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NONDIMENSIONAL TRANSPORT SCALING in Dlll-D: BOHM VERSUS GYRO-BOHM RESOLVED GA-A21904 NONDIMENSIONAL TRANSPORT SCALING IN Dlll-D: BOHM VERSUS GYRO-BOHM RESOLVED by C.C. PETTY, T.C. LUCE, K.H. BURRELL, S.C. CHIU, J.S. deGRASSIE, C.B. FOREST, P. GOHIL, CM. GREENFIELD, R.J. GROEBNER, R.W. HARVEY, R.I. PINSKER, R. PRATER, R.E. WALTZ, R.A. JAMES,* and D. WROBLEWSKI* This is a preprint of an invited paper presented at the 1994 American Physical Society Division of Plasma Physics Meeting, November 7-11,1994, Minneapolis, Minnesota, and to be printed in the Proceedings. Work supported by U.S. Department of Energy under Contracts DE-AC03-89ER51114 and W-7405-ENG-48 *Lawrence Livermore National Laboratory GENERAL ATOMICS PROJECT 3466 FEBRUARY 1995 ASTER DISTRIBUTION QE IHIS DACUlvlENT IS UNIJ^O Ul ' ' *|* GENERAL ATOMICS 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, 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. DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. (-^ is l ?-"~ / / ' ~s J y / NOMDIMENSIONAL TRANSPORT SCALING IN DIII-D: Petty et al. BOHM VERSUS GYRO-BOHM RESOLVED Nondimensional transport scaling in Dili—D: Bohm versus gyro-Bohm resolved* C.C. PETTY,* T.C. LUCE, K.H. BURRELL, S.C. Cmu, J.S. DEGRASSIE, C.B. FOREST, P. GOHIL, CM. GREENFIELD, R.J. GROEBNER, R.W. HARVEY, R.I. PINSKER, R. PRATER, and R.E. WALTZ General Atomics San Diego, California 92186-9784, U.S.A. R.A. JAMES and D. WROBLEWSKI°) Lawrence Livermore National Laboratory Livermore, California 94550, U.S.A. Abstract The scaling of cross-field heat transport with relative gyroradius />„, was mea• sured in low (L) and high (H) mode tokamak plasmas using the technique of dimen- sionally similar discharges. The relative gyroradius scalings of the electron and ion thermal diffusivities were determined separately using a two-fluid transport analysis. 1 0 3 For L-mode plasmas, the electron diffusivity scaled as %e ex XBP*' ^ ' (gyro-Bohm- 0 S±0 3 like) while the ion diffusivity scaled as %; oc XBP7 ' ' (worse than Bohm-like). The results were independent of the method of auxiliary heating (radiofrequency or neutral beam). Since the electron and ion fluids had different gyroradius scalings, the effective diffusivity and global confinement time scalings were found to vary from gyro-B ohm• like to Bohm-like depending upon whether the electron or ion channel dominated the heat flux. This last property can explain the previously disparate results with dimensionally similar discharges on different fusion experiments that have been pub• lished. Experiments in H-mode were also done with the expected values of beta, collisionality, safety factor, and plasma shape for thermonuclear ignition experiments. For these dimensionally similar discharges, both the electron and ion diffusivities scaled gyro-Bohm-like, XeiXi ^ XBP*I as ^d the global thermal confinement time. This leads to a very favorable prediction for the confinement time of future ignition devices. *Paper 3D33, Bull. Am. Phys. Soc. 39, 1577 (1994). t Invited speaker. "'Present address: Maxwell Laboratories, San Diego, California. GENERAL ATOMICS REPORT GA-A21904 NONDIMENSIONAL TRANSPORT SCALING IN DHI-D: Petty et al. BOHM VERSUS GYRO-BOHM RESOLVED CONTENTS Abstract iii I. Introduction 1 II. Experimental Setup 5 III. Two-Fluid Analysis of L-Mode 7 IV. Two-Fluid Analysis of ITER-Relevant H-Mode 15 V. Summary and Conclusions 21 VI. Acknowledgements 23 VII. References 25 Figures 1. Radial profiles for case (a) of Table I 9 2. Radial profiles for case (b) of Table I 10 3. Radial profiles for case (c) of Table I 11 4. Measured value of the exponent xp from Eq. (2) for case (a) of Table I ... 12 5. Measured value of the exponent xp from Eq. (2) for case (b) of Table I ... 13 6. Measured value of the exponent xp from Eq. (2) for case (c) of Table I ... 14 7. Radial profiles of H-mode discharges 17 8. Measured value of the exponent xp from Eq. (2) for H-mode discharges ... 18 Tables I. Engineering parameters for three pairs of L—mode dimensionally similar discharges 8 II. Engineering parameters for H—mode dimensionally similar discharges on DIII-D and projection to ITER 16 GENERAL ATOMICS REPORT GA-A21904 V NONDIMENSIONAL TRANSPORT SCALING IN DIII-D: Petty et al. BOHM VEEISUS GYRO-BOHM RESOLVED I. INTRODUCTION Although it is widely believed that some form of plasma turbulence is respon• sible for the anomalous cross-field diffusion of heat in tokamaks and stellaxators, the specific nature is still unknown despite much experimental effort. Historically, anomalous heat transport has been studied by systematically varying the engineering parameters such as the plasma current J, magnetic field strength B, plasma density n, and heating power Ptot- Recently there has been a growing interest in measuring the scaling of confinement with the nondimensional parameters (for comparison with theoretical scalings1) such as safety factor q ~ Ba/I, beta ft ~ nT/B2, collisionality 2 vm <N/ qna/T , and relative gyroradius pm = r-^/a (in these relations, T is the plasma temperature, a is the plasma minor radius, and rL is the Larmor radius). Plasmas which have identical values for all nondimensional parameters of interest except /)„ are referred to as being "dimensionally similar." Of particular interest is the scaling of anomalous heat transport with p+, since the confinement results of existing fusion experiments can be scaled to ignition devices of larger size and magnetic field by keeping all the nondimensional parameters fixed except for the relative gyroradius.1 A basic assumption of nondimensional scaling experiments is that transport is dependent only upon local quantities. Thus, following the scale invariance approach to confinement scaling,2'3 the thermal diffusivity x ca& be written as p -Z-=P: F(q,0,vm,Te/Ti,an,aT,.-.) , (1) XB — ffl2 7,2 , where %B = cTe/eB is the Bohm diffusion coefficient and O^T = ( ~ )/2T £I1)T (Ln,T is the density or temperature scale length). Comparing the diffusivities for dimensionally similar discharges with different values of pm allows the exponent xp to be determined since the unspecified function F remains constant. In order to keep /3, i/#, and q fixed while varying the magnetic field strength and minor radius, the engineering parameters need to be scaled as n oc i?4/3a-1/3, T oc 52/3a1/3, and I oc Ba while keeping the magnetic geometry fixed. The scaling of the thermal diffusivity for dimensionally similar discharges therefore has the form GENERAL ATOMICS REPORT GA-A21904 1 NONDIMENSIONAL TRANSPORT SCALING IN DHI-D: BOHM VERSUS GYRO-BOHM RESOLVED Petty et al. 1+2l 3 2 5 6 Xa5^ ^/ a< - ^/ . (2) The value of the exponent xp could be interpreted as indicating the characteristic wavelength A of the plasma turbulence responsible for anomalous heat transport: (a) xp = 1 would imply A ~ T^, which is called gyro-Bohm-like, (b) xp = 0 would imply A ~ a, which is called Bohm-like, and (c) xp = —1 would imply A » a, which could arise from having stochastic magnetic fields throughout the plasma. Theoretical work to explain anomalous transport has concentrated on turbulence with characteristic wavelengths of A ~ T%. Disparate results for the pm scaling of the effective diffusivity (the weighted average of the electron and ion diffusivities) have previously been reported in low (L) mode experiments. In stellarators, dimensionally similar discharge experiments using electron cyclotron heating (ECH) found that the confinement scaling was gyro-Bohm- like4; the same conclusion was reached in the DIII-D tokamak5 for radiofrequency (RP) heating experiments of low density plasmas.6 However, other tokamak exper• iments using neutral beam injection (NBI) heating or ion cyclotron heating (ICH) showed that the effective diffusivity followed Bohm-like scaling.7'8 Experiments with NBI heating of high density plasmas in Dili—D could be fit with either gyro-Bohm- like or Bohm-like models.9 The radial power flow was dominated by the electron channel (due to direct electron heating) for the experiments which reported gyro- Bohm-like scaling, whereas the radial power flow in the ion channel was significant for the experiments which reported Bohm-like scaling; therefore, one may wonder if the conflicting pt scaling results may be due to different transport scalings for the electrons and ions. A key component in the transport analysis of the dimensionally similar discharge experiments discussed in this paper is the separation of the electron and ion fluids. The rest of this paper is organized as follows: Section II describes the Dili—D tokamak, auxiliary heating systems, and plasma diagnostics used in these transport experiments. In Section III, the scalings of the electron and ion thermal diffusivities with relative gyroradius for L—mode plasmas are shown, the results of which have been previously reported.10 In Section IV, dimensionally similar discharges are analyzed for high (H) mode plasmas which match the expected values of /3, v*, q, and plasma shape for the International Thermonuclear Experimental Reactor11 (ITER).
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