Bers, A.

Cairns, R.A.

Davies, C.N.

Decker, J.

Efthimion, P.C.

Peysson, Y.

Ram, A.K.

Taylor, G.

DSpace@MIT

PSFC/JA-04-23Current Drive by Electron Bernstein Wavesin Spherical TokamaksJ. Decker, A. K. Ram, A. Bers,Y. Peysson,a C. N. Lashmore-Davies, R. A. Cairns,'G. Taylor," and P. C. EfthimiondJuly 2004Plasma Science and Fusion Center, Massachusetts Institute of TechnologyCambridge, MA 02139 U.S.A.a Commisariat A l'Energie Atomique (CEA), Centre d'1tudes de CadarcheF-13 108 St. Paul lez Durance, Franceb Culham Science Centre, United Kingdom Atomic Energy Authority (UKAEA)Abingdon, Oxon OX14 3DB United Kingdom'University of St. AndrewsFife KY16 9SS Scotlandd Princeton Plasma Physics LaboratoryPrinceton, NJ 08543 U.S.A.This work was supported by the U.S. Department of Energy, Grant No. DE-FG02-91ER-54109,by the U.S. Department of Energy jointly with the National Spherical Torus Experiment, GrantNo. DE-FG02-99ER-54521, and U.S. Department of Energy, Cooperative Grant No. DE-FC02-99ER-54512. Reproduction, translation, publication, use and disposal, in whole or in part, by orfor the United States government is permitted.To appear in Proceedings of the 31st European Physical Society (EPS) Conference on PlasmaPhysics, London, England, June 28-July 2, 2004.Current Drive by Electron Bernstein Waves in SphericalTokamaksJ. Decker, A. K. Ram, A. Bers, Y. Peyssona,C. N. Lashmore-Daviesb, R. A. Cairnsc, G. Taylord, and P. C. EfthimiondPlasma Science & Fusion Center, M.L T, Cambridge, MA 02139, U.S.A.a CEA Cadarache, F-13108 St. Paul lez Durance, Franceb Culham Science Center, Abington, Oxon. OX14 3DB, U.K.University of St. Andrews, St. Andrews, Fife KY16 9SS, U.K.d Princeton Plasma Physics Laboratory, Princeton, NJ 08543, U.S.A.IntroductionSpherical tori (ST) are tight aspect ratio machines (Ro/a ~ 1.5 in NSTX, whereRo is the major radius and a is the minor radius) that are attractive as fusion energydevices due to their accessibility to high-#3 regimes (0 = 2pop/Bo, where P is thevolume averaged pressure and B0 the plasma toroidal field on axis). Since STs areoverdense (Pce < wp, where w,, is the electron cyclotron frequency and wp, is theelectron plasma frequency), current drive (CD) using electron cyclotron (EC) wavesis difficult and inefficient, particularly near the outboard edge where trapping ofelectrons in the magnetic field is significant. However, it has been shown that, inthe EC range of frequencies, it is possible to externally excite electron Bernsteinwaves (EBW) by mode conversion (MC) at the outboard edge of a ST plasma [1]. Inaddition, EBWs can propagate in the plasma without density limits and are stronglydamped at any harmonic of the EC resonance [2]. Current drive by EBW has beenrecently demonstrated in toroidally confined fusion plasmas [3]. Using our kineticcode DKE [4], we solve the kinetic equation with Fokker-Planck (FP) collisions andquasilinear (QL) diffusion due to EBW. In addition, we account for the effects ofmagnetic trapping of electrons, which are important in ST. We show that large currentdensities can be driven in high-Q regimes of ST, and that off-axis current is primarilydriven by the Ohkawa [5] mechanism while near-axis current is driven by the Fisch-Boozer [6] mechanism.Modeling of CD by EBWIn this study, we do not investigate the problem of EBW excitation and propa-gation, which requires a modeling of the MC and also ray-tracing calculations [1, 2].Instead, we concentrate on the EC resonance (ECR) region. Because of the strong,complete absorption of the EBW power at the Doppler-shifted ECR, the width of the1radial power deposition profile is typically very narrow compared to the equilibriumscale lengths in the plasma. As a consequence, it is reasonable to assume the paral-lel index of refraction N11 to remain constant across the deposition region, where, inaddition, the propagation path is assumed to be locally straight. Consequently, inour simulations, the EBW beam is modeled by a single, straight ray with a Gaussianparallel spectrum centered around a constant kii, and is assumed to be well focused,meaning that the poloidal extent of the beam satisfies A0 b < 27r. The ray is thencharacterized by a parallel spectrum width Akji ~ 1/ (rA6b). In addition, we assumea circular cross-section plasma.Given the plasma equilibrium and the kl spectrum of the wave, we calculate k1and the wave polarization and power flow by solving the wave equation, using ourfully relativistic dispersion solver R2D2 [7].We use these wave properties to evaluate the EBW QL diffusion coefficient and cal-culate the steady-state FP Equation with QL diffusion. The electron guiding-centerdrift velocities across flux-surfaces are generally small compared to the streamingvelocities along the field lines, and can be neglected in first approximation. In addi-tion, for the equilibrium under consideration, we are in the low-collisionality (banana)regime in which the bounce time of trapped electrons is much shorter than the colli-sional detrapping time. As a consequence, the distribution function is uniform alongthe field lines, and can be obtained by solving the 2D momentum space (P1,1 p-)bounce-averaged FP equation {C (f) + Q (f)} = 0. We solve the FP equation usingthe code DKE and calculate the distribution function. Taking moments of the dis-tribution, we calculate the flux-surface averaged current density (J) and density ofpower absorbed (P). From these moments we calculate the local normalized figure-of-merit 17 = (J/enevT,)/(P/nemev v), where n, is the electron density, v, is thee-e collision frequency and VT, = /rTe/m6 is the thermal velocity.Kinetic Calculations of Ohkawa EBWCD in NSTXIn order to study EBWCD in a realistic ST scenario, we consider a typical NSTXplasma, with the following NSTX-type parameters: RO = 0.9 m, a = 0.6 m, BO = 0.35T, Io = 0.8 MA, TeO = 3.0 keV, neo = 3.0 x 1019 M 3 . In this high-3 regime, thepoloidal magnetic field off-axis becomes comparable to the toroidal magnetic field,which creates a dip in the total magnetic field profile, as shown in Figure 1, wherewe plot the Doppler-shifted second harmonic of the cyclotron frequency. We choosea frequency between the first and the 2nd harmonic on the LFS, w/27 = 12 GHz,which is shown as a red line in Fig. 1. The value N11 = 1.5 is chosen because it isthe one for which we find the largest driven current. It is interesting to note that the220N4-1510500 0.5P1Figure 1: Frequency versus minor radius: EBW (red), 2fce (blue), and Doppler-shiftedfor N11 =1.5 (green).maximum CD is obtained for a value of N11 such that the EBW frequency is tangentto the profile of Doppler-shifted 2nd harmonic cyclotron frequency. This result canbe explained by the fact that in the present optimized case, the magnetic field profileis locally flat, meaning that the optical depth in very large. As a consequence, thepower is deposited on energetic electrons far in the tail, which leads to larger CDefficiencies. The non-monotonic magnetic field profile has therefore important andpositive implications for EBWCD in STs. The driven current density profile is shown0.8 1100.6EZ 0.4, .2r8.3 0.4 0.5 0.6P842Figure 2: Driven current density (red) and figure of merit (blue) versus minor radius.in Figure 2. It is centered around the peak value Ppeak = 0.53. We also show thefigure of merit 77. In this case, a total beam power of Pinc = 1MW is absorbed, and32fce2f 3.5kvfwa total current of I = 87 kA is driven.101A0 0 10P//PTeFigure 3: Top: Distribution function in EBWCD (red) and EBW QL diffusion coeffi-cient (green). The unperturbed Maxwellian is in black. Bottom: Parallel distributionfunction.In general, EBW are mostly electrostatic waves and therefore NJ > 1. In thepresent case, we have N1 = 12 at p = preak. As a consequence, finite Larmor radius(FLR) effects are significant, and the QL diffusion coefficient, shown as green linesin momentum space in Figure 3 (top), has several peaks in the p direction. In thisfigure are also plotted the unperturbed Maxwellian and the steady-state distributionfunction in EBWCD. The region of maximum diffusion is situated very near thetrapped/passing boundary, and, since the diffusion is mostly in the perpendiculardirection, a large EBW-induced trapping takes place. As a consequence, a largeOhkawa current is driven. This current is more easily visualized on the "parallel"distribution function, obtained by integration over pIF11 (p11) = 27rj p1 dp1 f (pI,p±) (1)The depletion of electrons due to wave-induced trapping on the resonant side, andthe accumulation of electrons due to detrapping on the opposite side, both contributeto driving a large Ohkawa current.4ConclusionWe have shown that a large Ohkawa EBW current could be driven off-axis (p >0.5) in ST plasmas. The Ohkawa effect is dominant because of (1) the large fractionof trapped particles, (2) the dominantly perpendicular QL diffusion, and (3) thelarge FLR effects which allow a positioning of the diffusion region right near thetrapped/passing boundary in momentum space. The large figure of merit is due tothe very strong damping of the EBW, so that most of the power is deposited on veryenergetic, weakly collisional electrons. This effect can be enhanced, and the figure-of-merit improved, by locally flat magnetic field profiles in high-f ST. The resulting CDefficiency turns out to be several times larger than for typical off-axis (Fisch-Boozer)ECCD efficiencies in tokamaks.Work supported by U.S. DoE Grants DE-FG02-91ER-54109 and DE-FG02-99ER-54521, and U.S. DoE Cooperative Grant DE-FC02-99ER-54512.References[1] J. Preinhaelter and V. Kopecky, J. Plasma Phys. 10, 1 (1973); A. Bers et al., inProc. 2nd Europhysics Topical Conf. on RF Heating and Current Drive, Brussels,pp. 237-240 (1998); A. K. Ram et al., Phys. Plasmas 9, 409 (2002).[2] A. K. Ram and S. D. Schultz, Phys. Plasmas 7, 4084 (2000).[3] V. Shevchenko et al., Phys. Rev. Lett. 89, 2650054 (2002).[4] J. Decker et al., in Proc. 12th EC Conf., Aix-en-Provence, France, pp. 113-118(2002).[5] T. Ohkawa, General Atomic Report No. 4356.007.001 (1976).[6] N. J. Fisch and A. Boozer, Phys. Rev. Lett. 45, 720 (1980).[7] A. K. Ram et al., in Proc. 15th Topical Conf. on RF Power in Plasmas, AIPConf. Proc. 694, pp. 392-395 (2003).5

Current Drive by Electron Bernstein Waves in Spherical Tokamaks

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Current Drive by Electron Bernstein Waves in Spherical Tokamaks

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