D. P. Schissel General Atomics, P.O. Box 85608, San Diego, USA
The deuterium single-null plasmas were operated at Bt = 2.0 T, kappa = 1.8, and with the plasma current between 0.75 MA and 1.5 MA. Approximately the first 100 ms of the H-mode was free of edge localized mode (ELM) activity. The remainder of the H-mode had frequent ELM activity and all of our results were obtained in this phase. Since our chosen time of analysis was during the ELMing phase, a quasi steady state existed where the time rate of change of the stored energy averaged over several ELM periods was close to zero.
Global confinement analysis has been performed in the usual manner [1-2]. The radial energy transport properties were analyzed using the standard steady state power balance technique via the transport code ONETWO with the assumption of purely diffusive heat transport. ONETWO inputs are the measured profiles of ne, Te, Ti, Zeff, and the radiated power, together with the magnetic geometry determined from magnetic probe measurements. The diffusivity is defined by the total radial heat flux available for transport divided by the density times the temperature gradient. Transport properties are calculated only between 0.2 < rho < 0.8 since there is a lack of experimental data for rho < 0.2 and the substantial ELM activity for rho > 0.8 creates a large uncertainty in the energy transport.
tth = 0.18 Ip^0.91+/-0.08 ne^0.18+/-0.09 PL^-0.5, (1)with units of seconds, MA, 1019 m^-3, and MW. The Ip and ne scaling results from this subgroup are, within the stated uncertainty, consistent with the DIII-D/JET scaling [1] and therefore verify the earlier assumption that tth depends weakly on ne. In Eq. (1), setting PL^-0.5 accounts for the small range in power [5.7 < PL (MW) < 6.6] when combining both plasma currents.
In these discharges it is clear that as ne was increased Te and Ti responded by decreasing. This decrease in temperature was enough to keep the stored energy (W=INT(nTdV) )approximately constant which is consistent with the observation that tauth is independent of density. Therefore, in these discharges density and temperature are inversely coupled.
To eliminate this coupling a second set of discharges were operated at 1.0 MA where Te and Ti were kept constant by increasing the neutral beam power (PNBI) at higher density. Te and Ti profiles were matched (Figure 1) in H-mode discharges with an ne of 2.9x10^19 m^-3 and PNBI of 3.5 MW, and ne of 5.4x10^19 m^-3 and PNBi of 8.5 MW. The global analysis finds that the tauth values are consistent with Eq. (1). The local analysis finds that the ion diffusivity remains unchanged within the calculated uncertainties [Figure 2(a)]. The electron diffusivity remains unchanged in the core of the discharge but in a small region around rho = 0.75 decreases with decreasing density. The shape of the neutral beam deposition profile, which is peaked on axis, remains very similar at the two densities.
The antithesis of varying the density at fixed temperature is to vary the temperature at fixed density. A series of discharges were operated with PNBI of 4.7 MW and 13.6 MW at an ne of 5.0x10^19 m^-3 and Ip of 1.0 MA. Globally tauth of these discharges agrees with Eq. (1). Locally, both the electron and ion diffusivities [Figure 2(b)] increase with increasing temperature. At the half radius, the electron diffusivity increases by approximately Te^3/2 and the ion diffusivity by Ti.
The results of the RLW simulation of the two discharges at constant temperature but different density are shown in Figure. 1. Te in the higher density discharge is well simulated while the Ti is overestimated in the core of the plasma. Reducing ne at constant temperature results in a better simulation of Ti and a slight overestimate of the Te inside of rho = 0.3. These results indicate that the density scaling of the RLW model agrees reasonably well with DIII-D data. The edge of these two discharges was able to be modeled with the same values of the Hinton-Staebler coefficients. The simulation results of the constant ne different temperature discharges are shown in Figure 3. Both the Te and Ti profiles are well simulated at low power but are overestimated inside rho = 0.5 at the higher power. For both of these discharges the Hinton/Staebler coefficients needed to be adjusted to properly match the plasma edge.
These discharges have also been compared to the dimensionally correct version of the Hsieh transport model [5] which was developed by studying L- and H-mode plasmas and assuming that the thermal diffusivity has a power law dependence on the temperature gradient scale length. The electron diffusivity is calculated by adding the anomalous term chiH
chiH=Ce(ne Te^3/2/mi^1/2 Bp^2) r (r/Te dTe/dr)^2 , (2)to the ion neoclassical value (chie = chiH + chiineo) and the ion diffusivity is calculated by multiplying a constant times the electron diffusivity (chii = Ci chie). The comparison was done by determining, in a least squares sense, the electron (Ce) and ion (Ci) multiplier. In the density scan, the ion and electron multipliers were the same within the uncertainties indicating that the Hsieh model adequately describes the change in density. The temperature scan also had similar multipliers between the two discharges. However, comparing the density to the temperature scan finds that the ion multiplier stays the same while the electron multiplier must be reduced by a factor of 2. This result indicates that an additional functional dependence might be required to properly describe the electron transport.
[1] Schissel D.P. et al. 1991 Nucl. Fusion 31 73 [2] Schissel D.P. et al. 1994 Nucl. Fusion 34 1401 [3] Rosenbluth M. et al. Plasma Phys. and Contr. Nucl. Fusion Research, to be published [4] Hinton F.L. and Staebler G.M. 1993 Phys. Fluids B5 1281 [5] Hsieh C. et al. 1994 Bul. Am. Phys. Soc. 39 1645
Figure 2. Power balance ion and electron diffusivities (a) remain mostly unchanged in the density scan at 1.0 MA, and (b) increase with temperature in the temperature scan at 1.0 MA and 5.0 ´ 1019 mÐ3.
Figure 3. RLW simulation fits the data well at low temperature but is too optimistic at high temperature.
