G A-A22096

EXPERIMENTAL DETERMINATION OF THE DIMENSIONLESS SCALING PARAMETER OF

ENERGY TRANSPORT IN TOKAMAKS

bY T.C. LUCE and C.C. PETTY

This is a preprint of a paper presented a t the 22nd EPS Conference on Controlled Fusion and Plasma Physics, July 3-7, 1995, Bournemouth, United Kingdom, and to be printed in the Proceedings.

Work supported by U.S. Department of Energy

Contract DE-AC03-89ER511.14

GENERAL ATOMICS PROJECT 3466 J U LY 1995

DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED oa, GENERAL ATOMfCS

DISCLAIMER

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, make 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.

DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

Luce U Pet ty EXPERIMENTAL DETEFIMINATION OF THE DIMENSIONLESS

PARAMETER SCALLING OF ENERGY TRANSPORT IN TOKAMAKS

Experimental Determination of the Dimensionless Parameter Scaling of Energy Transport in Tokamaks

TC Luce and CC Petty General Atomics, San Diego, California 92186-9784, U. S.A.

1. Introduction Controlled fusion experiments have focused on the variation of the plasma characteristics as the engineering or control parameters are systematically changed. This has led to the development of extrapolation formulae for prediction of future device performance using these same variables as a basis. Recently [l], it was noticed that present-day tokamaks can operate with all of the dimensionless variables which appear in the Vlasov- Maxwell system of equations (including device geometry) at values projected for a fusion powerplant with the exception of the parameter p*, the gyroradius normalized to the machine size. The scaling with this parameter is related to the benefit of increasing the size of the machine either directly or effectively by increasing the magnetic field. It is exactly this scaling which is subject to systematic error in the inter-machine databases and the cost driver for any future machine. If this scaling can be fixed by a series of single machine experiments, much as the current and power scalings have been, the confidence in the prediction of future device performance would be greatly enhanced. While carrying out experiments of this type, it was also found that the p, scaling can illuminate the underlying physics of energy transport. Conclusions drawn from experiments on the DIII-D tokamak in these two areas are the subject of this paper.

2. Background The fundamental assumption is that the energy difhsivity x can be written as x = xB pz F(P, v,, q, R / a , n, T'/Ti, . . . ), where x is normalized to xB, the Bohm dif- fusivity, by convention. The goal is to change p, while holding the functional F fixed to determine a. As explained elsewhere [2], a = 1 is known as gyro-Bohm scaling, a = 0 is B o b scaling, a = -1/2 is Goldston scaling, and a = -1 is stochastic scaling. Drive-wave theories of cross-field transport generally have gyro-Bohm scaling.

Experiments in L-mode plasmas with low p (pN - 0.5) and high q (q - 7) found [2] that the global confinement scaling changed from gyro-Bohm scaling to Bohm scaling as the density increased. However, these experiments allowed for the first time separate determination of the p, scaling of the electron and ion diffusivity. The experiments clearly showed that the electron scaling was always gyro-Bohm, while the ion scaling was always Goldston. The global scaling varied with the fractional power exhausted in the electrons. The strong deviation of the ion scaling from gyro-Bohm remains unexplained; however, one hypothesis is that it arises from orbit averaging over the turbulence when the ion gyroradius is larger than the turbulent eddy size. The ion scaling should return to gyro-Bohm in the limit p, + 0.

GENERAL ATOMICS REPORT GA-22096 1

Luce U Petty EXPERIMENTAL DETERMINATION OF THE DIMENSIONLESS

PARAMETER SCALLING OF ENERGY TRANSPORT IN TOKAMAKS

Another series of experiments [3] designed to lie on a dimensionless scaling path to ITER was performed in H mode plasmas at lower safety factor (q = 3.8) and higher p (& - 2.2). The result was that both the electrons and ions (and therefore the global) scaling was gyro-Bohm. This result leads to a very optimistic confinement prediction for ITER, as discussed below.

3. Understanding the Ion p, Scaling

Equally interesting is the dramatic change in ion pa scaling. Four quantities have changed between the two experiments - L mode to H mode, which changes the density scale length; high q to low q, which changes the shear length; low p to higher p; and T e / q > 1 to T e / q < 1. These variations are listed in the order in which the effect of their variation will be tested. The density scale length is interesting since it changes dramatically in the classic phenomenology of the transition from L mode with peaked profiles to H mode with flat profiles. The magnetic shear length is chosen because the current scaling is the strongest of the engineering parameter scalings. Also, scale lengths rather than the dimensionless quantities themselves are chosen because of the working hypothesis of orbit averaging. If the turbulent eddy scale is determined by some scale length in the plasma, then a dramatic change in that scale length would correspondingly change the critical p* at which the ion scaling transitions from gyro-Bob to cy. < 0. The new experiments reported here are the f is t in a series to investigate the source of the variation in the ion p* scaling.

The strategy to find the effect of the density scale length L, on the ion p* scaling was to run Gmode discharges with dimensionless parameters as close as possible to the H-mode discharges discussed above. The aspect ratio, elongation, q g 5 , and Te/T were nearly the same; however, it was not possible to remain in L mode with as high triangularity or p . With this caveat, any change in the ion p, scaling will be attributed to the change in L,. Some of the dimensionless parameters for a pair of such L-mode discharges are shown in Fig. 1. Also shown are the parameters from one of the ITER- like H-mode discharges for comparison. The ratio of the diffusivities for electrons, ions, and a single fluid are shown in Fig. 2. The electron d i h i v i t y has gyro-Bob scaling as always, but the ion scaling is now approximately Bohm. The single fluid scaling lies about halfway between indicating a nearly even split of the transported power between electrons and ions. This global scaling is reminiscent of the original dimensionless scaling experiments on DIII-D which for low-q, Gmode discharges found a global scaling between B o b and gyreBohm [l]. Unfortunately, the scaling of the individual species could not be determined in those experiments due to the high density.

The correlation between the ion p* scaling and the density scale length can be clearly seen using al l of the datasets for which the ion p* scaling can be determined (Fig. 3). While the two quantities are correlated, causality is much more difficult to establish.

GENERAL ATOMICS REPORT GA-22096 2

Luce 0 Petty EXPERlMENTAL DETEFLMINATION OF THE DIMENSIONLESS

PARluMETER SCALLING OF ENERGY TRANSPORT IN TOKAMAKS

The same unknown mechanism which controls the ion p, scaling could also affect the particle transport.

4. Prediction of Future Device Performance The H-mode discharges discussed above have the same dimensionless parameters as the ITER EDA design from summer 1994, with p, increased by a factor of 8. The DIII-D plasma scales to a plasma at a = 3.01 m, I = 19.6 MA, and Pr, = 1.5 GW (with 50% tritium). The power necessary to support the profiles against the gyro-Bohm scaled transport is only 41 MW (with no mass compensation for tritium), considerably less than the 300 Mw of a-heating power. The bremsstrahlung losses of - 70 MW must also be included, but the total losses are less than the a power. Therefore, gyro-Bohm scaling provides a large ignition margin.

It is implicitly assumed in this extrapolation that the discharge will be H mode. Di- mensionless scaling formulae for the H-mode threshold are now available [4]. Along a p* scaling path, the formula & cc n0*75BS (where S is surface area) has a Goldston p, scaling (pL3) . [It is interesting to note that this is the same scaling as the original L-mode ion p* scaling, suggesting the transition is related to ion transport. However, the comments which follow pertain to any H-mode threshold scaling stronger than gyro- Bohm as p, + 0.1 The H-mode threshold curve crosses the gyro-Bohm confinement projection at a p, value between DIII-D and the design point (see Fig. 4). Therefore, while the confinement would be excellent for the ITER design, there is no gyro-Bohm scaling path to the point, since the threshold scaling predicts L mode at the design point. Presumably, the power required to continue the dimensionless scaling path would then follow the Goldston scaling of the threshold. There is evidence of this from recent JET data [5]. The larger p, discharges from JET lie along the gyr+Bohm path from DIII-D, but the smallest pa point tracks the threshold curve, giving Goldston scaling (see Fig. 4). Based on this interpretation, either the fusion powerplant must operate at the H mode threshold with relatively poor confinement or an ignition point must be found well on the H-mode side of the threshold. This suggests operation at higher 0 through more highly shaped tokamaks or, if necessary, actively controlled advanced tokamaks.

This is a report of work sponsored by the U.S. Department of Energy under Contract NO. DE-AC03-89ER51114.

References [l] Waltz RE, DeBoo JC and Rosenbluth MN, Phys. Rev. Lett. 65 2390 (1990) [2] Petty CC, Luce TC, et al., Phys. Rev. Lett. 74 1763 (1995); Luce TC, Petty CC,

[3] Petty CC, Luce TC, et al., Phys. Plasmas 2 2342 (1995) [4] Iter H-Mode Database Working Group, Proc. 21st EPS Cod. on Controlled Fusion

[5] Balet B, this conference

Physica Scripta

and Plasma Physics (1994), Vol I, p 334

GENERAL ATOMICS REPORT GA-22096 3

Luce U Petty

1.6

1- *

f 0.6-

: 0

10

n

- 1 Q

s

0.1 3

2

1

0

............................................ Goldston

.......................... ....... /-- - rurcLI) ............... ...................... gyro-Bohm

1 ’ 1 ‘ 1 . 1 .

0 0.6 1 r/a

EXPEFUMENTAL DETEFWENATION OF THE DIMENSIONLESS PARAMETER SCALLING OF ENERGY TRANSPORT IN TOKAMAKS

2

I= . 1

0 3

2

e* 1

0 0 0.5 1

r/a Fig. I : Dimensionless parametea for the higher-/3 L-mode discharges (soLid lines). The data for the H-mode discharge is shown for comparison (dashed line). The quantities an and a. the power to which a parabolic radial dependence must be raised to get the local scale length for denu-ty and shear, respectively.

1.0

U

0.0

-1.0 0.5 1.0 1.5 2.0

LJa Fig. 3: Exponent of p. scaling vezsus density scale length. Points are average values for p = 0.54.7. Bars are range of values not error.

Fig. 2: Ratio of Musivities for b h e r - f l L-mode discharges. The filled squares are the ion data, the filled cirdes are the elec- tron data, and the open triangles are the effective diihsivity data.

= DIII-D 10’

4 = JET

(3 e a ’‘1 1 0’

A = ITER

\ loo ! I 1 I I I I l l )

lo-’ loo

Fig. 4: Loss power versus p. for a p. scan. The appropriate “djmensionles” variables are plotted (constants with dimensions are not shown). The dashed line is 8 gvrczBohm extrapolation based on the DIII-D points only. The solid line is the H-mode threshold &om Ref: 4. The dotted line ir twice the power threshold.

GENERAL ATOMICS REPORT GA-22096 4