Fairfax, S.

Gwinn, D.

Hutchinson, I.H.

Kusse, B.

Marmar, E.S.

Overski, D.

Pappas, D.

Parker, R.R.

Porkolab, M.

Scaturro, L.S.

Schuss, J.J.

Wolfe, S.

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LOWER HYBRID WAVE HEATINGIN THE ALCATOR A TOKAMAKJ.J. Schuss, S. Fairfax, B. Kusse*, R.R. Parker,M. Porkolab, D. Gwinn, I.H. Hutchinson, E.S. Marmar,D. Overskei, D. Pappas, L.S. Scaturro, and S. WolfeApril 1979, PFC/JA-79-4*Laboratory of Plasma Studies, Cornell University, Ithaca, New YorkLOWER HYBRID WAVE HEATINGIN THE ALCATOR A TOKAMAKJ.J. Schuss, S. Fairfax, B. Kusse, R.R. Parker, M. Porkolab, D. Gwinn,I. Hutchinson, E.S. Marmar, D. Overskei, D. Pappas, L.S. Scaturro, and -S. WolfeAbstractWe report the results of injecting 90 kW of microwave power nearthe lower hybrid frequency into the Alcator A tokamak through a twowaveguide array. The observed plasma heating is in diaagreemant with thatdxpected from linear waveguide-plasma coupling theory. From theseresults and auxiliary rf probe measurements we infer the nonlinear for- .mation of a high kfi wave power spectrum at the plasma edge.2There is currently extensive interest in raising plasma tempera-tures in tokamaks through auxiliary heating methods. Microwave heatingof tokamaks near the lower hybrid frequency has been tried on ATC,1-23 4 5 6Wega, Petula, Doublet IIA, and recently on JFT2. In these experimentsion heating was obtained when the wave frequency was in the vicinity ofthe central lower hybrid frequency, and some electron heating was alsoobserved at lower densities. This ion heating was accompanied by adensity rise and some impurity influx. No contradiction with theBrambilla waveguide - plasma coupling theory was reported in theseexperiments.Here we report the results of injecting 90 kW of microwave powerat 2.45 GHz into the Alcator A tokamak through a split waveguide array.Ion heating occurs at well defined values of central plasma density;below these densities electron heating occurs. No density changes orimpurity influx take place during the rf pulse. Contrary to previousexperiments, the waveguide phasiig has no effect on plasma heating. Inaddition, the densities at which heating occurs are significantly reduced7from those expected from waveguide-plasma coupling theory. These resultsand the frequency spectra obtained from an rf probe suggest that .the wave power spectrum formed near the plasma edge is shifted to higher7k,1= k-B/IBI than predicted by linear theory.The waveguide array employed here consists of two adjacent.independently driven waveguides mounted flush with the vacuum vesselwalls; each has inner dimensions of 1.275 cm by 8.13 cm and are separatedby a 0.09 cm .wide, septum. Toroidally the array is located 1800 away'from the limiter, which extends out 2.5 cm from the wall and defines aplasma minor radius of 10.0 cm with a major radius of 54 cm. The vacuumwindows in the waveguide were located outside the toroidal field magnets,-so that the w=w layer was within the evacuated section of waveguide;cenevertheless, no breakdown in the waveguide was observed at power2densities up to 4.5 kW/cm , averaged over the waveguide mouth. With the.exception of PetulakA, this power density is substantially higher than thosereported in previous experiments. During this high power operat'ion over85% of the incident power was coupled into the vacuum Viessel by the array.3The linear *theory of lower hybrid waves is well developed.?-10Warm plasma theory predicts that k =k x B / will become largenear the warm plasma mode conversion layer, at a densityW2 = W2 /[l - W2 /w c,+ 2 nz(M~ /2(12 22 2 2pi = [ (ce~c) 2 z( /me) ]()where n = kc/, and a = 3 T /M.c + 0.75(w 2W )2T /M c2. When kz 'i i ce 11 e .is large, ion absorption of the lower hybrid wave can occur. l Inaddition if w/k'\3 v t, the wave will be absorbed by electron Landaudamping.1 2  (This condition corresponds to n = 5 for T = 1 keV.)-2 -1/2 Z eWaves with nz wWcei) will mode convert into whistlermodes; for a given nz this occurs at a density which satisfies the relAtionnnzw 2 W2 + 1 ]1/2 (2)ce ci cii cice ciFor nz =1.5, B = 53 kG (the value of BT at the outside plasma edgewhen the central B = 62 kG)and deuterium this corresponds to ne= 7 x 1013 -3which occurs at r > 9 cm. Waves that mode convert into whistlers do notpenetrate and do not heat the plasma center.7,13Waveguide-plasma coupling theory is also well developed. Forthe double waveguide employed here the theory predicts a wave power spectrumthat monotonically decreases as nz increases past 1 for oppositelyphased waveguides ( =180*); the part of the spectrum which penetrates tothe plasma center is characterized by n z 3, which for BT= 62 kG,14 -3Te= 1.0 keV, and Ti= 0.8 keV would mode convert at ne= 3.:8 x 10 cmFurthermore, only about 30% of the power spectrum has nZ < 1.5 and thus over70%-of the power penetrates at least past the plasma edge. Whenthe waveguides are in phase (0 = 0*) the power spectrum is compressednear nz = 1 with over 80% of the wave power having n < 1.5 and beingconfined to the plasma exterior. We therefore would have expected amarked reduction in central plasma heating when 4 = 0* over * = 180*.4Fig. la shows a typical plasma shot in the ion beating mode. Therf pulse produces no increase in density or loop voltage and no effecton the nitrogen, oxygen, carbon, or molybdenum impurity radiation;however, the fusion neutron flux increases by a factor of 15. Fig. lbshows the results of many such shots; enhanced neutron rates are-14 -3 14 -3observed at R = 1.6 x 10 cm or central-n = 2.4 x 10 cm . The peak -neutron rate obtained was 2 x 10 1 1 /sec. Sawteeth are clearly observableon the enhanced neutron rate, which indicates that its origin is withinthe q = 1 surface. During the rf pulse a high energy tail appears onthe charge exchange en'ergy spectrum which is well correlated to theoccurrance of neutron enhancement. Any change in bulk ion temperaturedue to wave heating is less than the 100 eV resolution of the charge-exchange diagnostics; this is expected since the net rf power radiatedby the array is 75 kW which is much less than the ohmic heating power of270 kW. It should be noted that the observed charge-exichange particlesoriginate from ions superbanana trapped in the magnetic well of theflange which rapidly VB drift out of the plasma. An up-down charge -exchangescan exhibits an asymmetry due to this drift and indicates that theenergetic ion production is localized near the plasma center.The experimental ion heating density bands for both D2 and H2discharges are plotted in Fig. 2 for different values of B . Thedensity at which ion heating occurred in hydrogen was ascertained fromincreases in the 8 keV charge-exchange flux, while in deuterium theneutron enhancement was used. The curves are theoretical predictionsof the densities at which the mode conversion layer will appear at theplasma center for typical Alcator A parameters. The curve for nz = 3,which is the principal n expected theoretically, results in a higherzdensity for heating than experimentally observed in deuterium. At n z= 5the theoretical curve is in good agreement with the experimental points.A solution of the WKB wave equationil incorporating perpendicular ionLandau damping shows that for Alcator A parameters and n = 5 ion heatingzwill occur at a density 10% below that of Fig. 2 in deuterium, whichis in even better agreement with the experiment.When the density is lowered below the ion heating density band,electron heating is observed. At B = 62 kG and 1.0 x 10 cm < e <14 -3 T1.2 x 10 cm a 10% increase in central T is obtained from bothe5electron cyclotron emission at w=2w ce and Thomson scattering measurements takenover consecutive identical shots. No energetic ion tail is measuredby the charge-exchange diagnostics, indicating direct wave-electronheating. Electron Landau damping at T = 1100 eV would requirew/kjv T = 3 or nz 5, which is far above that predicted by waveguideplasma coupling theory, but consistent with the ion heating densitiesof Fig. 2. Thus both the electron and ion heating can be explainedby an upshift in the wave power spectra to n z 5.The experimental results strongly suggest that this high nz spectrumoriginates near the plasma edge. The neutron flux is found to change byless than + 10% when the waveguide phase is varied from 0* to 180* overidentical plasma shots. From linear theory we would expect a factor of4 change in the power that can penetrate past the plasma edge when 0 isvaried from 0* to 180*. From this we postulate that the shift to highernz occurs at r > 9 cm, and thereby allows unchanged accessibility evenas $ varies from 0* to 1800.In Alcator A this upshift in n from 3 to 5 would be more n6ticeablethan in previous tokamak experiments. From Eq. (2) we can cAlculate the-magnitude of the thermal correction to the lower hybrid densityC = 2 nz Mia/meM - W /Wceci), which for n = 3 is about 0.5 for previousexperiments, 1-6 but 2.1 for Alcator A. Thus due to the high T rV800 eVand w W wceWci of Alcator A, a upshift in nz from 3 to 5 would lowern.H by 31%, while in previous experiments nm could decrease only 18%.Due to the high rf power densities present in Alcator A, theparametric decay of the pump wave into lower hybrid waves and ion acousticwaves could occur at the plasma surface and cause an upshift in nz. Aspreviously shown, this decay process can significantly deplete the pumpsince the lower hybrid decay wave then propagates along the pump waveresonance cone. 4 For our plasma edge parameters (ne < 5 x 10 1 3 cm-3,Te < 10 eV) 1 5 and Te >> T the inhomogeneous plasma convective thresholdconditions can be satisfied for total waveguide powers of the order or lessthan 1 kW, which we easily exceed; the finite pump extent and homogeneousplasma threshold powers are even lower. It.should be noted that we havenot measured the edge Ti; if Ti T and the acbustid7wave is stronglyedamped, the inhomogeneous plasma threshold power might be considerablyhigher.6Fig. 3 a shows the frequency spectrum obtained from the coaxialrf probe having a 1mm diameter by 3 mm long tip bent in the poloidaldirection. This probe is located 90* toroidally away from the waveguidesand 1.5 cm from the vacuum vessel wall in the limiter shadow; it canbe shown that the ray originating from the waveguide mouth will notstrike the probe due to the low density at the plasma edge(i.e., ne <5 x 10 13cm-3).15 The probe will therefore observe either surface wavesor waves that cross the plasma column. The probe spectrum of Fig. 3 ais asymmetrically downshifted and broadened in frequency. In addition,during the rf pulse a strong enhancement occurs in the amplitude of thelow frequency fluctuations, as shown in Fig. 3 b. (In the absence of rfthe low frequency spectrum has a FWHM of 150 kHz.) The reflected waveguidepower spectrum also exhibits an asymmetrically frequency downshiftedsideband of 2 to 4 MHz FWHM, whose amplitude is 30 db down from the pump.Similarly frequency downshifted spectra are observed in the plasma interior16by CO2 laser scattering.Fig. 3 c shows the integrated intensity of the probe signal vs i .As the density rises, lower values of nz are absorbed by the plasma column(as indicated by the arrows) and cannot reach the probe. The collected14 -3signal sharply drops an n is raised above 1.5 x 10 cm , which indicatesthat a major part of the power spectrum traversing the plasma has nz ' 5.Furthermore, the low level of signal at high density suggests a smallamplitude surface wave. From this probe data we infer that the pump wavemay be significantly depleted while decaying into high n lower hybridwaves near the plasma surface, which results in the anomalous heatingresults obtained.In conclusion, we have presented experimental plasma heating dataand rf probe spectra from which we infer a nonlinear increase in nz ofthe lower hybrid waves near the plasma surface. This nz upshift couldplay an important role in future high power rf heating experiments ontoroidal plasma devices.We are happy to acknowledge the diagnostic work carried out byD. Cope, M. Greenwald, Y. Takase and J. West, and the engineeringassistance of G. Chihoski and H. Israel. This work was supported by D.O.E.Contract No. ET-78-C-01-3019.7ReferencesPermanent address: School of Applied and Engineering Physics, CornellUniversity, .Ithaca, N.Y.S. Bernabei, et al., in Proceedings of the Third Symposium on PlasmaHeating in Toroidal Devices, International School of Plasma Physics,Varenna, Italy.1976.-2M. Porkolab, et al., Phys. Lett. 38, .230 (1977).3C.Gormezano, et al, in Proceedings of the Third Topical Conferenceon Radio Frequency Plasma Heating, California Institute of Technology,Pasadena, paper A3 (1978).4P. Briad et al, in Proceedings of the Seventh International Conferenceon Plasma Physics and Controlled Nuclear Fusion Research, Innsbruck,Austria, (1978).5J.L. Lugor, et al, Bull. Am. Phys. Soc., 23, 821 (1978).6JFT2 Group (to be published).M. Brambilla, Nuc. Fusion 16, 47(1976).8Thomas H. Stix, Phys. Rev. Lett. 15, 878(1965).9Thomas H. Stix, The Theory of Plasma Waves (McGraw-Hill, New York, 1962).10A. Bers, in Proceedings of the Third Symposium on Plasma Heating inToroidal Devices, International School of Plasma Physics, Varenna,Italy (1976).11M. Brambilla, Plasma Physics, 18, 669 (1976).12H. Brambilla, Nuc. Fusion 18, 493 (1978).8Ref. cont.- 13 S. Bernabei, et al, Nuc. Fusion 17, 929 (1977).14 K.L. Wong, P. Bellan, and M. Porkolab, Phys. Rev. Lett., 40, 554 (1978);K.L. Wong, J.R. Wilson, and M. Porkolab, Princeton Plasma PhysicsLaboratory Report PPL-1499, Princeton, N.J. 1979.15 L.S. Scaturro and B. Kusse, Nuc. Fusion 18, 1717(1978).16 C.M. Surko, R. E. Slusher, J. J. Schuss, R. R. Parker, I. H. Hutchinson,D. Overskei, and L. S. Scaturro, (to be published).Figure CaptionsFig. 1 a) Typical plasma shot in ion heating mode: B = 62 kG,P rf= 90 kW, deuterium, and = 180, b) neutron rates fromseveral shots vs R ; B T 62 kG, I= 150 kA, P r 90 kW,e' TO p rfand * = 180*.Fig. 2 Theoretically expected central densities at which mode convertionwill occur for n = 3.0 and n = 5.0 in deuterium and hydrogen.z z* = experimental heating density in deuterium and M= in hydrogen.Fig.3 a)High frequency spectrum of rf probe (linear scale). BT= 62 kG,14 -3deuterium plasma, n e= 2.8 x 10 cm , Ip= 150 kA, and P rf 80 kW;the sudden drop in amplitude occurred at the end of the rf pulse.b) Low frequency spectrum of rf probe with and without rf power14 -3(10db/div). BT= 62 kG, deuterium plasma, ne = 1.6 x 10 cm ,I = 150 kA and P = 80 kW. (The peak at OH is a referencep rfzmarker.) In (a) and (b) the spectrum analyzer bandwidth was300 kHz. c)Amplitude of high frequency integrated probe Aignal vsn efor deuterium plasma, Ip= 150 kA, BT= 62 kG and P rf= 75 kW.The arrows indicate the values of n that will mode convert atthe plasma center.000 060 0000to0N~0 .0 S0Se 000000I I I I I I ItOc (D ItO(SJJNfl8ndH IflOHIJM 31"~ NOHfl3N -J8 HiMr.00CMNCLcr.-o'C('J-31V8 NO8in3Nwz0w-ZL0w0N~Iv,ELO VC0m-4-;ZIi IC~CLC50~ 0If If Cci~ cNIIq 0II IIaC9 L0 0ro C(D0N~0O i 0qQ 0000.00(0(10II I ICN* -qCCxJ(SIINO 98v)(80) 8JMOd 38O08d A~(HV3NI) 3afl1f~dOV(D-(AI/8001) J3flifldlNV0roCQ EC\i -C)Ic:0DUn) 0 0rf)C\Jui4- 1 1

Lower hybrid wave heating in the Alcator A tokamak

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Lower hybrid wave heating in the Alcator A tokamak

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