A highly radiating zone (MARFE) just above the divertor X-point has been used to access the marginal transition regime P{sub sep} {approx} P{sub thres} to study the existence of a critical point for the L to H transition. Phase transition models predict that at the critical point, the transition duration increases and the plasma parameters vary continuously between L-mode and H-mode. In these experiments, the L to H transition duration increased 50--100 times over fast transitions. However, the evolution of E{sub r} shear, edge density gradient, H-mode pedestal, and fluctuations is essentially unchanged from that in fast transitions. The only difference is in the speed with which and the degree to which the fluctuation amplitudes are transiently reduced. This difference is understandable in terms of the time scales for fluctuation amplitude reduction ({le} 100 {micro}s) and edge pressure gradient increase (several ms), provided the edge fluctuations are pressure-gradient driven

Moyer, R. A.

Rettig, C. L.

Rhodes, T. L.

UNT Digital Library

G A-A22726 cod=- Y709/00-- STUDY OF THE PHASE TRANSITION DYNAMICS OF THE L TO H TRANSITION A$R 2 '1 1998 R.A. MOYER, T.L. RHODES, C.L. RETTIG, E.J. DOYLE, K.H. BURRELLQ s 1 1 by J. CUTHBERTSON, R.J. GROEBNER, K.W. KIM, A.W. LEONARD, R. MAINGI, G.D.PORTER, and J.G. WATKINS DECEMBER 1997 G€NEHL ATOMICS ~~ This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. G A-A22726 STUDY OF THE PHASE TRANSITION DYNAMICS OF THE L TO H TRANSITION by R.A. MOYER,~ T.L. RHODES,* C.L. RETTIG? E.J. DOYLE> K.H. BURRELL, J. CUTHBERTSON? R.J. GROEBNER, K.W. KIM3 A.W. LEONARD, R. MAINGI,O G.D.PORTER,A and J.G. WATKINS# tuniversity of California, San Diego *University of California, Los Angeles OOak Ridge National Laboratory ALawrence Livermore National Laboratory #Sandia National Laboratories, Albuquerque This is a preprint of a paper to be presented at the IAEA Technical Committee Meeting on H-mode Physics, September 22-24, 1997, Kloster-Seeon, Germany and to be published in Special Issue of Plasma Physics & Controlled Fusion. Work supported by the U.S. Department of Energy under Contract Nos. DE-AC03-89ER51114, W-7405-ENG-48, DE-AC05-960R22464, DE-AC04-94AL85000, and Grants DE-FG03-95ER54294, DE-FG03-86ER53266 GA PROJECT 3466 DECEMBER 1997 GEMEHL ATOMICS R.A. MOYER, et a/. STUDY OF THE PHASE TRANSlTlON DYNAMICS OF TH€ L TO H TRANSlTlON ABSTRACT A highly radiating zone (MARFE) just above the divertor X-point has been used to access the marginal transition regime Psep = Pthres to study the existence of a critical point for the L to H transition. Phase transition models predict that at the critical point, the transition duration increases and the plasma parameters vary continuously between L-mode and H-mode. In these experiments, the L to H transition duration increased 50-100 times over fast transitions. However, the evolution of Er shear, edge density gradient, H-mode pedestal, and fluctuations is essentially unchanged from that in fast transitions. The only difference is in the speed with which and the degree to which the fluctuation amplitudes are transiently reduced. This difference is understandable in terms of the time scales for fluctuation amplitude reduction (I 100 ps) and edge pressure gradient increase (several ms), provided the edge fluctuations are pressure- gradient driven. ! GENERAL ATOMlCS REPORT GA-A22726 1 R.A. MOYER, et a/. STUDY OF THE PHASE TRANSlTlON DYNAMlCS OF THE L TO H TRANSlTlON 1 INTRODUCTION Quantitative understanding of the physics of the L to H transition and H-mode confinement remains an important goal of international fusion research due to its relevance to ITER and its intrinsic merit as a basic plasma science problem. Several years of concentrated experimental and theoretical study (see reviews in [ 1,2]) have led to the development of a “standard model” for the L to H transition based upon the suppression of turbulent transport in the plasma edge via enhanced decorrelation of the turbulent eddies by sheared E x B convection. Today, self-consistent phase transition models [3-61 show the most promise in explaining the experimental data [2,7]. These models predict the existence of a critical point for the L to H transition, where the transition duration approaches infinity and the edge conditions evolve continuously from L-mode to H-mode. But operation near this critical point is complicated by sawtooth heat pulses which trigger a fast L to H transition. To date, the most complete experimental study of L to H transition dynamics has focused on the limit-cycle-like dithering behavior encountered when the power flowing across the separatrix Psep is marginal for the L to H transition [8,9]. In the experiments reported here, a highly radiating zone inside the separatrix and just above the divertor X-point (an “X-point” MARFE [lo-121) was established in the L-mode target plasma to allow access to the marginal transition regime by preventing sawtooth heat pulses from triggering a fast L to H transition [13]. Preceding Page V Blank GENERAL ATOMlCS REPORT GA-A22726 3 R.A. MOVER, etal. STUDY OF THE PHASE TRANSITION DYNAMICS OF THE L TO H TRANSITION 2. EVOLUTION OF THE RADIAL ELECTRIC FIELD These experiments were carried out in lower single null, deuterium neutral beam heated deuterium discharges in DIII-D with a high target (ohmic) plasma density n = 4-4.5 x 1019 m-3, plasma current I, = 0.96 MA, toroidal magnetic field Bg = 1.75 T, and auxiliary heating power Pinj = 1.7 MW. Changes in the carbon ion temperature, rotation, and pressure gradient were monitored with charge exchange recombination (CER) spectroscopy [ 141. From these data, the contributions to the radial electric field Er were evaluated using the lowest order radial force balance equation for a single ion species: - E,. = - 1 VP, - vgi B4 + v4, Bo n,Zie where E, is the radial electric field, ni and Zie are respectively the ion species density and charge, VPi is the ion pressure gradient, V e i  and Vgi are respectively the ion poloidal and toroidal rotation velocities, and Bg and Be are respectively the toroidal and poloidal magnetic field. In previous L to H transition studies, we distinguished between “fast” transitions, in which the H-mode Er well developed too fast ( I 1  ms) to be resolved by CER spectroscopy, and “slow” transitions, in which the E$ evolution (2-3 ms) could be measured. Since both fast and slow transitions have fast (I 1-3 ms) recycling changes and very fast fluctuation suppression (I 100 ps), this distinction is unimportant for this paper, and both types of transition will be referred to in this paper as “fast”. In Fig. 1, the temporal variation of Er in a very slow L to H transition (right) is compared to that in a fast transition (left). In very slow L to H transitions (Fig. 1, right) Er and E, shear develop slowly as indicated by an increase in the carbon ion v x B contribution to Er inside the separatrix from 2460-2522 ms [Fig. l(h)]. During this time, the shear in the impurity ion VPi contribution to Er does not change [Fig. l(i)], GENERAL ATOMlCS REPORT GA-A22726 5 oss L OStr 1 OS6 1 0 0  9’0 Z’L R.A. MOYER, et ai. STUDY OF THE PHASE TRANSITION DYNAMICS OF THE L TO H TRANSITION and the Da emission begins to slowly decrease [Fig. I(&]. At 2522 ms, the fastest drop in Da begins, and the well deepens more rapidly as indicated by a more rapid increase in the shear in Er" B. At this time, the shear in ErVPi begins to increase, but remains small relative to the shear in bV B even after the Da drop is completed at 2600 ms. This sequence is identical to that in fast transitions (Fig. 1, left) aside from the increased time scale, and suggests that even in these cases, the main ion poloidal rotation is the trigger for the transition [7]. However, since the main ion and impurity ion poloidal rotation may be quite different, this inference must still be verified by measurement of the main ion contributions to Er for very slow transitions in helium plasmas where the main ions can be measured directly. GENERAL ATOMICS REPORT GA-A22726 7 R.A. MOYER, et a/. STUDY OF THE PHASE TRANSITION DYNAMICS OF THE L TO H TRANSITION 3. DEVELOPMENT OF THE EDGE DENSITY GRADIENT AND H-MODE PEDESTAL The variation of the edge electron density gradient Vne and the edge electron density pedestal height nePed in fast and very slow L to H transitions is shown in Fig. 2. The H-mode pedestal height nePed is the value of ne at the transition from the steep edge gradient region to the relatively flat inner core. These profile parameters are obtained from modified hyperbolic tangent fits to electron density profiles measured by the Thomson scattering system [15]. The hyperbolic tangent consists of a hyperbolic tangent, an offset, and a linear ramp in the plasma core and provides an excellent description of both L- and H-mode profiles in DIII-D. In both fast and very slow transitions, Vne and nePed do not change until the onset of the steepest portion of the I& drop, marked in each plot by the dashed line. In fast transitions, Vne jumps to 80% of the peak ELM-free H-mode value within 25 ms of the onset of the steepest Da drop. In contrast, Vne takes 140 ms to reach a similar level in the very slow L to H transition. After the steepest Da drop begins, n$ed evolves slowly over 150-200 ms to the steady state value just before the onset of ELMS in both the fast and very slow transitions. . L L *? z 3  2 -  1 -  0 -200 2300 2400 2500 2600 2700 2300 2400 2500 2600 2700 Time (ms) Time (ms) Fig. 2. Temporal variation of (top) D, emission, (middle) edge electron density gradient Vn,, and (bottom) edge electron density pedestal height n,Ped in (a) fast and (b) very slow L to H transitions. The very slow transition (b) is the same one plotted in Fig. 1.  GENERAL ATOMICS REPORT GA-A22726 9 R.A. MOYER, et a/. STUDY OF THE PHASE TRANSITION DYNAMICS OF THE L TO H TRANSITION 4. SUPPRESSION OF FLUCTUATIONS AND TURBULENT TRANSPORT The temporal variation of edge and scrape-off layer (SOL) density fluctuations ; was monitored with reflectometry. During the first stage (2460-2522 ms) of the very slow L to H transition (Fig. 1, right), the density fluctuation levels; don't change in either the edge [Fig. l(k)] or the SOL [Fig. 1(1)] although the shear in Er" increases [Fig. l(h)] and the recycling decreases [Fig. l(g)]. From Fig. 2(b), Vne and nepedalso do not increase during this time. This behavior is similar to the first stage (2-3 ms before the fast Da drop) of fast L to H transitions [Fig. 2(a)] and (Fig. 1, left) [7]. At 2522 ms in the very slow transition, the recycling decreases more rapidly and the edge density gradient begins to rise [Fig. 2(b)]. As the density profile steepens, the reflection layer for each reflectometer channel moves outward in radius. Consequently, the temporal variation in the reflectometer powers includes both temporal and spatial variations in the; levels. The edge channel decreases a modest amount over 30-50 ms as the reflection layer moves from the plasma interior into the steep edge gradient region [Fig. l(k)]. In the SOL, a similarly small reduction in is seen pig.  1(1)]. This differs from fast L to H transitions only in the speed with which the z levels respond, and in the overall reduction in [7]. The ; fluctuation power (= toz2) measured by FIR collective scattering in fast and very slow transitions is compared in Fig. 3. Since the power spectra for these measurements is dominated by the Doppler shift from the E x B rotation, the power in negative frequencies corresponds to fluctuations inside the negative Er well, while the power in positive frequencies corresponds to fluctuations deeper in the plasma interior where Er > 0 [16]. In the fast transition [Fig. 3(a)], the total power in the density fluctuations increases during the L-mode period up to the time of the fast Da drop. At 1520 ms, there is a fast 50% reduction in the density fluctuation power inside the negative E, well. The fluctuations in the plasma interior increase momentarily before GENERAL ATOMICS REPORT GA-A22726 11 STUDY OF THE PHASE TRANSlTlON DYNAMICS OF THE L TO H TRANSlTlON R.A. MOYER, et a/. 0.4 0.2 0.0 1300 1400 1500 1600 1700 1800 2200 2300 2400 2500 2600 2700 2800 Time (ms) Time (ms) Fig. 3. Evolution of the density fluctuation power = t i 2  in (a) fast and (b) very slow L to H transitions as measured by FIR collective scattering. The transition time, taken as the onset of the fastest measured drop in D,, is indicated by the dashed vertical line in each plot. Shown are, from top to bottom, the total power (all frequencies), the power from the interior (f > 0), the power from the edge (inside the E, well, f < 0), and the D, emission. decreasing several tens of milliseconds after the transition [17]. Just before ELMS begin at 1680 ms, the density fluctuations have recovered to nearly the L-mode levels in both the edge and core. In the very slow transition [Fig. 3(b)], the power in the density fluctuations inside the E,. well slowly decreases 30% over 40 ms after the onset of the Da drop, consistent with the edge reflectometry results [Fig. l(k)]. The fluctuations later recover to L-mode levels. In the plasma interior, the density fluctuations rise slowly throughout the Da drop while the edge density gradient is steepening [Fig. 2(b)]. The reflectometry and FIR scattering results show that the initial L-mode and final H-mode states are similar for fast and very slow L to H transitions. Only the duration of the transition, and the size of the absolute fluctuation amplitude reduction during the transition is different. Reciprocating Langmuir probe measurements taken in the L- and H-mode phases of very slow transitions confirm that after the Da drop, density fluctuation levels inside the & shear layer equal or slightly exceed L-mode levels. To within discharge reproducibility, the floating potential fluctuations in H-mode are also equal to L-mode levels. Although the rms amplitudes of the fluctuations in the established H-mode are similar to the Gmode values, the fluctuation-induced particle flux r, equal to the integral of the spectrally resolved particle flux T(o) over the frequency spectrum (Fig. 4), is reduced inside the E, well by a factor of about 3 . 12 GENERAL ATOMlCS REPORT GA-A22726 R.A. MOYER, eta/. STUDY OF THE PHASE TRANSITION DYNAMICS OF THE L TO H TRANSITION 1 r = 3.70 x I 017/crn2s 0 1 x105 2 x105 3 x105 4 x lo5 Frequency (Hz) Fig. 4. Comparison of the frequency-resolve turbulent particle flux rturb(W) in L-mode before the onset of the Da drop (solid lines) and in H-mode after the Da drop (dashed lines). The' total particle flux r obtained by integrating rtuh(w) over frequency o = 2 d  for each discharge is shown. GENERAL ATOMICS REPORT GA-A22726 13 R.A. MOYER, et ai. STUDY OF THE PHASE TRANSlTlON DYNAMlCS OF THE L TO H TRANSlTlON 5. DISCUSSION Phase transition models of the L to H transition predict that for conditions marginal for the L to H transition, the duration of the transition should lengthen and plasma parameters should vary continuously between the L-mode and H-mode states. A highly radiating zone inside the plasma core just above the divertor X-point (X-point MAWE) has been used to access the marginal transition regime Psep c- Pthres to study this prediction. Under these conditions, the duration of the L to H transition becomes 50-100 times longer than for fast transitions. However, the evolution of the Er shear, edge density gradient, H-mode pedestal, and fluctuations is essentially unchanged from fast transitions. The only difference is in the speed with which and degree to which the density fluctuation amplitudes are reduced. In fast transitions, the fluctuation amplitudes are rapidly reduced by a large factor. In contrast, in very slow transitions, the fluctuation amplitudes show only a small reduction on a time scale 50-100~ longer than the fast transitions. The density fluctuation amplitudes eventually recover to near L-mode levels before the onset of ELMS in both the fast and very slow transitions. If we postulate that the edge electrostatic fluctuations are pressure gradient driven, then the evolution of the fluctuation amplitudes is easily understood. The absolute fluctuation levels in the established ELM-free H-mode are at or near L-mode levels in the presence of a 4-5 times larger pressure gradient drive, which is evidence of suppression. The lack of a rapid, large reduction at the onset of the recycling drop in the very slow L to H transitions also follows from the realization that in fast transitions the fluctuations are suppressed within 100 ys [7] which is much shorter than an edge confinement time ‘&dge of several milliseconds. Since zedge sets the time scale on which the pressure gradient can change, there is initially a rapid reduction in fluctuation amplitude, followed by a slow increase as the edge pressure gradient responds to the reduced turbulent transport levels. In very slow transitions, the time scales for flucuation suppression and pressure gradient increase are comparable, and the absolute fluctuation amplitudes remain unchanged or increase a small amount. GENERAL ATOMlCS REPORT GA-A22726 15 R.A. MOYER, et a/. STUDY OF THE PHASE TRANSlTION DYNAMlCS OF THE L TO H TRANSITION REFERENCES [ 13 [2] [3] [4] [5] [6] [7] [8] [9] [lo] Baker, D., et al., Nucl. Fusion 22 (1982) 807. [ 111 Lipschultz, B., et al., Nucl. Fusion 24 (1984) 977. [12] Drake, J.F., Phys. of Fluids 30 (1987) 2429. [13] Moyer, R.A., et al., submitted to: Nucl. Fusion (1997) [14] Gohil, P., et al. in 14th Symp. on Fusion Engineering. 1992: IEEE. [15] Groebner, R.J., Proc. this conference; to be published in: Plasma Phys. Control. Burrell, K.H., Plasma Phys. Control. Fusion 36 (1994) A291. Burrell, K.H., Phys. Plasmas 4 (1997) 1499. Diamond, P.H., et al., Phys. Rev. Lett. 72 (1994) 2565. Carreras, B.A., et al., Phys. Plasmas 1 (1994) 4014. Carreras, B.A., et al., Phys. Plasmas 2 (1995) 2744. Charlton, L.A., et al., Phys. Plasmas 1 (1994) 2700. Moyer, R.A., et al., Phys. Plasmas 2 (1995) 2397. Zohm, H., Phys. Rev. Lett. 72 (1994) 222. Zohm, H., et al., Plasma Phys. Control. Fusion 37 (1995) 437. Fusion ( 1997) [16] Rettig, C.L., et al., Rev. Sci. Instrum. 66 (1995) 848. [17] Philipona, R., et al., Phys. Fluids B 5 (1993) 87. " GENERAL ATOMlCS REPORT GA-A22726 17 a R.A. MOYER. et a/. STUDY OF THE PHASE TRANSITION DYNAMICS OF THE f TO H TRANSITION ACKNOWLEDGMENT This work supported by U.S. DOE contracts DE-AC03-89ER51114, W-7405-ENG- 48, DE-AC05-960R22464, DE-AC04-94AL85000 and grants DE-FG03-95ER54294 and DE-FGO3-85ER53266. The assistance of the DIII-D Team and Operations Group in operating the tokamak and supporting diagnostics is gratefully acknowledged. GENERAL ATOMICS REPORT GA-A22726 19 ~ ~~~ M98004684 llllllllllll li1111111111 lllll1111 Il1 1111 Report Number (14) @A --A . .  ~ a 7 a b  ca.AJF - 9 1  0 9 / 0 0  -- Publ. Date (11) /VI op Sponsor Code (1 8) UC Category (19) DOE 

Study of the phase transition dynamics of the L to H transition

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Study of the phase transition dynamics of the L to H transition

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