Ram, A.K.

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PFC/JA-94-18CURRENT DRIVE BY THE COMBINATIONOF LOWER HYBRID AND ICRF WAVESA. K. Ram, A. Bers,V. Fuchs, and S. D. SchultzJuly 1994Plasma Fusion CenterMassachusetts Institute of TechnologyCambridge, Massachusetts 02139 USAThis work was supported by DOE Grant No. DE-FG02-91ER-54109,by NSF Grant No. ECS-88-2475, and in part by the Magnetic Fu-sion Science Fellowship Program. The CCFM is supported in part byAtomic Energy of Canada Ltd., Hydro-Quebec, and Institut Nationalde la Recherche Scientifique. Reproduction, translation, publication,use and disposal, in whole or part, by or for the United States Gov-ernment is permitted.To be published in Proceedings of the 21st European Physical Society(EPS) Conference on Controlled Fusion and Plasma Physics, Mont-pellier, France, 27 June - 1 July 1994.1CURRENT DRIVE BY THE COMBINATIONOF LOWER HYBRID AND ICRF WAVESA. K. Ram, A. Bers,V. Fuchs, and S. D. SchultzTABLE OF CONTENTSProperties of the Diffusion Coefficient Along RaysOptimizing FAW Power Mode Converted to IBW'sAcknowledgements . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . .Figures . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 1. . . . . . . . . . . . . . . . 3. . . . . . . . . . . . . . . . 4. . . . . . . . . . . . . . . . 4. . . . . . . . . . . . . . . . 5iiCurrent Drive by the Combination of Lower Hybrid and ICRF WavesAbhay K. Ram', Abraham Bers', Vladimir Fuchs2 , and Steven D. Schultz''Plasma Fusion Center and Research Laboratory of Electronics,Massachusetts Institute of Technology, Cambridge, MA 02139 U.S.A.2 Centre Canadien de Fusion Magnetique, Varennes, Qu6bec, CanadaCurrent drive by radio frequency waves is expected to play an important role infuture tokamaks, e.g. TPX and ITER, where RF waves will be used to modify thecurrent profile and/or drive central current in a plasma. The best results, so far, forRF current drive, in tokamaks with electron temperatures less than 10 keV, havebeen achieved using lower hybrid waves (LHW). It has been shown, experimentallyand theoretically, that the LH current drive (CD) efficiency can be enhanced byusing other RF waves, e.g. waves in the electron cyclotron and ion cyclotron rangeof frequencies (ICRF). This is accomplished primarily by pushing the electrons inthe tail of the LH generated distribution function to higher momenta, where theybecome less collisional. In the case of ICRF waves, it has been found that mode-converted ion Bernstein waves (IBW) are more effective in pushing the electronsto higher momenta than the fast Alfvdn waves (FAW) since the IBW diffusioncoefficient is much larger than the FAW diffusion coefficient [1, 2]. This explains,for example, the enhanced LHCD efficiency observed in JET [3]. In LHCD JETexperiments, with a minority ion resonance near the plasma center, FAW's werelaunched primarily for plasma heating, thereby resulting in a low engineering CDefficiency. However, there exist scenarios where direct ion heating is minimizedand mode conversion to IBW's is maximized, and this can lead to a considerableimprovement in the engineering CD efficiency. Numerical integration of a one-dimensional full wave code have recently shown [4] that in TFTR mode conversionfrom FAW to IBW can be significant and lead to electron heating, as suggestedsometime ago [5, 6].In this paper we discuss two crucial aspects of newly proposed scenarios forenhancing the current drive efficiency: the propagation and quasilinear deposition ofIBW's, and maximizing the power mode converted to IBW's. We give an analyticalform for the maximum mode-converted power which can form a basis for exploringoptimized scenarios for the interaction of mode-converted IBW's with electrons.Properties of the Diffusion Coefficient Along RaysAssuming concentric circular flux surfaces, the flux-surface averaged, normal-ized, quasilinear diffusion coefficient for electrons is:(D) 1 P (1)47r2 rRoa D, 6rwhere r is the radius of the flux surface, RO is the major radius, D, = m2 v is thecollisional diffusion, me is the electron mass, Vt. = /Te/me is the electron thermalvelocity, v, is the electron-electron collision frequency, 6t is the time taken by a ray1to cross a flux surface of radial thickness 6r, P is the power (in Watts) in the ray,a (eow/4)(&Dij/,w)(E*E /IE 2), Dij is the plasma dispersion tensor, and:T2 c E, 1 k-L-L) vLJ ki vi 2Do Im Jo + (Ji2w lviii E 9 / W e v11  We+ {Re ( ) Jo (kv6 ni - (2)EY WCe oilw is the wave frequency, k1l, k1 are the wave vectors along and perpendicular to thetotal magnetic field, respectively, nil = ckli/w, c is the speed of light, vil and v1 arethe parallel and perpendicular components of the electron velocity, respectively, Eis the wave electric field, and oc is the electron cyclotron frequency. The right handside of (2) can be evaluated for a local solution of the plasma dispersion relation.The flux-surface averaged diffusion coefficient in (1) can then be determined alongthe appropriate ray trajectories.In Fig. 1 we show the poloidal projection of a FAW ray launched after modeconversion. The parameters are: Ro = 3m, toroidal magnetic field on axis =3.2T, plasma current = 1.5 MA, peak electron density = 2 x 1019 m-3, hydrogenminority (3% of the electron density) in a deuterium plasma, peak ion and electrontemperatures = 5 keV, and the frequency of ICRF and LH waves is 48 MHz and3.7 GHz, respectively. This ray propagates out to the edge where it gets reflectedback into the plasma. Upon reaching the mode-conversion region the FAW raymode converts to the IBW ray. The IBW ray stops when it is completely dampedonto the electrons. The damping is enhanced due to a toroidal upshift of Ikll I as theIBW propagates away from the mode-conversion region [6]. Fig. 2 shows (D) permegawatt of power along this ray trajectory. The regions corresponding to FAW andto IBW are indicated on the figure. The increase in the IBW diffusion coefficient,and the comparison with the FAW diffusion coefficient, as the ray propagates awayfrom the mode-conversion region is evident. For comparison, for one megawatt ofpower in a given ray, (D) ~ 102 for LHW's; (D) ~ 10-2 for FAW's, and (D) ~ 1for IBW's.In advanced tokamak scenarios where the plasma temperature is higher, theIBW's offer a distinct advantage provided there is an effective mode conversion fromFAW's to IBW's. Unlike LHW's, which will damp near the edge of the plasma,FAW's and IBW's can propagate into the central part of the plasma. In addition,the LHW's have an accessibility limit at low k1 's which prevents their direct, phase-resonant interaction, with the fastest (and, hence, least collisional) electrons nearc; the FAW's and IBW's do not have such a limit. However, in contrast to LHW'swhich damp strongly for W/(k 1 vte) ~ 3, IBW's damp strongly for w/(klivte) ~ 2while FAW's damp strongly for w/(klivie) ~ 1. Thus, the IBW's are interactingwith a less collisional part of the electron distribution function than FAW's. Inaddition the diffusion coefficient for IBW's is much larger than for FAW's. Thetoroidal upshift in Ikil I of the IBW's depends on the plasma current and the toroidalmagnetic field and is not sensitive to the plasma temperature. The upshift is largeover short distances of propagation so that the IBW's interact strongly with theelectron distribution in a region close to mode conversion.2Optimizing FAW Power Mode Converted to IBW'SThe approximate cold plasma dispersion relation for the FAW is:(L - n' )(R - n')77 = 111(3)S -nwhere n_ = ck /, and S, R, and L are the usual Stix tensor elements. Thedispersion relation gives two types of cutoffs for the FAW: the right-hand cutoffs(RHC) (R = n ), one of which is on the low-BT side (LFS), usually near the plasmaedge for good antenna coupling, and the other on the high-BT side (HFS) that canbe inside the plasma; and a left-hand cutoff (L = n ) which, in plasmas withtwo ion species, can be centrally located near the ion-ion hybrid resonance givenapproximately by S = n . The propagation of the FAW through the resonance andcutoff(s) is given by:d2EYdX2 . + Q(x) E, = 0 (4)where EY is the normalized (poloidal) component of the electric field, x is thenormalized spatial coordinate along the equatorial plane, and Q(x) is the potentialfunction [7], which for a cold plasma is equal to the right hand side of (3). In theabsence of cyclotron absorption and in the case when the HFS-RHC is ignored, thepotential function is approximated by the Budden potential: Q(x) = y - /x =(x - XL)/x, where -y and 0 characterize the left-hand cutoff XL. The scatteringresults are given by the well-known Budden coefficients. However, the Buddenpotential does not always adequately describe the propagation of the FAW since itignores the HFS-RHC. The transmitted FAW can reflect back into the plasma fromthis cutoff. By increasing kI and/or decreasing the density, the HFS cutoff moves incloser to the Budden resonance-cutoff pair forming a cutoff-resonance-cutoff triplet.The approximate, lossfree, potential function for this case is Q(x) = x + y -- 0/x =(X - xL)(x - XR)/x where XR is the HFS-RHC. For this potential function (4) canbe solved approximately for EY . We find that the resultant power mode conversioncoefficient is:C = 1 - R, where R = (1 - T)2 + T 2 + 2T (1 - T) cos (0+ 20) (5)is the power reflection coefficient, T = exp(-rg) is the Budden transmission, 7 =/ V,'T is the phase difference between the transmitted FAW and the FAW reflectedat the HFS cutoff, and 0 is the (coupling) phase of F(-i17 /2) where F is the Gammafunction. By choosing these phases such that 0+20 = m7r (m being any odd integer)we find that Rmin = (1 -2T) 2 and Cma, = 4T(1 -T). Thus, for T = 1/2, Rmin = 0and Cmax = 1, i.e. for these conditions the FAW is completely mode converted toIBW's. The phases 0 and 4 depend on the (HFC) right-hand and left-hand cutoffswhich, in turn, depend on the plasma parameters and k1j. Thus, by modifyingthese parameters, the location of the RHC can be changed in order to maximize themode conversion coefficient. For example, the HFS-RHC can move into the plasmaas kii is increased and/or the density is decreased; the LFS-RHC must be kept near3the plasma edge for good antenna coupling. We find that for different tokamakscenarios, using realistic potentials for Q(x) that account for finite Larmor radiuseffects and plasma profiles [7], mode-conversion coefficients very close to unity canbe obtained. Figure 3 gives some numerical examples.A simple physical picture of such strong (almost complete) absorption emergesby regarding the triplet Q(x) as a resonant system coupled to by the FAW incidentfrom the LFS. Complete absorption results when the incident FAW is criticallycoupled to the resonator formed by the cutoff-resonance-cutoff plasma system; theHFS right-hand cutoff adjusts the resonator, while the spacing between the left-hand cutoff and the resonance adjusts the coupling. This picture is borne out bythe calculations of R(k11) which exhibit the expected resonance behavior.This work was supported by DOE Grant No. DE-FG02-91ER-54109, by NSFGrant No. ECS-88-2475, and in part by the Magnetic Fusion Science FellowshipProgram. The CCFM is supported in part by Atomic Energy of Canada Ltd.,Hydro-Quebec, and Institut National de la Recherche Scientifique.REFERENCES1. A. K. Ram, A. Bers, and V. Fuchs, Proc. 20th EPS Conference on ControlledFusion and Plasma Physics, Lisboa, Portugal, Vol. III, p. 897 (1993).2. A. K. Ram, A. Bers, V. Fuchs, and R. W. Harvey, Proc. of the 10th TopicalConference on RF Power in Plasmas, Boston, MA, 1993, A.I.P. Conf. Proc.289, New York, p. 293 (1994).3. C. Gormezano, ibid., p. 87.4. R. Majeski et al., ibid., p. 401.5. F. W. Perkins, Nucl. Fusion 17, 1197 (1977).6. A.K. Ram and A. Bers, Phys. Fluids B3, 1059 (1991).7. C. N. Lashmore-Davies, V. Fuchs, G. Francis, A. K. Ram, A. Bers, and L.Gauthier, Phys. Fluids 31, 1614 (1988).4L0-4) 0e 803402--oo0a4'II.-)5LI I I I liii,,, I I I II II A .i~i I A III I ~ I~*I-II I 3 III -. I.'-40.10.1C,,0.10.1ho0'Io6v0:r--.1-I I I-D0:00C ) 4-.--Zo0E0-.0C)CC7

Current drive by the combination of lower hybrid and ICRF waves

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Current drive by the combination of lower hybrid and ICRF waves

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