Birkenmeier, G.

Chusov, A.

Diez, P.

Feuer, A.

Holzhauer, E.

Höfe, U.

Höhnle, H.

Kasparek, W.

Köhn, A.

Merli, S.

Ramisch, M.

Seifert, J.

Stroth, U.

Wolf, S.

English

MPG.PuRe

Schemes of microwave heating of overdense plasmas in the stellarator TJ-K

1This is an author-created, un-copyedited version of an article originally publishedin Plasma Physics and Controlled Fusion. IOP Publishing Ltd is not responsiblefor any errors or omissions in this version of the manuscript or any version derivedfrom it. The Version of Record is available online at http://dx.doi.org/10.1088/0741-3335/55/1/014010.Schemes of microwave heating of overdense plasmasin the stellarator TJ-KA Kohn1, G Birkenmeier2, A Chusov1, P Diez1, A Feuer3,U Hofel1, H Hohnle1, E Holzhauer1, W Kasparek1,S Merli1, M Ramisch1, J Seifert1, S Wolf1 and U Stroth1;21Institut fur Plasmaforschung, Universitat Stuttgart, 70569 Stuttgart, Germany2Max-Planck-Institut fur Plasmaphysik, EURATOM Association, Garching,Germany3Institut fur Strahlwerkzeuge, Universitat Stuttgart, 70569 Stuttgart, GermanyE-mail: koehn@ipf.uni-stuttgart.deAbstract. Microwave heating of overdense low-temperature plasmas, whosedensity exceeds the cuto density of the injected microwave, is described for thestellarator TJ-K. Three dierent methods featuring each their own characteristicsare briey presented. It is shown that TJ-K allows both fusion relevantscenarios like heating by electron Bernstein waves and fundamental wave-plasmainteractions like parametric decay instabilities to be investigated.PACS numbers: 52.25.Xz, 52.35.Hr, 52.35.Mw, 52.50.Sw, 52.55.Hc, 52.70.Ds,52.70.Gw, 52.70.KzSubmitted to: Plasma Phys. Control. Fusion1. IntroductionMicrowave heating is a widely-used method in plasma physics. It suers, however, fromthe fact that the propagation of microwaves is limited to densities below the cutodensity. In addition, in low-temperature plasmas heating at the electron cyclotronresonance frequency (ECRF) cannot be used as opposed to hot-temperature plasmas,since it requires electron temperatures of Te  1 keV to be ecient [1]. In thiswork, three alternative methods of microwave heating of overdense low-temperatureplasmas are presented for the stellarator TJ-K. These are: (i) heating at the upper-hybrid resonance (UHR) with 2.45 GHz, (ii) heating with electron Bernstein waves(EBWs) at the ECRF and its harmonics by injection of microwaves with 8 GHz and(iii) non-resonant heating with 2.45 GHz below the ECRF.This paper is organized as follows: The stellarator TJ-K is described in Sec. 2.UHR heating and the observation of a parametric decay instability is reported inSec. 3. Section 4 describes EBW heating and current drive at TJ-K. Non-resonantheating with microwaves of 2.45 GHz being below the ECRF is described in Sec. 5.The summary in Sec. 6 concludes this paper.Overdense plasma heating in the stellarator TJ-K 3Figure 1. (a) Phased array antenna and (b) numerically optimized lens for the8 GHz microwave heating system.2. The stellarator TJ-KTJ-K is an l = 1, m = 6 torsatron with major and minor radii of 0.6 and 0.1 m,respectively [2, 3]. Typical plasma parameters are electron temperatures of Te  10 eVand plasma densities of ne  1018 m 3. The background magnetic eld can becontinuously ramped up to a maximum value of B0 = 400 mT.2.1. Microwave heating hardwareTwo microwave heating systems are installed at TJ-K. The rst one is based on amagnetron which produces microwaves at 2.45 GHz with a maximum power of 3 kW.The vacuum transition is realized by a quartz window and a simple horn antennaemits the microwaves. The second microwave system consists of a klystron amplifyingmicrowaves in the frequency range 7:9   8:4 GHz to a maximum power of 3 kW. Aphased array antenna, as shown in Fig. 1a, is used for emitting the microwaves: thepower is split up into 8 waveguides, which act as delay lines and feed 8 H-plane sectoralhorn antennas. A frequency change results in a variation of the phase dierencebetween the waveguides and thus in a dierent injection angle. A variation from 7.9to 8.4 GHz corresponds to an angle variation of 45. As a vacuum transition, alens made of PMMA is used (see Fig. 1b). It focuses the microwave beam onto thepredicted position of the O-X mode conversion layer, which has been shown to beimportant for high conversion eciencies [4]. The nal shape of the lens has beendened in an optimization process with the full-wave code IPF-FDMC [4, 5]. Grooveson both sides of the lens minimize microwave reection [6]. The phased array antennais installed such that its angle variation is in toroidal direction. Since this correspondsmainly to the direction of the magnetic eld, an O-wave is incident into to plasma.2.2. DiagnosticsTo obtain the line-averaged density, a Mach-Zehnder interferometer operating at64 GHz is used [2]. Langmuir probes can be used for measuring density andtemperature proles and for direct investigation of plasma turbulence [7, 8]. Amonopole antenna is used to acquire frequency spectra around 2.45 GHz. It waspreviously used to measure wave electric elds [9]. To acquire low frequency spectraOverdense plasma heating in the stellarator TJ-K 4Figure 2. (a) Spectra obtained with a monopole antenna (large plot) and witha loop antenna (small plot) during a helium discharge. (b) Comparison of thespectral width at a decay of  10 dB of the high-frequency spectrum (horizontalaxis) and the low-frequency spectrum (vertical axis) for dierent gases.up to 100 MHz, a loop antenna made of stainless steel with a diameter of approximately37 mm is used. A similar antenna was successfully used at the W7-AS stellarator todetect lower-hybrid waves [10].An eight channel bolometer system designed at IPP Garching [11] is used at TJ-Kto measure the radiation power losses of the plasma. An external Rogowski coil hasbeen constructed for measuring toroidal net currents. The plasma energy content isobtained from an internal diamagnetic loop.3. Heating at the upper-hybrid resonanceHeating at the UHR is observed at TJ-K with 2.45 GHz in highly overdense plasmasat a magnetic eld strength of B0  70 mT, i.e. close to the corresponding ECRF.A maximum of the wave electric eld was measured at the UHR [9]. These highvalues of the wave electric eld can give rise to nonlinear phenomena, like parametricdecay instabilities [12, 13]. The simplest case of such an instability is the three wavecoupling in which a pump wave with the frequency f0 excites two waves with thefrequency f1 and f2. According to the Manley-Rowe relations [14, 15], the frequencyand wavenumber matching conditions must be fullled: f0 = f1+f2 and k0 = k1+k2.Figure 2a shows frequency spectra obtained in a helium discharge. The incidentmicrowave at f0 = 2:45 GHz can be clearly identied. A broad sideband on thelow-frequency side of f0 with a continuous decay down to the edge frequency off1  2:4 GHz can be recognized, which corresponds to the high-frequency decayspectrum. In the low-frequency spectrum the corresponding component f2 = f0   f1is found. In Fig. 2b, the width of the low-frequency spectrum at a decay of  10 dB isplotted as a function of the corresponding high-frequency spectral width for varyingion masses. Both values match well. The scaling with the ion mass, clearly visible inFig. 2b, points to two candidates in the low-frequency regime: lower-hybrid waves andion acoustic waves. For the plasma parameters at TJ-K, both waves can exist in theobserved frequency regime [16] and it is not possible to exclude one. It seems likelythat both are involved in the parametric decay process. From energy conservation(f0 = f1 + f2), it follows that a maximum power of 20 W can be transferred into thelow-frequency component. This power can contribute to ion heating.Overdense plasma heating in the stellarator TJ-K 5Figure 3. (a) Diamagnetic energy content of the plasma and (b) toroidal netcurrent as a function of the injection angle obtained from a series of heliumdischarges heated with 8 GHz, where the ECRF was located inside the plasma.Figure 4. (a) Toroidal net current as a function of the electron-ion collisionfrequency and (b) as a function of the injected microwave power obtained froma series of helium discharges heated with 8 GHz, where the ECRF was locatedinside the plasma.4. Heating with electron Bernstein wavesEBWs are electrostatic waves and they are absorbed almost completely at the ECRFand its harmonics in high- and low-temperature plasmas [17]. One possibility toexcite them is the O-X-B mode conversion process: an injected O-mode is convertedto an X-mode around the O-mode cuto and then into a backwards propagatingEBW at the UHR. The eciency of the whole process depends strongly on theeciency of the O-X conversion which itself depends on the injection angle of themicrowave beam with respect to the background magnetic eld. Deviations fromthe optimum angle result in reduced eciencies, where the degradation is smaller forsteeper proles [5]. The steepness can be characterized by the normalized density scalelength k0Ln = k0  n=jrnj in the mode conversion region.At TJ-K, heating with EBWs at the ECRF can be achieved in discharges heatedwith microwaves around 8 GHz (3 kW) at B0  270 mT. In these discharges, k0Ln  8.Figure 3a shows the energy content of the plasma as a function of the injection angleof the microwave, obtained during a series of helium discharges with B0  270 mT.Each point represents an average over multiple discharges. The energy content ofthe plasma clearly depends on the injection angle, having its maximum around thecalculated optimum value, as indicated by the dashed line. Thus, these measurementsrepresent a strong indication for successful mode conversion and subsequent EBWheating at the fundamental ECRF.With the Rogowski coil, a toroidal net current on the order of a few amperesOverdense plasma heating in the stellarator TJ-K 6Figure 5. Discharge with heating at harmonics of the ECRF by EBWs.Figure 6. Non-resonantly heated argon discharge.owing into counter-B0 direction has been detected in this regime. As shown in Fig. 3b,the same angle dependence as for the energy content is found. Two mechanisms canbe responsible for current drive by EBWs [18], the Ohkawa and the Fisch-Boozermechanism, which is more likely to apply here [19]. The expected scaling [20] of thecurrent density J with the electron-ion collision frequency ei and the absorbed powerPabs, J /  1ei Pabs, was conrmed experimentally. Figure 4a shows the current asa function of ei, which was varied by changing the neutral gas pressure in a seriesof helium discharges. The decrease of the current with increasing collision frequencycan clearly be seen. In Fig. 4b, the current is shown as a function of the injectedmicrowave power and an increase of the current with increasing power is also clearlyvisible. Both experimental results shown in Fig. 4 strongly support the assumption ofan EBW driven current by the Fisch-Boozer mechanism.The EBW experiments presented so far were performed with the fundamentalECRF located inside the plasma. Recently, EBW heating at high harmonics of theECRF has been achieved in TJ-K. A time trace of such a discharge is shown inFig. 5. First, B0 is ramped up and the plasma is started. Then B0 is ramped downto B0  100 mT, where the 4th harmonic is situated close to the plasma center.With decreasing B0, the density starts to increase, reaching its highest values atthe lowest value of B0  100 mT. The bolometer in contrast, has its highest valuearound B0  160 mT, where the density is strongly uctuating. Interestingly, forB0  100 mT, the signal of the line-averaged density shows almost no uctuations,pointing to a very stable plasma. Indeed, using local Langmuir probe measurements,the density uctuation level has been veried to be as low as a few percent, only.5. Heating below the electron cyclotron resonance frequencyTo achieve non-resonant heating at TJ-K, the plasma has to be started resonantlywith 8 GHz at B0  280 mT, where there are no resonances for 2.45 GHz inside theOverdense plasma heating in the stellarator TJ-K 7plasma. Nevertheless, when microwaves at 2.45 GHz are injected, additional heatingis observed as shown in Fig. 6. A strong increase in the density can clearly be seen atthe moment when the 2.45 GHz is switched on. After the 8 GHz heating is switchedo, the density stays at its high level.The 2.45 GHz is well below the ECRF over the whole plasma cross section andalso well below the plasma frequency. Since it is still above the lower-hybrid resonancefrequency, we suggest that the heating is due to absorption of Whistler waves insidethe plasma. These waves can be absorbed at the so-called O-resonance inside theplasma [21]. Possible absorption mechanisms are collisional damping and Landaudamping. The Whistler waves must be excited via a conversion processes at theplasma boundary [22]. At the moment, further investigations, including full-wavesimulations, are performed.6. SummaryThree dierent schemes of generating overdense low-temperature plasmas have beenbriey described for the stellarator TJ-K. It has been shown experimentally thatheating at the UHR is accompanied by a parametric decay instability, which can inprinciple contribute to ion heating. After appropriate shaping of the microwave beam,heating at the ECRF by EBWs and subsequent current drive was found. High densityplasmas with very little uctuations could be produced by high-harmonic heatingof EBWs. Finally, an interesting plasma regime, which is heated non-resonantly andcharacterized by highly overdense plasmas, was presented. In summary, the stellaratorTJ-K has proven a device that allows to study both fusion relevant heating scenariosas well as fundamental microwave-plasma interactions.References[1] Bornatici M, Cano R, De Barbieri O, and Engelmann F 1983 Nucl. Fusion 23 1153[2] Krause N et al 2002 Rev. Sci. Instrum. 73 3474[3] Stroth U et al 2004 Phys. Plasmas 11 2558[4] Kohn A et al 2008 Plasma Phys. Control. Fusion 50 085018[5] Kohn A et al 2011 Phys. Plasmas 18 082501[6] Petelin M I, and Kasparek W 1991 Int. Journal of Electronics 71 871[7] Ramisch M et al 2010 Plasma Phys. Control. Fusion 52 124015[8] Birkenmeier G, Ramisch M, Manz P, Nold B, and Stroth U 2011 Phys. Rev. Lett. 107 025001[9] Kohn A et al 2010 Plasma Phys. Control. Fusion 52 035003[10] Suvorov E V et al 1998 Nucl. Fusion 38 661[11] Mast K F et al 1991 Rev. Sci. Instrum. 62 744[12] Yadav V K, and Bora D 2004 Phys. Plasmas 11 3409[13] Lin A T, and Lin C-C 1981 Phys. Rev. Lett. 47 98[14] Manley J M, and Rowe H 1956 Proc. IRE 44 904[15] Rowe H 1958 Proc. IRE 46 850[16] Stix T H 1992 Waves in plasmas (American Institute of Physics, New York, 1992)[17] Laqua H P 2007 Plasma Phys. Control. Fusion 49 R1[18] Urban J et al 2011 Nucl. Fusion 51 083050[19] Preinhaelter J et al 2009 Plasma Phys. Control. Fusion 51 125008[20] Hansen F R, Lynov J P, and Michelsen P 1985 Plasma Phys. Control. Fusion 27 1077[21] Heald M A, and Wharton C B 1965 Plasma Diagnostics with Microwaves (John Wiley & SonsInc., New York, 1965)[22] Golant V E, and Piliya A D 1972 Sov. Phys. 14 413

Schemes of microwave heating of overdense plasmas in the stellarator TJ-K

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