Bers, A.

Ram, A.K.

Schultz, S.D.

DSpace@MIT

MODE-CONVERTED ELECTRON BERNSTEIN WAVES FOR HEATINGAND CURRENT DRIVE IN NSTXS.D. SCHULTZ, A.K. RAM, A. BERSPlasma Science and Fusion CenterMassachusetts Institute of TechnologyCambridge, MA, USA 02139AbstractThe power coupled to electron Bernstein waves in a triplet mode conversion resonator from a fast X-mode atthe plasma edge in NSTX is shown to be > 80% for fc, < f < 2fc,. The EBW damping in the plasma is strongand localized and, thus, should be useful for heating, current drive, or profile control.1. INTRODUCTIONThe excitation and localized damping of electron Bernstein waves (EBW) in toroidally confinedplasmas presents the possibility of efficient means for plasma heating, current drive, and currentprofile control with external power in the electron cyclotron range of frequencies (ECRF). Suchuse of EBW is particularly interesting for high-a plasmas at low magnetic fields (e.g., MAST,NSTX) in which the usual heating by O-mode excitation and propagation into the plasma canonly be assured for frequencies at very high harmonics of the electron cyclotron frequency wheredamping is rather weak. A new aspect for wave coupling and propagation in these high-0 plasmasis that their equilibria entail poloidal magnetic fields that are not negligible compared to toroidalfields as is the case in most low-,a tokamaks.In principle, excitation of EBW's is possible by mode conversion from externally launchedelectromagnectic power in 0-mode, X-mode, or mixed O/X-mode polarizations [1-6]. For high-f,spherical-type tokamaks (NSTX, in particular) we have recently proposed a scenario for fast-X toEBW mode conversion that shows promise of high mode-conversion efficiency over a broad rangeof frequencies in the vicinities of the fundamental and second harmonic of the electron cyclotronfrequency [7,8]. For the low magnetic field of such high-fl plasmas this falls in a frequency regimein which high-power cw sources are readily available. Furthermore, for these frequencies andmoderate nl we find effective and localized damping of the generated EBW's in the vicinity ofthe Doppler-shifted electron cyclotron resonance. This type of fast-X to EBW mode conversion(which has been independently considered in [5] but not dealt with in detail) is based upon settingup at the plasma edge a mode conversion resonator, with the mode conversion to a propagatingEBW as an effective "dissipation" in this resonator. In this paper we present the results of fast-Xto EBW mode conversion for NSTX, compare it to the O-X-EBW mode conversion process, andillustrate the propagation and damping of the EBW's.2. THE TRIPLET MODE CONVERSION RESONATOR IN ECRFFigure 1 shows the spatial distribution of various critical frequencies in propagation across thetoroidal and poloidal magnetic fields, calculated along the major radius of the equatorial planefor an NSTX equilibrium [9]. As can be appreciated from the simplest cold plasma dispersion [7]and Figure 1, at low electron cyclotron harmonics a fast X-mode launched from the outboard willencounter a right (R) cutoff in close proximity to the upper-hybrid resonance (UHR), followedby a slow X-mode which connects back to the UHR (and kinetically, to the EBW) and continuesto the left (L) cutoff. This combination of R-cutoff/UHR followed by the L-cutoff forms a tripletresonator containing the mode conversion "dissipation", which, in a cold plasma description isresonant absorption at the UHR, and in a kinetic description is energy flow in the EBW. Sucha triplet mode conversion resonator can achieve 100% mode conversion from X to EBW. Thecritical parameters for achieving this follow from a simplified (neglecting variations in magneticfields and n1) cold-plasma full-wave analysis expanded in the vicinity of the UHR, and solutionof the associated differential equation for the X-mode electric field.120 -UHRf (GHz) R-CUTOFF40 -L-CUTOFFO-CUTOFF30-20- ----------------100 5 10 15 20 25 30 35 40x (cm)Figure 1: Location of critical frequencies as a function of minor radius along the equatorial plane, as calculated forNSTX parameters [9].The results, which can be carried over from our previous analysis of a triplet resonator modeconversion from fast Alfv6n waves to ion-Bernstein waves [10], give a power mode conversioncoefficientC = 4e-"(1 - e-"7) sin 2  +) (1)where the Budden-parameter 77 is found to be [7]= ce(X = XUH) L ; L. = dnnO(X) (2)v'2 c dx X=XUH0 = phase of the gamma function 1(-i77/2), and # is the phase difference between the slowX-mode propagating toward the L-cutoff and the reflected component propagating toward theUHR. Equation (1) shows that 100% mode conversion (C = 1) is possible for q = 0.22, and(0 + 0/2) = .r/2. To acheive near optimal mode conversion for NSTX one finds from (1), (2)and Figure 1 the need for setting up the triplet mode conversion in the density gradient near theplasma edge, and in the frequency range near 2f,.A full-wave cold plasma slab code, for arbitrary n, and ny, similar to what was used in [4]but including the full description of both toroidal and poloidal magnetic field variations, gives themode conversion as a function of frequency, for both n, = 0 and n, = 0.1, as shown in Figure 2.We observe that high mode conversion efficiencies (> 80%) are obtained over a broad range offrequencies of about 4 GHz around the peak in C ~ 0.97 at f = 16 GHz. Furthermore, introducinga change in the edge-density by 5% shifts the peak by about 1 GHz, but does not change its peakvalue or shape. We thus conclude that this X-EBW triplet mode conversion for NSTX is bothvery efficient and quite robust. The optimal parameters based upon (1) and (2) are essentiallyverified by the full-wave code results.We have also generated and run an approximate full-wave kinetic code that removes the coldplasma resonance absorption at the UHR and describes the mode conversion as energy flow(electromagnetic and kinetic) onto the EBW [8]. The results are also shown in Figure 2 andare observed to be close to those based upon the full-wave cold-plasma description; however,the kinetic code gives the correct energy flow description, particularly in the transition of theupper-hybrid frequency from below to above the second electron cyclotron harmonic.2x0.9 - -.- - - - -'0.8-X0.7 -C0.3 --b0.5 - -0.4 - (a)-x0.3 - - - - - - -(b)X0.2. X X X X X (c)0.1 -0113 14 15 16 17 18 19 20 21f (GHz)Figure 2: Mode conversion of fast X-mode to EBW as a function of frequency in a plasma with NSTX parameters[9] from full-wave calculations [8] using (a) a cold-plasma model with n, = 0, (b) a cold-plasma model withn. = 0.1, and (c) an approximate kinetic model with q, = 0.3. COMPARISIONS OF O-X-B AND X-B MODE CONVERSIONAs in Ref. [4], we can also integrate the cold-plasma equations to derive a mode-conversioncoefficient for O-X-B mode conversion. Figure 3 shows the resonant absorption mode conversionof an O-mode launched into a plasma with the same NSTX parameters as in Section 2. In each case,we observe that the mode conversion fraction peaks at the optimal value of n, n = ce/(w+wce)[1]. The peak in mode conversion increases with frequency, but significant mode conversion isthen achieved only over a narrow range in n,. We remark that although it is possible to obtainfull mode conversion from the O-mode to the slow X-mode (albeit at a substantial nz,op) thesubsequent conversion of this slow X-mode to EBW is at most (1 - T), where T is the Buddentunneling factor T = exp (-7rq), with r7 given by (2). Thus high mode conversion for O-X-Brequires T < 1. At high frequencies (28GHz) the confluence of the O-mode and L cutoffs at n2,4,2is farther into the plasma where density gradients are weaker and T is negligible; however, asn. deviates from no,, the separation between the 0 and L cutoffs increases rapidly, drasticallyreducing O-mode to slow X-mode conversion. For the low frequency case (14GHz), we see thateven at n,Op only ~ 40% mode conversion is possible, since the confluence point is closer to theedge where the higher density gradients mean T is not negligible, and our calculations show thatmost of the reflected power leaves the plasma on the fast X-mode. Hence we conclude that at14GHz, the tunneling of the X-mode is more advantageous to the triplet mode conversion of thefast X-mode to the EBW, as shown in Section 2.4. PROPAGATION AND DAMPING OF THE MODE-CONVERTED EBWBeyond mode conversion, the location of the damping of the EBW must be determined byray tracing. The poloidal magnetic field leads to changes in the poloidal mode numbers of theEBW and, subsequently, a change in kl [11]. With these changes it is possible for EBWs toLandau damp on electrons in a region which is not near the electron cyclotron resonance or itsharmonic. Using a non-relativistic, hot Maxwellian plasma ray tracing code [11] we have carriedout preliminary studies of the propagation of mode-converted EBWs launched at the equatorialplane in plasmas similar to high-,a scenarios of NSTX. We find that the EBW propagate away fromthe mode-conversion region towards the center of the plasma and damp near the Doppler-shiftedelectron cyclotron resonance. In the poloidal plane the EBWs remain close to the equatorial planeand even though there are significant changes in kil along the EBWs, there is no electron Landaudamping prior to the encounter with the position of the Doppler-shifted cyclotron resonance.30.9 - (a)/ \0.8 (b)0.7- -- * (C)0.6 -0.5 -0.4-0.30.2-01'0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1nzFigure 3: Mode conversion of 0-mode to EBW (0-X-B conversion) as a function of n, at (a) f = 14GHz, (b)f = 21GHz, and (c) f = 28GHz, in a plasma with NSTX parameters [9] from cold-plasma full-wave calculations.5. ACKNOWLEDGEMENTS .Work supported by DoE Contract DE-FG02-91ER-54109 and by NSTX.References[1] PREINHAELTER, J., KOPECKY, V., J. Plas. Phys., 10 (1973) 1.[2] WEITZNER, H., BATCHELOR, D.B., Phys. Fluids, 22 (1979) 1355.[3] NAKAJIMA, S., ABE, H., Phys. Lett. A, 124 (1987) 295.[4] HANSEN, F.R., LYNOV, J.P., MARDI, C., PETRILLO, V., J. Plas. Phys., 39 (1988) 319.[5] NAKAJIMA, S., ABE, H., Phys. Rev. A, 38 (1988) 4373.[6] LAQUA, H.P., ERKMANN, V., HARTFUSS, H.J., LAQUA, H., Phys. Rev. Lett., 78 (1997)3467.[7] WU, K.C., RAM, A.K., BERS, A., SCHULTZ, S.D., in Proceedings of the 12th TopicalConference on RF Power in Plasmas, eds. P. M. Ryan and T. Intrator, AIP Conf. Proc. 403, AIP,New York (1997) pp. 207-210.[8] BERS, A., RAM, A.K., SCHULTZ, S.D., in Proceedings of the 2nd Europhysics TopicalConference on RF Heating and Current Drive in Plasmas, Brussels, Belgium, eds. J. Jacquinot,G. Van Oost, and R. R. Weynants, EPS Conf. Abs. Volume 22A, Brussels (1998) pp. 237-240.[9] Courtesy R. MAJESKI, PPPL, USA.NSTX: R = 1.05m; a = 0.44m; neo = nE + (no - nE)(l -- 2/a 2 )1/ 2 ; n = 3 x1019/M3BT and Bp fit to profiles. Teo = TE + (To - TE)(I - X2 /a2 )2 ; T0 = 3keV; (nE, TE) = 0-02 (no, TO).[10] RAM, A.K., BERS, A., SCHULTZ, S.D., FUCHS, V., Phys. Plas., 3 (1996) 1976.[11] RAM, A.K., BERS, A., Phys. Fluids B 3 (1991) 1059.4

Mode-converted electron Bernstein waves for heating and current drive in NSTX

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Mode-converted electron Bernstein waves for heating and current drive in NSTX

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