Bonoli, P.

Cool, S.

Dermott, F.S.

Fiore, C.

Knowlton, S.

Porkolab, M.

Takase, Y.

Terry, J.L.

Texter, S.

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PFC/JA-86-4Energy Confinement ofLower Hybrid Current Driven Tokamak PlasmasKnowlton S.; Porkolab M.; Takase Y.; Texter S.;Bonoli P.; Fiore C.; McCool S.; McDermott F.S.;Terry J.L.February 1986Plasma Fusion CenterMassachusetts Institute of TechnologyCambridge, MA 02139 USASubmitted for publication in: Physical Review LettersThis work was supported by the U.S. Department of Energy ContractNo. DE-AC02-78ET51013. Reproduction, translation, publication, useand disposal, in whole or in part by or for the United States govern-ment is permitted.By acceptance of this article, the publisher and/or recipient ac-knowledges the U.S. Government's right to retain a non-exclusive,royalty-free license in and to any copyright covering this paper.Energy Confinement of Lower Hybrid Current DrivenTokamak PlasmasS. Knowlton, M. Porkolab, Y. Takase, S. Texter, P. Bonoli,C. Fiore, S. McCool,() F.S. McDermott, and J.L. TerryPlasma Fusion Center, Massachusetts Institute of Technology,Cambridge, Massachusetts 02139(ReceivedABSTRACTThe energy content of high density purely lower hybrid current-driven plas-mas has been measured under a variety of operating conditions on the Alcator Ctokamak. The energy stored in the current-carrying electron tail can be a largefraction of the total kinetic energy in an rf-driven plasma, while the energy residingin the bulk plasma is comparable to that of a similar ohmic discharge. At densitiesiie < 3 x 1013 cm- 3 , the global confinement time of the rf-driven plasma is similarto that of an ohmic plasma, but degrades relative to its ohmic counterpart at higherdensities and/or rf powers.PACS numbers: 52.50.Gj, 52.35.Hr, 52.55.Fa, 52.55.Pi1Tokamak plasma currents sustained completely by lower hybrid rf current drivehave been achieved in a number of experiments.' Experimental findings have sup-ported the basic predictions of the Fisch theory:2 the rf-driven current is carried bya superthermal electron tail in the distribution function, and the rf power requiredto maintain this tail current is proportional to the density and plasma current. OnAlcator C, an empirical current drive efficiency, defined as 7 = eIPRo/Prf (10 20 m-2MA/MW), of 77 =0.12 has been measured for densities up to -ne= 1x1014 cm-3. 3Here, ii is the line-averaged electron density, I, is the plasma current, R, is theplasma major radius, and Prf is the net injected rf power. The density scaling ofthe current drive efficiency is in agreement with the theoretical supposition that themajor loss of the superthermal electrons is due to collisions with bulk electrons; i.e.that tail energy is transformed primarily into plasma thermal energy. Regardingthe overall energy confinement properties of such plasmas, it is important to notethat rf current-driven plasmas represent auxiliary-heated discharges in which theplasma is maintained and heated entirely by non-ohmic power. In this Letter, wepresent measurements of the energy content and global energy confinement timesof rf-driven plasmas and compare them with measurements in similar ohmic plas-mas. Energy confinement studies of lower hybrid current-driven discharges at lowdensities (ie < 1013 cm~3 ) have also been reported recently from the PETULA-B4 and ASDEX 5 tokamaks. In the present study however, experiments have beenperformed in a reactor-relevant regime at densities up to ie = 8 x 1013 cm~3The confinement experiments were performed on the Alcator C tokamak (R,=64 cm., a=16.5 cm.) in the parameter range ,e=2-8x 1013 cm-3, B=7-11 T,I,=100-200 kA, q(a)>8, Zeff=1.5-2, Prf < 1.0 MW at f = 4.6 GHz in hydrogendischarges with molybdenum limiters. Electron temperature profiles were measuredwith a five-channel Thomson scattering system and the central ion temperature was2determined by charge-exchange analysis. Plasmas of constant current were main-tained by injection of sufficient rf power into ohmically-created target plasmas;during the rf current-drive phase, no current flowed in the ohmic primary circuitand the loop voltage was reduced to zero. Following temperature measurements onrf-driven plasmas, conventional ohmic discharges of identical current and densitywere studied in order to make comparisons under as similar conditions as possible.The results of a typical comparison are shown in Fig. 1. The evolution of thecurrent, loop voltage, density, central electron temperature, and equilibrium quan-tity Op + 4i/2 are illustrated for both an rf current-driven and an ohmic discharge.For the rf-driven plasma, the loop voltage is zero, Ip = 135 kA, iie = 4 x 1013 cm- 3 ,and the rf power is 460 kW; for the corresponding ohmic discharge, the ohmic poweris 200 kW. Within experimental error, the central electron temperatures of boththe ohmic and rf-driven plasmas are the same, and the electron temperature pro-file widths are also very similar; consequently the thermal energy content of bothdischarges (Wbulk(rf) -Wbulk (oh) =1.4 kJ) are nearly identical. The observed in-crease of /3, + 4/2 in the rf-driven plasma relative to that of the ohmic plasma isattributed to the kinetic energy stored in the current-carrying superthermal elec-tron tail of the former. This conclusion is supported by measurements of the plasmahard X-ray emission spectrum (E,=30-500 keV) performed with an eight-channelvertically-viewing array and a five-channel array which views the plasma at differentangles with respect to the toroidal field.' Using the techniques of Ref. 7, we havemodelled the two dimensional shape of the fast electron distribution function fromX-ray measurements taken at a density of i, = 3 x 1013 cm-3 and a current of I, =140 kA. Since the loop voltage is zero, it is reasonable to assume that the entireplasma current is carried by the electron tail; therefore the macroscopic parametersof the tail can be calculated.7 In particular, the fractional density of the tail relative3to the bulk is 0.7% and the energy moment over the tail distribution gives a valueof 1.4± 0.3 kJ, with the estimated error arising primarily from the ambiguity in themodelling of the fast electron distribution.The variation of 3, with density is shown in Fig. 2 for plasma currents ofI, ~140 kA and a toroidal magnetic field of B=8 T. The triangles at the bottom ofthe graph represent the values of 3, calculated from kinetic measurements of thebulk plasma. Up to a density of ii = 6 x 1013 cm- 3, the bulk stored energy of theohmic and rf-driven plasmas is similar, while at higher densities some additionalheating of the bulk plasma is occurring in the rf-driven case. Over the range ofdensities illustrated in the figure, the input power to the ohmic discharges remainedat Poh ~200 kW. To perform the density scan for the purely rf-driven plasmas, the rfpower was raised from Prf r=200 kW at , 1.5x 1013 cm-3 to Pf =950 kW at ne=8 x 1013 cm- 3 in order to keep the current constant. The data points at the top of thegraph indicate the measurements of 3, + 1i/2 from the equilibrium measurements.Though the absolute level of the magnetic 3, + 4/2 measurement is too low (basedon the kinetic measurements) due to baseline errors, comparisons of relative valuesremain valid. We note that the measured , + li/2 in rf-driven plasmas is alwayshigher than in their ohmic counterparts. For the case in which the tail was measuredby hard X-ray spectrometry (Hi, ~ 3 x 1013 cm- 3 ), the difference in 0p,, +li/ 2 betweenthe ohmic and rf-driven cases is approximately 0.18, which corresponds to Wail0.9 kJ. In deducing this value, the equilibrium field measurement was corrected forthe pressure anisotropy of the tail' and 14/2 was assumed to be unchanged from theohmic case. The magnitude of the tail energy estimated in this fashion is in thesame range as that from the X-ray measurements. The difference in the two may beattributed to experimental error and a possible lowering of the internal inductancein the rf-driven plasma relative to the ohmic one. In rf-driven plasmas, the current4profile cannot necessarily be computed from the temperature profile; in fact, inrecent ASDEX experiments, the temperature profile was found to narrow during rfcurrent drive while the current profile broadened slightly.9 If we assume that thesame fractional change in inductance occurs in our experiment as in ASDEX, thetail energy increases by approximately 20% above our previous estimate and thetotal stored energy by approximately 10%. In subsequent calculations of the plasmaenergy content, the internal inductance is taken to be the same for rf and ohmicplasmas over the density scan, which may result in the energy in the tail beingunderestimated.The global energy confinement time for both the rf-driven and ohmic plasmasis shown in Fig. 3 as a function of density. The confinement time in these quasi-steady-state discharges is defined as TE = Wtot/Pm, where W *t is the total storedenergy in the electron and ion populations (including the electron tail) and Pi isthe net input power to the plasma. For the rf-driven plasmas, we have used thenet transmitted rf power for Pin. We may add that experimental measurements ofthe current drive efficiency suggest that the absorbed fraction of rf power does notvary strongly over the density range of our experiment. Moreover, code simulationsof Alcator C current-driven plasmas which successfully reproduce the experimentalcurrent drive efficiencies suggest that over 95% of the injected rf power is absorbedby electron Landau damping. 10The global energy confinement time of the ohmic plasmas increases linearlywith density, as expected from neo-Alcator scaling." However, the confinement ofthe rf-driven plasmas shows a decreasing trend with density and/or power. Shownby solid circles are the calculated confinement times of the rf-driven plasmas if onlythe bulk energy is taken into account, as in the case of ohmic plasmas. Thesevalues are not to be taken as good estimates of the true bulk confinement times5because of the possibility of radial loss of tail electrons. The difference betweenthese calculated values and the true global confinement time rE (shown in opencircles) defined earlier indicates the importance of the stored tail energy in theoverall energy balance. At densities ie < 3 x 1013 cm- 3 , the global confinementtimes of the rf-driven plasmas are similar to and may even exceed that of the ohmicplasmas because of the presence of the energetic electron tail. As the density (and rfpower) are raised, the rf confinement time degrades relative to the ohmic value, andthe tail energy represents an increasingly smaller fraction of the total plasma energycontent. The decreasing trend of confinement time with injected power is similarto Kaye-Goldston scaling for neutral beam-heated L-mode plasmas." Comparisonsof ohmic and rf confinement times have also been made as functions of the plasmacurrent and toroidal field. As the current is raised from I, = 100 to 200 kA, rkdecreases by 25% while TE increases by approximately the same fraction owingto an increase in the estimated tail energy with plasma current. The value of rincreases by at most 20% as the toroidal field is raised from BT = 7 to 11 T,with rOh remaining constant over the same range. The major difference in theconfinement properties of the two types of discharges appears to be the unfavorabledensity dependence of r7V relative to ohmic plasmas, or degraded confinement withincreased total input power.The impurity behavior was monitored in some of these experiments to assessthe role of radiation in the power balance of current-driven plasmas. Spectroscopicmeasurements of the light impurity (C,O) emissions indicated that their densi-ties were unchanged or increased by at most a factor of two during rf injection.Molybdenum emissions increased between a factor of 5 and 15, while the bolometersignal increased by roughly a factor of 5 during rf injection. The radiated power asmeasured by the bolometer, and inferred from the molybdenum line brightnesses,6was observed to decrease with increasing density. The Zff measured by visibleBremsstrahlung showed a similar trend. The absolute calibration of the bolometeris presently in some doubt; however, the total fraction of radiated power due tohigh-Z impurities based on spectroscopic measurements and the cooling rates ofRef. 13 was estimated to be Pad/Pf < 0.15 at the highest powers employed inthis experiment. Although the radiation levels are strongly enhanced during rf in-jection, radiation appears to play a less important role in the overall power balanceof the rf-driven plasma as the density and rf power are raised, and therefore doesnot explain the diverging trend in rf and r'h at the higher densities.In order to investigate other possible reasons for the different scaling in theconfinement times, we have simulated these discharges with a detailed Fokker-Planck-ray tracing-transport code.10 The radial loss time for fast electrons is takento be a constant (3 msec) multiplied by a velocity-dependent factor." The bulkelectron thermal conductivity X, is modelled in both ohmic and rf discharges byCoppi-Mazzucato diffusion;5 in the latter case, we allow X, to be multiplied by anadjustable factor to match to the experimentally-obtained temperatures. As men-tioned earlier, this code models the macroscopic parameters and current drive effi-ciency of rf-driven discharges with fair accuracy. For the simulations of the AlcatorC experiments, the main energy loss of the current-carrying fast electrons was foundto be collisional absorption on the bulk. Radial losses of tail electron energy wereapproximately one-third of the input rf power at a density of i, = 3 x 1013 cm- 3 ,but only one-sixth of the input power at n-, = 7 x 1013 cm-3 . If the confinementtime of the tail electrons (typically 4-6 msec) was significantly reduced, flat-top cur-rent drive could not be maintained in the simulations with the experimentally giveninput powers. Although the rf deposition profiles are predicted to be broader thanohmic ones, almost all the rf power is calculated to be absorbed inside r/a = 0.47for all densities in this experiment. Thus, the apparent degradation in confinementrelative to the ohmic plasma is not explained by either unfavorable rf power depo-sition profiles or poor confinement of the superthermal electrons. To attain similarbulk temperatures in the code to those observed experimentally, it was necessary toincrease X, in the rf-driven plasma above that of the ohmic plasma at higher den-sities; an acceptable match of the simulation and experiment could be achieved bysetting X = X*o at _e = 3 x 1013 cm- 3 and ' = 2.3X*h at i, = 7 x 1013 cm- 3 .Thus a plausible explanation of our experimental results is that the confinementof the thermal component of the rf-driven plasma degrades relative to that of theohmic plasma with increasing density. This finding is consistent with X'f remainingnearly independent of density, or increasing with increasing total input power.In summary, the energy content of purely lower hybrid current-driven plasmashas been compared with that of ohmic plasmas. The bulk plasma energies of thetwo types of discharges are found to be similar over a wide range of parameters.In rf-driven discharges, a significant amount of additional kinetic energy resides inthe superthermal electron tail. Under plausible assumptions of the rf absorptionefficiency, the global energy confinement time is found to be lower in rf current-driven plasmas than in ohmic ones for densities ii > 3 x 1013 cm-3.We thank Mr. David Griffin for his tireless rf engineering support, and the Al-cator C technical and professional staff for their many contributions to this experi-ment. This work was supported by the U.S. Department of Energy under ContractNo. DE-AC02-78ET51013.8(a) Present address: Univ. of Texas, Austin, TexasREFERENCES'For recent reviews of lower hybrid current drive experiments, see: W. Hooke,Plasma Phys. and Cont. Fusion 26, 133 (1984); M. Porkolab, in Wave Heating andCurrent Drive in Plasmas, ed. by V.L. Granatstein and P.L. Colestock (Gordon andBreach, New York, 1985) 219.2 N.J. Fisch, Phys. Rev. Lett. 41, 873 (1978); C.F.F. Karney and N.J. Fisch,Phys. Fluids 22, 1817 (1979).3M. Porkolab et al., Phys. Rev. Lett. 53, 450 (1984).4 C. Gormezano et al., Proc. 6th Top. Conf. on RF Plasma Heating, Pine Moun-tain, Ga. 1985, ed. by D.G. Swanson, (American Institute of Physics, New York,1985) 111.'F. S6ldner et al., Proc. 12th Eur. Conf. on Cont. Fusion and Plasma Phys.,Budapest, Hungary, 1985, ed. by L. P6cs and A. Montvai, (European PhysicalSociety, 1985) Vol. II, 244.'S. Texter et al., MIT Plasma Fusion Center Report PFC/JA-86-10 (1986);S. Texter, Ph.D Thesis, Massachusetts Institute of Technology, 1986, MIT PlasmaFusion Center Report PFC/RR-85-24 (1986).7S. von Goeler et al., Nucl. Fusion 25, 1515 (1985); J. Stevens et al., Nucl.Fusion 25, 1529 (1985).'A. Mondelli and E. Ott, Phys. Fluids 17, 1017 (1974).'K. McCormick et al., Proc. 12th Eur. Conf. on Cont. Fusion and Plasma Phys.,Budapest, Hungary, 1985, ed. by L. P6cs and A. Montvai, (European PhysicalSociety, 1985) Vol. I, 199.910P. Bonoli, R. Englade, and M. Porkolab, Proc. 4th Int. Symp. on Heating inToroidal Plasmas, Rome, Italy, 1984, ed. by H. Knoepfel and E. Sindoni, (Int. Schoolof Plasma Phys., Varenna, 1984) Vol. II, 1311; P. Bonoli and R. Englade, MITPlasma Fusion Center Report PFC/JA-86-5 (1986) [submitted to Phys. Fluids]."B. Blackwell et al., Proc. 9th Int. Conf. on Plasma Phys. and Cont. Nucl.Fusion Res., Baltimore, Md., 1982 (IAEA, Vienna, 1983) Vol. II, 27."S.M. Kaye and R.J. Goldston, Nucl. Fusion 25, 65 (1985); S.M. Kaye, Phys.Fluids 28, 2327 (1985)."D.E. Post et al., At. Data and Nucl. Tables 20, 397 (1977)."H.E. Mynick and J.D. Strachan, Phys. Fluids 24, 695 (1981).1 B. Coppi and E. Mazzucato, Phys. Lett. 71A, 337 (1979).10FIGURE CAPTIONSFIG. 1. Comparison of the plasma parameter time histories of an rf-drivendischarge (solid lines) and an ohmic discharge (dotted lines) for B=8 T. From topto bottom: plasma current, line-averaged density, loop voltage, O3 + i/2, centralelectron temperature obtained on a shot-by-shot basis, and rf power.FIG. 2. 13, and 3, + l/2 vs. density for rf-driven and ohmic plasmas for I, ~140 kA, B=8 T. Triangles represent kinetic 3, measurements (Thomson scatteringand charge-exchange), while the circles depict equilibrium field measurements.FIG. 3. Global energy confinement time of rf-driven and ohmic plasmas vs.density. The closed circles are the represent the quantity Wb"lk/Pf calculated forthe rf-driven plasmas.111IC2001000to1.00.503201.51.00.52101000*5000 200TIME (ms)300-7--0-0-S-ow'--SRFOH--SoCN+a400FIG. 1I I I1.0C'j0.5AKIN0p0e-e0.0 w000.< 0000*1 o Oq0A LAAA 4A&A~tI I I I3 4e (10135cm~3 )1.5-RF0OHo ap+lj/2 0A1 A0'C) I 2 6 7 8FIG. 2I II I I I IA-Ie.ro12108A£ A04AAAA0a0.0 0it.000.00.000.20e cm- 3 )oo RFAOHAALAAAAAA"AAA AE~'60A42A0 00@.-4(I 6II8I I I I I I I IA A I 'tI I | I I I I

Energy confinement of lower hybrid current driven tokamak plasmas

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Energy confinement of lower hybrid current driven tokamak plasmas

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