Confinement physics of H-mode discharges in DIII-D

The authors' data indicate that the L-mode to H-mode transition in the DIII-D tokamak is associated with the sudden reduction in anomalous, fluctuation-connected transport across the outer midplane of the plasma. In addition to the reduction in edge density and magnetic fluctuations observed at the transition, the edge radial electric field becomes more negative after the transition. They have determined the scaling of the H-mode power threshold with various plasma parameters; the roughly linear increase with plasma density and toroidal field are particularly significant. Control of the ELM frequency and duration by adjusting neutral beam input power has allowed us to produce H-mode plasmas with constant impurity levels and durations up to 5 s. Energy confinement time in ohmic H-mode plasmas and in deuterium H-mode plasmas with deuterium beam injection can exceed saturated ohmic confinement times by at least a factor of two. Energy confinement times above 0.3 s have been achieved in these beam-heated plasmas with plasma currents in the range of 2.0 to 2.5 MA. Local transport studies have shown that electron and ion thermal diffusivities and angular momentum diffusivity are comparable in magnitude and all decrease with increasing plasma current.


INTRODUCTION
Understanding and improving energy confinement remains a major goal of tokamak research. The H-mode of confinement, first observed on ASDEX (Wagner et al., 1982), is one of the most robust 1649 and reactor-compatible of the improved confinement regimes that have been obtained in tokamaks over the last several years since it offers the potential for an improved confinement regime that can persist for long periods of time without the need for extreme wall pumping. Since the initial observation of the H-mode on DIII-D (Luxon et al., 1986), H-mode studies have been a major part of our experimental program. H-mode investigations have been carried out in limiter and single-and double-null divertor discharges with Ohmic heating, electron cyclotron heating (ECH), and neutral beam heating (NBI) over a range of parameters: toroidal field 0.7 5 BT (T) 5 2:1, plasma current 0.2 f I, (MA) 5 2.5, vertical elongation 1.45 n f 2.4, line averaged density 0.1 5 5, (lo2' m-3) 5 1.4, total plasma energy WT 5 1.4 MJ, volume averaged toroidal PT 5 8 %, neutral beam injection power PB 5 12 MW and ECH power 51.2 MW. Most of our work has concentrated on studies in divertor discharges, with the primary emphasis on the singlenull configuration; H-mode has also been observed in elongated plasmas limited on the graphite centerpost of the vacuum vessel.
In order to gain the knowledge needed to apply the H-mode in the reactor regime, we have been studying the physics of the L to H transition, investigating the physics of the edge localized modes (ELMs), and working on the global and local confinement behavior of H-mode plasmas.
At the transition between Land H-mode, the edge density and magnetic fluctuations decrease as does the heat flux asymmetry between the inner and outer divertor hit spots. This indicates to us that the transition is associated with the reduction in anomalous, fluctuation-driven transport across the outer midplane of the plasma. In addition to the changes in fluctuations, spectroscopic observations of edge poloidal and toroidal rotation have allowed us to infer that the radial electric field just inside the separatrix is negative in the L-mode and becomes more negative at the transition. Furthermore, we have determined the scaling of the H-mode power threshold with various plasma parameters; the roughly linear increase of the threshold with line-averaged density and toroidal field are particularly noteworthy. Finally, we have critically compared published theories of the L to H transition with our data and find need for improvement in those theories.
Investigations of the physics of ELMs over the past two years have allowed us to devise means of controlling the ELMS and utilizing ELMS to produce H-mode plasmas with durations up to 5 sec and with constant or decreasing impurity levels. This work provides evidence that H-mode plasmas can be utilized for long burns in a fusion reactor. As part of this work, we have developed evidence that after the onset of an ELM the plasma transiently returns to L-mode.
Partial installation of neutron shielding has allowed us to begin systematic studies of energy confinement in deuterium plasmas with deuterium neutral beam injection. Energy confinement time in these plasmas increases linearly with plasma current but shows a clear decrease with increasing neutral beam power. At plasma currents between 2.0 and 2.5 MA, we have found that energy confinement time in H-mode can exceed the saturated Ohmic confinement time by more than a factor of two. Confinement times above 0.3 s have been obtained. This observation, coupled with our previous observation of confinement improvement in H-mode with Ohmic heating alone (Osborne et al., 1988;Burrell et al., 1988), demonstrates that saturated Ohmic confinement time does not represent a limit even in discharges with broad, flat density profiles.
Energy confinement does not increase indefinitely with plasma current. At current levels where the safety factor at the 95% flux surface 495 is approximately 3, the confinement improvement with current ceases. At 495 values below this, energy confinement time depends approximately linearly on BT at constant q95.
Local energy and angular momentum transport studies have shown that the electron and ion thermal diffusivities and the angular momentum diffusivity are comparable and that they all decrease as I, is increased. The comparable magnitude of the diffusivities and the similar dependence as current is increased impose significant constraints on theories of plasma transport.
In addition to studying the H-mode, we have used the improved H-mode confinement as a tool in our high PT program. We have obtained PT as high as 8 % in n = 2 double-null divertor discharges with deuterium NBI.

Transition Phenomena
The initially reported signatures of the H-mode (Wagner et al., 1982) were a sudden reduction in the H, emission all around the plasma and an equally sudden increase in the plasma energy and particle confinement times. In addition to observing these signatures , we have also observed a clear decrease in the edge magnetic and density fluctuations at the L to H transition and a decrease in the heat flux asymmetry at the inner and outer divertor hit spots.
As is illustrated in Fig. 1, at the L to H transition, the magnetic fluctuations in the 10 to 30 kHz range decrease abruptly. This change in the frequency spectrum is seen most clearly on the rnagnetic probes located where the inner and outer separatrix field lines intersect the wall of the vacuum vessel, possibly due to line-tying effects (Ohyabu et al., 1988). It is also seen on magnetic probes located on the centerpost of the vacuum vessel near the vessel midplane. By looking at the signal on magnetic probe sets at various toroidal locations, we have determined that these fluctuations have toroidal mode number TI = 1. When L to H transitions occur in plasmas limited on the centerpost, this change in fluctuation spectra can be seen on most of the magnetic probes on the centerpost. These measurements allow an approximate determination of the poloidal mode number as m 2 6 in these limiter H-modes.
Density fluctuations in the 0-200 kHz range have been measured at the outside midplane of the plasma using a microwave reflectometer with multiple, fixed frequency channels (Lehecka et al., 1989). The fluctuations decrease at the L to H transitions on the 3 channels which measure densities that span from just inside to just outside the separatrix. The lower frequency channel, which measures A, well outside the separatrix, does not show this behavior. The highest frequency channel, which measures fie further inside the separatrix than any other, shows this reduction in fluctuations sporadically, depending on discharge conditions (Lehecka et al., 1989).
The time dependence of various edge parameters during the L to H transition indicates that the transition is connected with a reduction in the anomalous heat transport across the outer midplane of the plasma. The density fluctuations at the outside midplane and the magnetic fluctuations decrease at the time of the earliest Ha drop. Changes in the magnetic fluctuations detected at various points around the plasma are coincident within measurement uncertainties. However, the H, signals at the outer divertor hit spot decrease about 0.5 ms before the H, signal from the inner divertor . This time delay in the H, signals is part of the evidence supporting the idea that the transition starts at the outside midplane. The change in the asymmetry of the heat flow to the inner and outer divertor hit spots at the L to H transition is more evidence for that idea. As is shown in Fig. 2, significantly more power flows to the outer divertor hit spot than to the inner during the L phase of the discharge. This asymmetry is reduced by more than a factor of two after the transition to the H-mode. The observed asymmetry during L-mode is much larger than can be explained due to toroidal effects and suggests that there is an extra, anomalous heat flow across the outside midplane region of the plasma (Hinton and Staebler, 1988a).
The heat flux asymmetry is evidence for an anomalous transport in the bad curvature region at the outer midplane, associated with density and magnetic fluctuations, which is reduced when the fluctuations are stabilized at the H-mode transition. The location in the bad curvature region suggests the stabilization of ballooning modes by entry into the second stable region at the L to H transition (Bishop, 1986). However, comparison of measured edge pressure gradients with the high n, ideal ballooning mode limits (Gohil et al., 1988;Lao et al., 1989) demonstrates that the pressure gradients are at least an order of magnitude below the first stable regime boundary at the L to H transition. Accordingly, stabilization of ideal ballooning modes cannot account for the L to H transition.
In addition to changes in the edge fluctuations and heat flux asymmetry at the L to H transition, we have also seen changes in the edge poloidal and toroidal rotation which indicate that the edge radial electric field becomes more negative at the transition (Groebner et al., 1989). (A negative field points towards the center of the plasma and would tend to confine ions.) The radial electric field can be determined$m the lowest order force balance equation for a single ion species, E, = (ZIenI)-l dpI/dr -(Gx B)?. Here, ZI is the charge of the ion, n1 is the ion density and PI is the ion pressure. At present, we only have information on the -(Gx g)r term; however, since the pressure gradient term is negative, a negative contribution from the -(ax G), term is sufficient to establish that E, is negative. As shown in Fig. 3, this 2.0 contribution to E, is negative prior to the L to  Fig. 3 are for neutral beam heated discharges; however, a poloidal rotation also develops at the L to H transition in Ohmic H-mode and ECH H-mode discharges, indicating that the electric field change is fundamental to the H-mode and not a beam-specific effect. At present, the time resolution of our rotation speed measurements is insufficient to determine whether the change in the electric field takes place early enough to be a cause of the L to H transition or whether it is produced by the changes in the profiles that occur at the L to H transition.
We have checked the consistency of our poloidal rotation measurements with the lowest order force Fig, 2. balance equation by investigating the poloidal rotation in plasmas with both signs of BT and with divertor X-points at both the top and bottom of the vacuum vessel. In all cases, the contribution from the observed poloidal rotation gave an inward contribution to the radial electric field. In other words, the poloidal rotation changes sign when the toroidal field changes sign, but the poloidal rotation is in the same direction for an X-point on the top and the bottom of the vacuum vessel.  The initial observations of the H-mode in AS-DEX (Wagner et al., 1982) established that there are certain thresholds in A, and PB that must be crossed to establish the H-mode. Early observations on DIII-D  demonstrated that at BT = 2.1 T and I, = 1.0 MA, we must have a total input power (Ohmic plus NBI) the H-mode in deuterium plasmas wit,h hydrogen beam injection and with the ion VB drift towards the X-point. We have subsequently established that the threshold power Pth depends on fie, BT, heating method, plasma ion species, direction of the ion VB drift, direction of NBI rela- tive to I,, distance between the divertor X-point and the floor of the vessel and distance between the separatrix flux surface and the graphite centerpost of the vacuum vessel. We have seen no dependence of Pth on I,, in contrast to the results from JFT2-M .
As is discussed in detail in the conference (Carlstrom et al., 1989), Pth depends approximately linearly on fie and BT. In the experiment used to produce this scaling data, the lower density limit for the H-mode could not be observed owing to the onset of locked MHD modes, which seriously degrade confinement; these modes were not present at the lower current used in the initial experiments .
Utilizing the linear dependence of Pth on A, and BT allows us to make a comparison of Pth for various types of plasma heating. As shown in Fig. 4, both ECH and Ohmic heating are slightly more efficient than NBI at producing the H-mode. The lowest threshold seen to date is Pth = 0.8 MW for ECH in a deuterium plasma at I, , = 0.5 MA, (Lohr et al., 1987). Achieving H-mode with Ohmic heating alone requires high currents (21.2 MA) at low toroidal field (51.1 T ) and moderate A, = 4 x lo1' m-' to obtain sufficient Ohmic power to cross the threshold.
Since the H-mode can be created using a variety of heating methods, we can definitely conclude that the physics of the H-mode transition is independent of heating method. Accordingly, models of the L to H transition need not consider the specifics of the heating method.
Deuterium plasmas have the lowest Pth of any studied to date. In contrast to Pth = 2 MW at 2.1 T and fie = 3 x lo'' m-' , Pth is about 5 MW in a hydrogen plasma with hydrogen NBI or in a helium plasma with hydrogen, deuterium or helium NBI. Pth increases by a factor of about 2.2 when the direction of the ion VB drift is changed by reversing the direction of BT. Pth for double-null divertors is intermediate between that for single-null divertors with ion VB drift towards the X-point and those with ion VB drift away from the X-point. In addition, changing from CO-NBI to counter-NBI lowers Pth by about 20% (Schissel et al., 1988b). Since a negative change in the edge electric fields seems to be associated with the L to H transition (Groebner et al., 19891, this lowering of the power threshold with counter-NBI may be associated with the negative electric field produced by neutral-beam-induced toroidal rotation counter to the plasma current. Furthermore, reducing the distance between the divertor X-point and the floor of the vacuum vessel from 25 cm to 3 cm lowers Pth by almost a factor of two (Carlstrom et al., 1989). Finally, limiting the plasma on the graphite centerpost of the vacuum vessel raises Pth. When the separatrix flux surface is 4 cm behind the limiter, Pth is a factor of two higher than in a divertor discharge with a 4 cm gap between the limiter and the separatrix. In spite of the higher power threshold, elongated limiter H-mode plasmas can have confinement times as good as those in divertor H-mode.
There has been considerable speculation in the community that the edge T,, or something related to it, is the critical parameter for the H-mode transition (Wagner et al., 1984;'Keilhacker et al., 1986;Keilhacker et al., 1987). As is shown in Fig. 5, we observe that the ratio of T,/BT must reach a critical value before H-mode is obtained (Carlstrom et al., 1989).
If edge T, is a critical parameter, then we can understand the linear scaling of Pth with ne. Since energy confinement time is basically independent of ne, increasing the density causes T, to drop, thus requiring more power to reach the threshold. If one could work in an Alcator-like regime, where confinement improves linearly with density, then P t h would be independent of ne.

ELM CONTROL AND LONG-DURATION H-MODE
The confinement improvement in the H-mode is due to the creation of a transport barrier just inside the separatrix flux surface (Wagner et al., 1984). Periodically, this barrier is breached by the ELMs, which transiently allow a burst of particles and energy to flow into the divertor. Up to 20% of the energy and particles in the plasma can be lost during an ELM. Although this loss can affect energy confinement, having a controlled level of ELM activity actually allows control of impurities. By properly tailoring the ELM activity, we have produced basically steady-state H-mode plasmas which have lasted for up to 5 s (Mahdavi et al., 1989). Impurity content, radiated Dower and enerev confinement are all constant "I throughout these long-duration H-mode plasmas. Achievement of such steady-state plasmas demonstrates that H-mode can be used for long bums in reactor plasmas.
Over the last year and a half, we have developed a model of ELM behavior which allows us a reasonable level of control over the ELMs. This model is based on two main points. First, we have demonstrated that the ELM onset t ccurs when the edge pressure gradient reaches the first regime, ideal ballooning mode stability limit (Gohil et al., 1988;Burrell et al., 1988;Lao et al., 1989). Second, once the ELM has started, there is considerable evidence that the plasma behaves as though it has retumed to L-mode. This suggests the hypothesis that the ELM event is terminated by the L to H transition. A corollary to this is the idea that the ELM duration should depend on the same parameters that we have found to be important in    Matsumoto et al., 1987).
The earliest theory of the H-mode was the thermal barrier theory of Ohkawa et al. (1983). The theory involves creation of a thermal barrier for electron heat flow along the open field lines in the scrape off layer just outside the separatrix in a divertor plasma. The theory was devised when some experimental observations seemed to show that the steep edge gradients in density and temperature in the H-mode occurred on the open field lines. Observations on DIII-D and, earlier, on ASDEX (Wagner et al., 1984) indicate that the steep edge gradients exist inside the separatrix. In addition, in limiter H-mode plasmas in DIII-D, the steep gradient region occurs inside the limiter defined flux surface. The presence of a transport barrier just inside the plasma edge is also indicated by the simultaneous increase in the density and temperature inside the plasma edge and the decrease in the density and temperature on the open field lines (Wagner et al., 1984;Allen et al., 1988). Since the theory of Ohkawa et al. does not consider the physics on the closed field lines inside the plasma edge, it is inapplicable to t8he region when the main confinement improvement occurs. Hinton (1985), Tang and Hinton (1987), and Staebler (1988a, 1988b) have considered how known, calculable neoclassical effects would modify modify the edge physics of the H-mode. Although this theory in its most recent form does not try to propose an H-mode threshold condition, it can explain the experimentally observed factor of two increase in the H-mode power threshold when the ion VB drift is changed from toward the divertor X-point to away from the X-point. An earlier version of this theory (Hinton, 1985) speculated that the H-mode threshold would occur when the edge ion collisionality parameter yi+ dropped below unity. This speculation agreed with observations on ASDEX (Wagner et al., 1985); however, measurements in the edge of DEI-D show that vi* is in the range of 2-5 even after the transition to the H-mode. The success of this theory in explaining the VB drift effect indicates that, even when we identify the anomalous transport mechanism that is stabilized at the L to H transition, one will still have to include neoclassical effects in order to produce a complete theory. Saito et al. (1985) have postulated that the L to H transition is caused by a bifurcation caused by the physics of the plasma in the divertor itself. The equations that describe the plasma flow along the open field lines in the scrape-off layer have a character that admits two seemingly stable solutions, called the high and low recycling solutions. The high recycling solution has electron temperatures near the divertor plate around 10 eV and densities around 10" m-' while the low recycling solution has divertor plate temperatures of several hundred eV and densities around 10" m-'. The low recycling case is identified with the L-mode while the high recycling case is identified with the H-mode. Unfortunately, the low recycling case, with its extremely low density, has never been observed in a tokamak; most divertor measurements, even in the L-mode, yield temperatures and densities more like those predicted by the high recycling solution. In addition, the divertor density in DIII-D L-modes is usually higher than in the H-mode. Accordingly, the data do not agree with this theory. An additional problem with theories based on the physics of the divertor is that they cannot explain the edge transport barrier inside the separatrix. Hahm and Diamond (1987) have suggested tha.t the increased pressure gradient in the edge of the H-mode plasma might suppress either the ideal ballooning and/or the resistive ballooning mode at the plasma edge by increasing the diamagnetic drift speed, thus altering the edge transport. The stabilization of ideal ballooning modes echos the previous suggestion of Bishop (1986). As we have mentioned in the last section, the edge plasma in DIII-D is well below the ideal ballooning limit at the L to H transition (Gohil et al., 1988), so there is no unstable ideal ballooning mode present prior to the L to H transition. If one considers the resistive ballooning mode, one can obtain an expression for the electron thermal diffusivity by combining the expression for the electron thermal diffusivity caused by resistive ballooning modes (Carreras et al., 1983) with the correction caused by a diamagnetic drift frequency large compared with the resistive ballooning mode growth rate (Diamond et al., 1985). This produces an expression that scales like As the plasma in DIII-D goes from L-mode to H-mode, edge density rises proportionally more than edge temperature and the edge density and temperature gradients steepen. Accordingly, each ratio in this expression gets larger, pr-edicting an electron thermal diffusivity that would be larger in H-mode than in L-mode. Accordmgly, the proposed diamagnetic stabilization of resistive ballooning modes cannot account for the reduced edge transport in the H-mode. An additional problem with this theory is the continuous dependence of the transport rates on the plasma parameters. Such continuous dependences make it difficult to obtain the bifurcation needed to explain the rapid L to H transition.
Work by Ohyabu et al. (1987) has considered the possibility that stabilization of microtearing modes at the plasma edge might be the cause of the L to H transition. This is based on theoretical work by Gladd et al. (1980) concerning the stability of high m tearing modes. Gladd et al. (1980) have shown that, under certain conditions, the microtearing modes can be stabilized if the electron temperature gradient at the edge of the plasma is sufficiently large. This effect is attractive for a theory of the L to H transition, since experimental evidence points to edge T. or VT, as a key factor in the L to H transition. Ohyabu et al. have stated the stability criterion as vei < q,we*, where v.; is the electron-ion Coulomb collision frequency, w e , is the electron diamagnetic drift frequency and q, is the ratio of the logarithmic derivatives of electron temperature and density (exact definitions can be found in Gladd et al., 1980). This can be restated as T:I2VTe > Cn,BT/m, where C is a constant and m is the poloidal mode number. Since T:"VT, should increase with power, this stability criterion is , . c -0.5 reminiscent of the experimental result that the 'E H-mode power threshold increases linearly with (U 0.4 fie and with BT. However, as is shown in Fig. 9, a plotting Tz/2VTe versus ne BT does not seem to 3 lead to a natural division of the H-mode and 3 Om3 L-mode points, although the points for shots + that went into H-mode do cluster at one edge N D 0.2 of the parameter space covered. This lack of a ; l i clear separation indicates that this parameteri-k 0.1 zation may not be the proper stability criterion. The stability criterion for the microtearing mode is actually sufficiently complex that the relation 0.0 given by Ohyabu et al. is a considerable overdence are suggestive of the experimental results, considerable work needs to be done to compare the actual stability criterion to the experimental results. In addition, since these modes turn on gradually after the stability boundary is crossed, it is not clear whether this theory can produce the bifurcation needed to explain the L-H transition.
Two theories of L-H transition involve the effects of radial electric field at the edge of the plasma.
In the first (Itoh and Itoh, 1988a,b;Itoh et al., 1988), the authors consider the effect of the electric field on loss of trapped ions at the plasma edge and couple this with a model of anomalous electron loss at the edge which is also electric field dependent. The structure of the theory contains a clear bifurcation. The theory predicts, however, that the edge electric field should become more positive at the L-H transition. As we have shown in Fig. 3, experimental observations across the L-H transition show that the electric field becomes more negative. The second theory (Shaing et al., 1988a,b) is based on a generalization of neoclassical transport in a plasma containing a background of fluctuations. This theory produces a negative change in the electric field at the L-H transition, in accord with experimental observations. However, the transition criterion in the published work is vir = 1. As was mentioned previously, the edge ion collisionality in DIII-D is above unity even in the H-mode. Accordingly, revision of the stability criterion is needed and is in progress (Shaing, 1989). Rebut et al. (1988) have based an edge bifurcation theory on the transport equations for the plasma edge. The basis of this bifurcation is the nonlinear relationship between the total heat flow across the plasma edge and the heat flow in the electron channel. From the equations given in the paper, one can derive an equation involving the edge electron and ion temperatures, Here, Qe is the normalized heat flow in the electron channel and q = Xe/Xi is the ratio of the electron and ion thermal diffusivities. It is easy to show that the theory allows a bifurcation only when q < 1/24; this means that the ratio of the edge temperatures must satisfy Ti/T, < 115.
However, the measured edge electron and ion temperatures during H-mode in DIII-D show that edge Ti is comparable to or greater than edge T,. Accordingly, the temperature ratio demanded by the bifurcation condition in this theory is not seen in the experiments.
After considering all these theories, it is clear that none meet all the criteria that a theory of the H-mode needs to meet. Each one appears have part of what is needed but the complete theory remains elusive.

GLOBAL CONFINEMENT STUDIES Energy Confinement in Deuterium Plasmas with Deuterium NBI
Partial completion of the neutron shielding on DIII-D has allowed us to begin systematic experiments with deuterium beam injection icto deuterium plasmas. In order to minimize accumulated neutron production, we have made single parameter scans of the variation of energy confinement with total input power (PB 5 12 MW) at moderate current (I, = 1 MA) and with current (Ip 5 2.5 MA) at moderate input power (PB 5 5.5 MW). This work was done in H-mode in single-null divertor plasmas. The present power scan results should be superior to previous single parameter power scans which were done with hydrogen injection into deuterium plasmas. These suffered from potential systematic emors caused by changes in plasma isotopic composition with increasing beam power.
Even at the 1 MA level used for the data in Fig. 10, there is a clear increase in the energy confinement time m when the plasma goes from Ohmic to low power H-mode. In addition, these results are better than our best previous results from deuterium plasmas with low hydrogen fractions Schissel et al., 1988a). These new results also show a stronger decrease of ?.E with input power than our previous results . In spite of the degradation, the T E values are about 3 times the Kaye-Goldston value (Kaye and Goldston, 1985) at high power. A fit to the data using a functional form of PTa gives a value of a = 0.37. This is somewhat smaller than the Kaye-Goldston exponent of a = 0.58. Fitting the data in Fig. 10 with an offset linear model gives an incremental confinement time of about 95 ms. Since the global confinement time observed at the highest power is about 110 ms, only a minor decrease in ?.E with power above the 12 MW level is to be expected.
Variation of energy confinement time with plasma current is shown in Fig. 11. The slope of the deuterium beam data gives m/IP = 120 ms/MA. These data also show a significant improvement over the previously reported 85 ms/MA (Schissel et al., 1988a) obtained in a deuterium plasma with hydrogen injection. As was seen previously, from the 1.0 to the 2.0 MA levels, ?.E increases approximately linearly with plasma current. There is some sign of saturation in confinement above the 2.0 MA level. This may be the onset of the confinement saturation at low q discussed in the next section, or it may simply be due to lack of optimization at these new current levels. Based on our previous observations of confinement in Ohmic H-mode (Osborne, 1988) and at high current in H-mode plasmas with hydrogen NBI , we had concluded that it was possible for the energy confinement time in discharges with broad, flat density profiles to exceed the saturated Ohmic value. 'Our deuterium beam work has allowed us to extend our parameter range and make this conclusion even stronger. As is shown in Fig. 12, in deuterium H-mode plasmas with deuterium beam injection, the % of 340 ms at low input power is at least twice the saturated Ohmic Q of 150 ms in similar discharges. Previous work has shown that the saturated Ohmic confinement time can be exceeded in discharges with peaked density profiles (Greenwald et al., 1984;Sijldner et al., 1988). Our present results show conclusively that sat-

Energy Confinement at Low q
As the plasma current is increased in H-mode discharges, we find that a point is reached where the linear increase of with current ceases. As the toroidal field increases, the current at which saturation occurs increases linearly with the toroidal field. For discharge shapes that we usually run, this saturation occurs when the safety factor at the 95% flux surface q95 reaches 3. After this point, a is basically independent of plasma current, as is shown in Fig. 13, and, as is shown in Fig. 14, By varying the plasma elongation from 1.7 to 2.05 in an H-mode divertor discharge, we have varied q95 by about 30%. As is shown in Fig. 13(b), we find that the confinement saturation occurs at the same current and at a higher 495 value in the more elongated plasma. Accordingly, rion for confinement saturation with current, but E 160be the correct one.
y 140- We have looked into and rejected a number of 120 possible explanations for this loss of current scal-5ing. First, this saturation is not caused by reach-100ing the PT limit, since the saturation can occur at pT values only 50% to 60% of the ob-

40-
time scales linearly with BT (Shimomura et al., 1987), this saturation with increasing current is not due to reaching the saturated Ohmic value.
Ohmic confinement does not represent a limit to confinement in DIII-D. In addition, the value of 6 that some other quantity involving I p / B~ must * As was discussed in the last section, saturated (3 g 20- In addition to investigating global energy confinement as a function of plasma current, we have also studied local ion and electron thermal transport and global and local angular momentum transport (St. John et al., 1989) as a function of current in H-mode plasmas.
Local transport is inferred by steady-state transport analysis with the ONETWO transport code (Pfeiffer et al., 1985) using electron density a i d temperature profiles measured by a 28 point Thomson scattering system, ion temperature profiles measured by a 16 point charge exchange recombination spectroscopy system, angular rotation speed profiles from the 8 tangentially viewing chords of the charge exchange recombination spectroscopy system, Zeff profiles from a 16 chord visible bremsstrahlung measurement and radiated power profiles from a 21 channel bolometer system. Additional density profile information, including the normalization of the Thomson density data, was provided by a 4 chord CO2 interferometer system. All these experiments were done with hydrogen NBI into a deuterium plasma.

10"
Ip (MA) Fig. 15. Plot o f inferred electron and ion thermal Average o f the electron and ion thermal difdiffusivities and angular momentum diffu-fusivity plotted as a function o f the normalsivity a t the half-radius as a function o f ized minor radius coordinate for H-mode plasma current Also shown is the neo-discharges with different plasma currents. classical prediction for ion thermal diffusiv-Thermal diffusivity decreases everywhere as ity for the same discharges. All o f these the Ip increases. Plasma current and BT cases are for hydrogen beams injected into were such that all shots are in the regime deuterium plasmas. Plasma current and where global confinement depends linearly Foroidal field were such that all shots are on plasma current. in the regime where global confinement depends linearly o n plasma current. In the central two-thirds of the H-mode discharges, the overwhelmingly dominant energy loss process is electron and ion thermal conduction. We find that the local thermal transport decreases in both the electron and ion channels as the current increases. This is shown in Fig. 15. In addition, even at the highest currents, the inferred ion thermal diffusivity is still about a factor of three above the neoclassical prediction. In the H-mode, there is a linear relationship between the plasma current and the plasma density. Accordingly, at low plasma densities, the electron-ion energy exchange is relatively weak, and the thermal transport in the electron and ion channels can be readily separated. As current and density increase, the electron-ion coupling becomes stronger, leading to greater error bars on the individual thermal diffusivities. However, is spite of the larger error bars, the decrease in the thermal diffusivities is sufficiently rapid that we can still conclude that the diffusivities decrease as the current increases.
Because of the large error bars on the individual thermal diffusivities at high density, we have also considered the variation of the average thermal diffusivity as a function of current. As is shown in Fig. 16, the average diffusivity decreases everywhere in the confinement zone as the current increases.
The correlation of density and current in the H-mode makes it difficult to unambiguously distinguish a density dependence of confinement from a current dependence. We have some data  which indicates that the global confinement in H-mode is independent of density. However, a clearer determination of the density dependence of the confinement remains to be done when we have better tools for controlling density.
The angular momentum confinement also improves with increasing current in the H-mode plasmas (St. John et al., 1989). The global angular momentum confinement time increases with the current and, as is shown in Fig. 15, the local momentum diffusivity decreases as the current increases. Owing probably to the high densities in H-mode, the toroidal rotation speeds observed to date are small enough that viscous heating is a small contribution to the power input to the ions. In addition, the rotation speeds are small enough that no modifications are needed in the standard fast ion slowing down models, which assume negligible bulk plasma motion.
In ;he cases where we can separate the electron and ion channels, we h d that the electron and ion thermal diffusivities are comparable. In addition, as is shown in Fig. 15, the angular momentum diffusivity is usually within a factor of two of the others, although it is systematically somewhat higher than either. This near equality of the transport coefficients and their simultaneous decrease with increasing current should provide significant constraints on theories of transport in tokamaks.