a given 11

12 pressure, then, as is illustrated in Fig. 11, the intersection point moves out along the peeling-ballooning mode curve to higher pedestal pressure. This explains the seemingly paradoxical result that degrading the edge by increasing the transport actually improves pedestal stability, leading to an increase in pedestal pressure which then helps to improve the core plasma by increasing the boundary condition on the pressure for the core. A similar improvement due to the same physical process has also been seen in plasmas with repetitive lithium pellet injection [30]. IV. Wide pedestal, turbulence, transport and E x B shear In order to better understand the formation of the wide pedestal, we have investigated in detail the changes in profiles, turbulent density and magnetic fluctuations and E x B shear across the transition and into the stationary phase. The working hypothesis that we are using is based on the idea that changes in the input torque alter the plasma rotation, thus altering ω E and the E x B shear ω ExB ; these changes in turn alter the turbulence and turbulence-induced radial transport, leading to the changes in the pedestal width and height. As discussed in the last section, the changes in the width, coupled with the MHD stability limits, allow the increase in pedestal pressure to occur without violating MHD stability. Making definitive tests of causality in a feedback loop such as the one in this model is difficult, since each element in the loop influences the others. As a first step in testing this picture, one can look for spatial and temporal correlations in the changes in profiles, 12

13 fluctuations and ω ExB. One argument in favor of changes in ExB shear causing the wide pedestal formation is that, experimentally, the neutral beam torque was changed in order to alter the plasma rotation, thus changing ω E and ω ExB. Looking in detail at the time evolution of the density profile across the wide pedestal transition, data such as those in Fig indicate that the first change at the transition is the formation of a transport barrier around roughly ρ=0.9 followed by an increase in transport in the region outside of that. Although there may be a hint of a precursor around ρ=0.85, the time history in Fig. 12(a) shows that the main transport barrier appears between the traces for ρ=0.925 and 0.95 and subsequently moves into the region between ρ=0.85 and 0.9. The density at ρ=0.9 and drops again as the barrier moves in while that at ρ=0.95 shows a monotonic decrease. As is shown in Fig. 12(b), ω E changes in the same region at the same time. The intermediate k density fluctuations from the Doppler Backscatter System (DBS) measured at the top of the pedestal show a dramatic decrease right at the time of the transition; the Fourier spectrum of the fluctuations at the pedestal top is shown in Fig. 13 and the change in the fluctuation amplitude at several different ρ values is shown in Fig. 14(b). The points plotted at the smallest ρ values in Fig. 14(b) are for the data in Fig. 13. Figure 14(a) shows that the initial change in the density profile occurs near the top of the pedestal; the density profile in most of the steep gradient region only changes later. As is shown in Fig. 14(d), the shearing rate ω ExB increases inside of ρ =0.92 but decreases outside of that during the time interval when the wide pedestal is forming. These spatial and temporal changes in 13

14 ω ExB are consistent with the picture that profiles, turbulence-induced transport and ω ExB are involved in a feedback loop. The feedback loop in the present picture is basically the same as the one that has been used to explain the formation of edge and core transport barriers in tokamaks. One novel feature of the present case is that an increase in ω ExB near the top of the pedestal and a decrease in ω ExB in the steep gradient region are both involved in the process of forming the wide pedestal. As is shown in Fig. 3, the decrease in ω ExB in the outer portion of the plasma continues until the plasma reaches the stationary phase. As is shown in Fig. 15, in that later phase of the discharge, the intermediate k density fluctuations increase in the steep gradient region of the pedestal while they decrease in the outer core of the plasma. Transport analysis presented in Fig. 16 demonstrates that the local heat and particle transport in the outer portion of the core plasma decreases in the stationary phase after the formation of the wide pedestal. This is consistent with the changes in density fluctuations shown in Fig. 15 and the changes ω ExB in shown in Fig. 16. An improvement in transport in the outer core in QH-mode plasmas at low rotation has also been seen previously [12]. The picture that we are using to understand the wide pedestal state involves turbulencedriven transport. There is preliminary evidence that turbulence-driven particle transport is present in the edge of these plasmas. Figure 17 presents results from 2D measurements of density fluctuations from the Beam Emission Spectroscopy system. These can be used to produce a picture of the turbulent eddies such as that shown in Fig. 17(a). Processing a 14

15 sequence of such images using the velocimetry technique [31] applied to frequency filtered 2D density fluctuation data allows determination of the instantaneous velocity ũ of the plasma. Multiplying the density fluctuations ñ by the velocity fluctuations ũ gives the instantaneous particle flux Γ=ñũ. The probability distribution function for Γ is given at two different ρ values in Fig. 17(b) and (c). The skewness of this distribution to positive values in Fig. 17(b) indicates a net outward turbulence-driven particle flux. The result in Fig. 17(c) shows no skewness, indicating much less outward transport at this location. V. Questions for future work As with most new discoveries, the observation of the spontaneous transition to greater pedestal pressure and width in QH-mode plasmas has raised a number of questions. 1. What is the edge turbulence associated with the pedestal width increase? The turbulence is clearly electromagnetic, not electrostatic, since there are magnetic fluctuations as well as density fluctuations. 2. How can we make better tests of the working hypothesis that increased pedestal width is due to changes in transport caused by altered edge turbulence and E x B shear? In this hypothesis, alterations in the E x B shear change the turbulent transport, thus altering the plasma profiles which, in turn, feeds back on the electric field and the E x B 15

16 shear. To test this, we need to find ways to intervene in this feedback loop to better test causality. 3. What is the connection, if any, to the various edge modes seen in other ELM-free operating regimes such as EDA H-mode and I-mode in C-MOD [32,33] or lithium enhanced cases such as those in DIII-D [30] or EAST [34]? Qualitatively, all these operating modes have edge turbulent modes which affect the edge profiles and allow the plasma to move away from the ELMing stability boundary. In that sense, they are all quite similar. A key question, however, is the relationship, if any, between these various turbulent modes seen in the different machines. 4. Can we utilize wide pedestal QH-mode in future devices? Since this discovery is so recent, we have not had the opportunity to determine how broad the parameter space is for the wide pedestal condition. For use in future devices, one key subsidiary question is whether we can access wide pedestal QH-mode starting with zero injected torque rather than ramping the torque down from a high value. Another key question is what is the role of plasma shape and how broad a range of shapes will allow access to the wide pedestal state. A third, related question is whether wide pedestal QH-mode can be accessed using torque-free heating methods such as wave heating. Experiments in existing devices with strong, double-null shaping capability and wave heating (such as C- MOD or EAST) could answer this question. The upcoming balanced NBI capability in EAST also provides another opportunity for wide pedestal QH-mode experiments. 16

17 5. What sets the ultimate limit on the pedestal width? What is the optimum pedestal width? We know experimentally the edge transport in L-mode is too great to give the best confinement, so there must be a limit to how far the edge transport can increase before the overall discharges degrade. VI. Conclusions We have made a serendipitous new discovery of a rapid transition to QH-mode operation with increased pedestal pressure and width as the input torque is decreased. These discharges can operate in stationary conditions with no ELMs and with net zero injected torque; they have reactor relevant pedestal parameters. The transition is associated with changes in edge density and magnetic fluctuations and altered E x B shear. Consistent with peeling-ballooning stability, increased edge transport allows higher pedestal pressure owing to the way that the peeling-ballooning mode critical pressure increases with pedestal width. The edge plasma conditions are transport limited near but below peeling stability boundary. Our working hypothesis to explain the improvement is that the increased width is due to changes in turbulent transport caused by altered E x B shear. This ExB shear change is bimodal, exhibiting a decrease in the steep gradient region and an increase inside of that region. If we can find ways to exploit this operating mode in future devices, stationary operation with improved pedestal conditions is potentially highly significant, since operation without ELMs at low rotation and good confinement is key for fusion energy production. 17

18 ACKNOWLEDGMENT This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, using the DIII-D National Fusion Facility, a DOE Office of Science user facility, under Award DE-FC02-04ER54698, DE-FG02-08ER54984, DE-AC02-09CH11466, and DE-FG02-08ER DIII-D data shown in this paper can be obtained in digital format by following the links at 18

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20 T. L. Rhodes, J. C. Rost, B. W. Stallard, E. J. Strait, E. J. Synakowski, M. R. Wade, J. G. Watkins, and W. P. West, Phys. Plasmas 8, 2153 (2001). [8] W. Suttrop, M. Maraschek, G.D. Conway, H.-U. Fahrbach, G. Haas, L.D. Horton, T. Kurki-Suonio, C.J. Lasnier, A.W. Leonard, C.F. Maggi, H. Meister, A. Mueck, R. Neu, I. Nunes, Th. Puetterich, M. Reich, A.C.C. Sips and the ASDEX Upgrade Team, Plasma Phys. Control. Fusion 45, 1399 (2003). [9] W. Suttrop, V. Hynoenen, T. Kurki-Suonio, P.T. Lang, M. Maraschek, R. Neu, A. Staebler, G.D. Conway, S. Hacquin, M. Kempenaars, P.J. Lomas, M.F.F. Nave, R.A. Pitts, K.-D. Zastrow, the ASDEX Upgrade Team and Contributors to the JET- EFDA Workprogramme, Nucl. Fusion 45, 721 (2005). [10] Y. Sakamoto, H. Shirai, T. Fujita, S. Ide, T. Takizuka, N. Oyama and Y. Kamada, Plasma Phys. Control. Fusion 46, A299 (2004). [11] N. Oyama, Y. Sakamoto, A. Isayama, M. Takechi, P. Gohil, L.L. Lao, P.B. Snyder, T. Fujita, S. Ide, Y. Kamada, Y. Miura, T. Oikawa, T. Suzuki, H. Takenaga, K. Toi, and the JT-60 Team, Nucl. Fusion 45, 871 (2005). [12] A.M. Garofalo, W. M. Solomon, J.-K. Park, K. H. Burrell, J. C. DeBoo, M. J. Lanctot, G. R. McKee, H. Reimerdes, L. Schmitz, M. J. Schaffer, and P. B. Snyder, Nucl. Fusion 51, (2011) [13] A.M. Garofalo, K.H. Burrell, W.M. Solomon, M.E. Fenstermacher, J.M. Hanson, M.J. Lanctot, M. Okabayashi, P.B. Snyder, and the DIII-D Team High beta, high confinement, stationary ELM-free operation at low plasma rotation Proc. 39th European Physical Society Conf. on Plasma Physics (Stockholm, Sweden, 2012) 20

21 [14] K.H. Burrell, T. H. Osborne, P. B. Snyder, W. P. West, M. E. Fenstermacher, R. J. Groebner, P. Gohil, A. W. Leonard, and W. M. Solomon, Phys. Rev. Lett. 102, (2009). [15] K. H. Burrell, A. M Garofalo, W. M. Solomon, M. E. Fenstermacher, T. H. Osborne, J.-K. Park, M. J. Schaffer, and P. B. Snyder, Phys. Plasmas 19, (2012). [16] K.H. Burrell, A.M. Garofalo, W.M. Solomon,M.E. Fenstermacher, D.M. Orlov, T.H. Osborne, J.-K. Park and P.B. Snyder, Nucl. Fusion 53, (2013). [17] T.H. Osborne, P.B. Snyder, K.H. Burrell, T.E. Evans, M.E. Fenstermacher, A.W. Leonard, R.A. Moyer, M.J. Schaffer and W.P. West, J. Phys.: Conf. Ser. 123, (2008). [18] P.B. Snyder, K.H. Burrell, H.R. Wilson, M.S. Chu, M.E. Fenstermacher, A.W. Leonard, R A. Moyer, T.H. Osborne, M. Umansky, W.P. West, and X.Q. Xu, Nucl. Fusion 47, 961 (2007). [19] P. B. Snyder, T. H. Osborne, K. H. Burrell, R. J. Groebner, A. W. Leonard, R. Nazikian, D. M. Orlov, O. Schmitz, M. R. Wade, and H. R. Wilson, Phys. Plasmas 19, (2012). [20] T.S. Hahm and K.H. Burrell, Phys. Plasmas 2, 1648 (1995). [21] P.B. Snyder, H.R. Wilson, T.H. Osborne and A.W. Leonard, Plasma Phys. Control. Fusion 46, 131 (2004) [22] P. B. Snyder, H. R. Wilson, J. R. Ferron, L. L. Lao, A. W. Leonard, D. Mossessian, M. Murakami, T. H. Osborne, A. D. Turnbull, and X. Q. Xu, Nucl. Fusion 44, 320 (2004). [23] P. B. Snyder, H. R. Wilson, and X. Q. Xu, Phys. Plasmas 12,

22 [24] W.P. West, C.J. Lasnier, T.A. Casper, T.H. Osborne, K.H. Burrell, P.B. Snyder, D.M. Thomas, E.J. Doyle and A.W. Leonard, Plasma Phys. Control. Fusion 46, A179 (2004). [25] W.P. West, K.H. Burrell, T.A. Casper, E.J. Doyle, P.B. Snyder, P. Gohil, L.L. Lao, C.J. Lasnier, A.W. Leonard, M.F.F. Nave, T.H. Osborne, D.M. Thomas, G. Wang and L. Zeng, Nucl. Fusion 45, 1708 (2005). [26] W. M. Solomon, P. B. Snyder, K. H. Burrell, M. E. Fenstermacher, A. M. Garofalo, B. A. Grierson, A. Loarte, G. R. McKee, R. Nazikian, and T. H. Osborne, Phys. Rev. Lett. 113, (2014). [27] A.M. Garofalo, K.H. Burrell, D. Eldon, B.A. Grierson, J.M. Hanson, C. Holland, G.T.A. Huijsmans, F. Liu, A. Loarte, O. Meneghini, T.H. Osborne, C. Paz-Soldan, S.P. Smith, P.B. Snyder, W.M. Solomon, A.D. Turnbull, and L. Zeng, Phys. Plasmas 22, (2015). [28] Xi Chen, K.H. Burrell, N.M. Ferraro, T.H. Osborne, M.E. Austin, A.M. Garofalo, R.J. Groebner, G.J. Kramer, N.C. Luhmann, Jr., G.R. McKee, C.M. Muscatello, R. Nazikian, X. Ren, P.B. Snyder, W.M. Solomon, B.J. Tobias, Z. Yan, Rotational Shear Effects on Edge Harmonic Oscillations in DIII-D Quiescent H-mode Discharges, submitted to Nucl. Fusion (2015). [29] P.B. Snyder, R.J. Groebner, J.W. Hughes, T.H. Osborne, M. Beurskens, A.W. Leonard, H.R. Wilson and X.Q. Xu, Nucl. Fusion 51, (2011). [30] T.H. Osborne, G.L. Jackson, Z. Yan, R. Maingi, D.K. Mansfield, B.A. Grierson, C.P. Chrobak, A.G. McLean, S.L. Allen, D.J. Battaglia, A.R. Briesemeister, 22

23 M.E. Fenstermacher, G.R. McKee, P.B. Snyder and The DIII-D Team, Nucl. Fusion 55, (2015). [31] G. McKee, R. J. Fonck, D. K. Gupta, D. J. Schlossberg, M. W. Shafer, C. Holland and G. Tynan, Rev. Sci. Instrum. 75, 3490 (2004) [32] A. E. Hubbard, R. L. Boivin, R. S. Granetz, M. Greenwald, J. W. Hughes, I. H. Hutchinson, J. Irby, B. LaBombard, Y. Lin, E. S. Marmar, A. Mazurenko, D. Mossessian, E. Nelson-Melby, M. Porkolab, J. A. Snipes, J. Terry, S. Wolfe, S. Wukitch, B. A. Carreras, V. Klein and T. Sunn Pedersen, Phys. Plasmas 8, 2033 (2001). [33] D.G. Whyte, A.E. Hubbard, J.W. Hughes, B. Lipschultz, J.E. Rice, E.S. Marmar, M. Greenwald, I. Cziegler, A. Dominguez, T. Golfinopoulos, N. Howard, L. Lin, R.M. McDermott, M. Porkolab, M.L. Reinke, J. Terry, N. Tsujii, S. Wolfe, S. Wukitch, Y. Lin and the Alcator C-Mod Team, Nucl. Fusion 50, (2010). [34] J.S. Hu, Z. Sun, H. Y. Guo, J. G. Li, B. N. Wan, H. Q. Wang, S. Y. Ding, G. S. Xu, Y. F. Liang, D. K. Mansfield, R. Maingi, X. L. Zou, L. Wang, J. Ren, G. Z. Zuo, L. Zhang, Y. M. Duan, T. H. Shi, L. Q. Hu, and East team, Phys. Rev. Lett. 114, (2015). 23

24 FIGURE CAPTIONS Figure 1 Long-pulse QH-mode with counter-ip NBI. (a) Plasma current and divertor Dα emission, (b) edge magnetic field from the dominant n = 1 component of the coherent EHO, (c) ratio of energy confinement time to the ITER 89P scaling, (d) line-averaged and edge pedestal electron densities, (e) NBI power and total radiated power and (f) neutral beam torque (negative is counter-ip). Toroidal field is 2.05 T. The drop in the divertor Dα emission around 1000 ms shows the transition to H-mode while the step up in that emission at 1150 ms shows the onset of the EHO and the QH-mode. Note there are no ELMs throughout this shot. Figure 2. Time history of shot with a dual torque ramp showing the formation and collapse of the wide pedestal state when the NBI torque input is changed in a balanced double null plasma. The vertical lines indicate the formation and collapse times. (a) Divertor D α emission showing the complete absence of ELMs, (b) NBI torque T inj and power P inj input, (c) pedestal ion toroidal rotation speed measured using charge exchange spectroscopy on fully stripped carbon ions, (d) width of the electron edge pressure pedestal measured by Thomson scattering, (e) electron pressure at the top of the edge pedestal measured by Thomson scattering, (f) ratio of the energy confinement time to the ITER H 98y2 scaling, (g) normalized beta, β N = 80π<P>a/I p B T, where <P> is the volume averaged pressure, a is half the plasma width, I p is the plasma current and B T is the toroidal field on axis. This nondimensional definition of β N has the same numerical value as the more usual version with dimensions of %Tm/MA. 24

25 Figure 3. Radial profiles change substantially across the wide pedestal transition. The x- axis is square root of the toroidal flux enclosed within a given flux surface normalized by the value for the separatrix flux surface. (a) Electron density, (b) electron temperature, (c) electron pressure, (d) toroidal rotation speed associated with the E x B drift, (e) E x B shearing rate. Note that V ExB = Rω E ; hence, (d) shows the change in ω E. These profiles are at 2350 ms (before transition) and 4300 ms (after transition) in the discharge shown in Fig. 5. The electron quantities in (a), (b) and (c) are from Thomson scattering. The separatrix location for the Thomson measurement is determined by calculating separatrix electron temperature from a two point parallel transport analysis in the scrape off layer. The separatrix temperatures at the two times are different because of the change in the input power needed to keep β N nearly constant. Figure 4. Examples of plasma shapes where the wide pedestal transition is seen (a) and not seen (b). The unbalance in the shape is characterized by Drsep, which is the distance at the outer midplane of the plasma between the field lines which connect to the lower and upper X-points. The shape in (a) has Drsep 0 cm while the shape in (b) has Drsep = 2 cm. In both cases, the ion grad B drift is downwards. Figure 5. Demonstration of stationary operation of QH-mode plasma with the wide pedestal. (a) Line averaged and pedestal density, (b) Divertor D α emission, (c) NBI torque T inj and power P inj input, (d) ratio of the energy confinement time to the ITER H98y2 scaling and normalized beta, (e) pedestal ion toroidal rotation speed measured 25

26 using charge exchange spectroscopy on fully stripped carbon ions, (f) width of the electron edge pressure pedestal, (g) electron pressure at the top of the edge pedestal. Figure 6. Time histories of the pedestal width and the spectrogram of the poloidal magnetic field fluctuations determined by external magnetic probes in the discharge shown in Fig. 5. The magnetic spectrogram is the cross-power between two toroidally distributed magnetic probes on the outer midplane wall of the DIII-D vacuum vessel. The 30 degree difference in toroidal angle allows the determination of the toroidal mode number, which is indicated by the color plotted; the color scale on the right hand side of the plot shows the relation between color and mode number. The wide pedestal transition occurs at about 2490 ms at the time indicated by the vertical line in the plots. Figure 7. Time history of (a) density fluctuations measured by the Doppler backscatter technique and (b) the spectrogram of the poloidal magnetic field fluctuations determined by external magnetic probes. The wide pedestal transition occurs about 2500 ms in this shot. The density fluctuation measurement is made in the steep gradient region of the edge pedestal. See the caption for Fig. 6 for a description of the magnetic measurements. Figure 8. Comparison of time history of plasma parameters in two shots, one under stationary conditions and another where the input power was increased after the plasma reached net zero NBI torque. (a) Line averaged electron density, (b) injected NBI power, (c) ratio of confinement time to the ITER H 98y2 scaling, (d) pedestal electron density, (e) normalized beta, (f) divertor D α emission, (g) injected NBI torque, (h) pedestal ion 26

27 toroidal rotation speed measured using charge exchange spectroscopy on fully stripped carbon ions, (i) width of edge electron pressure pedestal, (j) pedestal electron pressure. Figure 9. Peeling-ballooning stability diagrams for four different times in shot , which has a dual torque ramp quite similar to that shown in Fig. 1. The horizontal axis is the normalized pedestal pressure gradient (MHD α parameter [21-23]) while the vertical axis is peak edge current density normalized by twice the volume averaged current density. The two times in (a) and (b) are periods of high NBI torque where the magnetic signals are dominated by the coherent EHO. The other two times (c) and (d) are during the low torque times with the wide pedestal and broadband MHD. PED Figure 10. Comparison of the electron pedestal pressure width w e with the width fit to the functional form found for standard ELMing H-mode discharges and QH-mode discharges with the EHO. (a) is from a discharge which has the dual torque ramp as shown in Fig. 2 while (b) is for one of the stationary, wide pedestal discharges as shown in Fig. 5. Before about 2500 ms in both discharges, the plasmas are the usual QHmode discharges with the EHO; this is also the case in (a) after 4600 ms. Note that the measured pedestal width matches the results from the functional form for these times while it is a factor 1.5 higher for the wide pedestal cases. Figure 11. Illustration of the different pedestal width dependences of the critical pressure for peeling ballooning stability (solid curve) and the critical pressure for kinetic ballooning stability (dashed curve) for a case with model profiles. The intersection point 27

28 gives the EPED prediction for the height and width. The red curve on lower right shows what would happen if an additional source of edge transport were to increase the pedestal width for a given pressure. Figure 12. (a) Density measured by profile reflectometry as a function of time at various minor radii ρ across a wide pedestal transition. (b) ω E = E r /RB θ as a function of time at various minor radii ρ. The time of the transition is marked with the vertical bar. This is for the same shot as in Figs. 13 and 14. Figure 13. (a) Spectrogram density fluctuations at the top of the edge pedestal as a function of time across the wide pedestal transition measured using the DBS system at intermediate k-vector values of kρ s 1. (b) RMS amplitude of the density fluctuations integrated over the frequency band from 0.75 to 1.75 MHz. The time of the transition is marked with the vertical bar. Note the substantial drop in the density fluctuations at the time of the transition. This is for the same shot as in Figs. 12 and 14. Figure 14. Radial profiles of (a) electron density, (b) RMS density fluctuation amplitudes from the DBS system, (c) ω E and (d) ω ExB at two times across the wide pedestal transition. This is for the same shot as in Figs. 12 and 13. Figure 15. (a) Density profile for a wide pedestal QH-mode showing the radial location of the DBS intermediate k measurements. (b) Comparison of RMS density fluctuation amplitudes at various minor radii ρ for two different times, one before and one well after 28

29 the wide pedestal transition. Note the substantial increase in fluctuations in the steep gradient region of the pedestal and the decrease in fluctuations inside of ρ=0.8. Figure 16. Radial profiles of (a) inferred effective thermal diffusivity, (b) inferred particle diffusivity, (c) toroidal rotation speed associated with the ExB drift v ϕ =Rω E comparing the measurements a two different times, one before and one long after the wide pedestal transition. Thermal and particle diffusivities are inferred from TRANSP analysis. Figure 17. 2D beam emission spectroscopy data for shot at 4000 ms used to infer the radial particle flux driven by turbulent fluctuations. (a) 2D image of fluctuating particle flux. (b) Probability distribution function (PDF) of the fluctuating particle flux at ρ=0.96 determined over a 10 ms time interval. (c) PDF as in (b) but at ρ=0.84. Note the positive skewness in the PDF in (b), indicating a net outward particle flux 29

30 List of Figures Burrell Fig. 1 30

31 Burrell Fig. 2 31

32 Burrell Fig. 3 32

33 Burrell Fig. 4 33

34 Burrell Fig. 5 34

35 Burrell Fig. 6 35

36 Burrell Fig. 7 36

37 Burrell Fig. 8 37

38 Burrell Fig. 9 38

39 Burrell Fig

40 Burrell Fig

41 Burrell Fig

42 Burrell Fig

43 Burrell Fig

44 Burrell Fig

45 Burrell Fig

46 Burrell Fig

47 I p (MA) H 89 n e (10 19 m 3 ) P NBI (MW) T inj (Nm) n e PED Divertor D α (au) EHO n=1 amp (G) P rad TOT (MW) (a) (b) (c) (d) (e) (f) Time (ms)

48 Divertor D α (a) 8 P inj (MW) T inj (MW) V PED φ (km/s) (b) (c) 10 w e PED (cm) (d) 1.6 P e PED (kpa) (e) 2 H 98y2 β N (f) (g) Time (ms)

49 3 n e (10 19 m 3 ) T e (kev) (a) (b) 8 After transition P e (kpa) 6 4 Before transition 2 0 (c) V ExB (km/s) (d) 2 ExB Shear Rate (Hahm-Burrell) (Mrad/s) ρ 0.95 (e) 1.00

50 (a) (b)

51 n e (10 19 m 3 ) n PED e Divertor D α (a) (b) 8 2 H 98y2 P inj (MW) T inj (MW) (c) β N V PED φ (km/s) w PED e (cm) (d) (e) (f) P e PED (kpa) (g) Time (ms)

52 6 3 W e PED (cm) f (khz) B ~ Mode Number Time (ms)

53 Shot , channel: d4a/d4b, 1/2 log scale of (coherent pwr spectrum) Intensity scale (a) ñ f (khz) e Time (ms) (b) ~ B Mode Number f (khz) Time (ms)

54 (a) Density (1019 m 3) 8 Pinj (MW) (b) 5 (c) H98y (h) VφPED (km/s) 6 (i) weped (cm) neped (1019 m 3) (e) 10 (j) βn Time (ms) (g) Tinj (MW) 0 (d) 2500 (f) Divertor Dα PePED (kpa) Time (ms)

55 1.1 (a) 1.1 (b) Edge Current [(j max + j sep )/2<j>] Edge Current [(j max + j sep )/2<j>] Shot ms Coherent EHO High Rotation Shot ms Broadband MHD Only Low Rotation Normalized Pressure Gradient (α) (c) Shot ms Coherent EHO High Rotation Shot ms Broadband MHD Only Low Rotation (d) Normalized Pressure Gradient (α)

56 Time (ms) Pedestal Width (ψ N ) Measured Width Standard H-mode (a) Pedestal Width (ψ N ) Measured Width Standard H-mode (b) 0.03

57 Pedestal Height (p ped, kpa) Illustration of EPED Model Peeling-Ballooning Constraint (A) KBM Constraint (B) EPED Prediction Pedestal Width ( N)

58 n e (10 19 m -3 ) 2450 ρ=0.88 ρ=0.90 ρ Time (ms) ω E (krad/s) (a) Shot ω E within Radius cm 40 ρ= ρ= (b) Time (ms)

59 Shot , Channel: d6a/d6b, Log Scale of (Quadrature) 1/ Intensity scale (a) f (khz) e Time (ms) A [=sqrt(p)] (au) Shot , Point: d6a, Time History of Amplitude MHZ Time (ms) (b)

60 (a) n e (10 19 m -3 ) ms ms ñ rms (au) , 2496 ms , 2501 ms (b) ω E = E r /RB θ (krad/s) (c) ms ms ω ExB (MRad/s) (d) ms ms ρ

61 4 3 Density shot: time: ±5.0 Density Profile Thomson Data = Core (a) n e (10 19 m 3 ) Normalized ρ ñ RMS, (au) Before elevated peped 2584 ms During elevated peped 3578 ms (b) ρ

62 χ eff (m 2 /s) D elec (m 2 /s) EHO Broadband only (a) (b) (km/s) (Mrad/s) V ExB ExB Shear Rate (Hahm-Burrell) (c) ρ (d) ρ

63 15 (a) Z (cm) 10 5 PDF PDF ρ PDF of Particle Flux =n u r =0.96 Outward = Flux Norm Amp. (b) (c)

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