Intense axisymmetric oscillations driven by suprathermal ions injected in the direction counter to the toroidal plasma current are observed in the DIII-D tokamak. The modes appear at nearly half the ideal geodesic acoustic mode frequency, in plasmas with comparable electron and ion temperatures and elevated magnetic safety factor (q_{min}&gt;or=2). Strong bursting and frequency chirping are observed, concomitant with large (10%-15%) drops in the neutron emission. Large electron density fluctuations (n[over ]_{e}/n_{e} approximately 1.5%) are observed with no detectable electron temperature fluctuations, confirming a dominant compressional contribution to the pressure perturbation as predicted by kinetic theory. The observed mode frequency is consistent with a recent theoretical prediction for the energetic-particle-driven geodesic acoustic mode

Austin, ME

Berk, HL

Budny, RV

Fu, GY

Gorelenkov, NN

Heidbrink, WW

Holcomb, CT

Kramer, GJ

Makowski, MA

McKee, GR

Nazikian, R

Shafer, M

Solomon, WM

Strait, EJ

Zeeland, MA Van

Van Zeeland, MA

eScholarship - University of California

UC IrvineUC Irvine Previously Published WorksTitleIntense Geodesic Acousticlike Modes Driven by Suprathermal Ions in a Tokamak PlasmaPermalinkhttps://escholarship.org/uc/item/3c1064k3JournalPhysical Review Letters, 101(18)ISSN0031-9007AuthorsNazikian, RFu, GYAustin, MEet al.Publication Date2008-10-31DOI10.1103/physrevlett.101.185001Copyright InformationThis work is made available under the terms of a Creative Commons Attribution License, availalbe at https://creativecommons.org/licenses/by/4.0/ Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaIntense Geodesic Acousticlike Modes Driven by Suprathermal Ions in a Tokamak PlasmaR. Nazikian,1 G.Y. Fu,1 M. E. Austin,2 H. L. Berk,2 R. V. Budny,1 N. N. Gorelenkov,1 W.W. Heidbrink,3 C. T. Holcomb,4G. J. Kramer,1 G. R. McKee,5 M.A. Makowski,4 W.M. Solomon,1 M. Shafer,5 E. J. Strait,6 and M.A. Van Zeeland61Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543, USA2University of Texas at Austin, Austin, Texas 78712, USA3University of California Irvine, Irvine, California 92697, USA4Lawrence Livermore National Laboratory, Livermore, California 94550, USA5University of Wisconsin-Madison, Madison, Wisconsin 53706, USA6General Atomics, San Diego, California 92186-5608, USA(Received 24 June 2008; published 30 October 2008)Intense axisymmetric oscillations driven by suprathermal ions injected in the direction counter to the to-roidal plasma current are observed in the DIII-D tokamak. The modes appear at nearly half the ideal geo-desic acoustic mode frequency, in plasmas with comparable electron and ion temperatures and elevatedmagnetic safety factor (qmin  2). Strong bursting and frequency chirping are observed, concomitant withlarge (10%–15%) drops in the neutron emission. Large electron density fluctuations (~ne=ne ’ 1:5%) areobserved with no detectable electron temperature fluctuations, confirming a dominant compressionalcontribution to the pressure perturbation as predicted by kinetic theory. The observed mode frequency isconsistent with a recent theoretical prediction for the energetic-particle-driven geodesic acoustic mode.DOI: 10.1103/PhysRevLett.101.185001 PACS numbers: 52.35.Bj, 52.50.Gj, 52.55.Fa, 52.65.WwA key goal of a future deuterium-tritium burning plasmaexperiment such as ITER [1] is to explore the accessibilityof steady state reactor regimes in plasmas that are pre-dominantly self-heated by 3.5 MeV alpha particles [2]. Asignificant issue for such regimes is whether alpha particles(together with suprathermal 1 MeV beam ions injectedinto the plasma) will undergo collective oscillations withdetrimental effects on fast ion confinement. The role ofpresent fusion experiments is, in part, to develop predictivetools for assessing collective fast ion phenomena in steadystate reactor regimes [3]. High energy hydrogenic beamsare a widely used source of plasma heating in presentfusion experiments. These beams are typically injected inthe direction of the plasma current (cobeam injection) inorder to capture the beam ions on well confined orbits forefficient central plasma heating [4]. As a consequence,extensive studies have been performed on Alfvén waveexcitation using coinjected beam ions [5–11]. However,comparatively little effort has been invested in exploringinstabilities driven by suprathermal ions injected counter tothe direction of the plasma current.In this Letter we show the surprising result that counter-beam injection excites intense axisymmetric oscillationsthat are not readily observed in comparable cobeam injec-tion plasmas on DIII-D [10,12] or JET [9,13]. The modeactivity exhibits bursting and frequency chirping concom-itant with sharp drops in the neutron emission, indicative ofstrong beam ion redistribution and/or loss. The mode fre-quency is 50% below the ideal geodesic acoustic mode(GAM) frequency [14,15]. The modes occur in plasmaswith elevated central magnetic safety factor (qmin  2) andwith comparable ion and electron temperatures, relevant tosteady state plasma regimes. A theoretical analysis [16]identifies a new nonperturbative beam driven instability,the energetic particle GAM (E-GAM), that arises at afrequency well below the standard GAM frequency [17].A new fluid-kinetic hybrid model using the measured DIII-D equilibrium profiles, including beam ions on counter-passing orbits, qualitatively replicates the mode character-istics in the experiment [16].Figure 1 shows a typical example of an axisymmetric(n ¼ 0) mode excited in DIII-D during counterbeam in-jection. 75 keV deuterium beams are injected into theplasma during the ramp-up phase of the toroidal plasmacurrent [Fig. 1(a)], resulting in mode bursting [Fig. 1(b)]and frequency chirping [Fig. 1(c)] on magnetic pickupprobes located external to the plasma. Each burst is onlyof a few milliseconds in duration and is accompanied by10%–15% drops in the 2.5 MeV neutron emission[Fig. 1(b)]. The neutron emission is predominantly due tobeam ion collisions with the background plasma [DþD ! nð2:5 MeVÞ þ 3He], and is thus proportional to thefast ion population. The neutron drops commence at thestart of the frequency chirps and no other mode activityoccurs in conjunction with the n ¼ 0 mode. The rapidbursting and frequency chirping is characteristic of hole-clump generation in the beam ion velocity distribution[18,19]. The magnetic field fluctuations measured at thewall are particularly weak ( ~B=B ’ 105) and have a clearn ¼ 0 mode pattern.Beam emission spectroscopy (BES) [20] and electroncyclotron emission (ECE) were used to map the internaldensity and temperature mode structure. The equilibriumsafety factor (q profile) was mapped using the motionalPRL 101, 185001 (2008) P HY S I CA L R EV I EW LE T T E R Sweek ending31 OCTOBER 20080031-9007=08=101(18)=185001(4) 185001-1  2008 The American Physical Societystark effect (MSE) diagnostic [21]. Figure 2(a) shows theradial profile of the rms electron density fluctuation ob-tained by integrating over the frequency bandwidth of themode. The density fluctuation level is measured along a 16channel BES radial array 12 cm in extent and located 6 cmabove the plasma midplane. The profile is obtained from acomposite of three reproducible discharges where the arraywas scanned radially between discharges. The data show abroad density mode structure with rapid fall off at largeradius. This is inconsistent with the highly localized struc-ture expected near the magnetic axis for the ideal GAM[14]. No detectable electron temperature fluctuations wereobserved down to the ECE noise floor of 0.2% correspond-ing to the yellow band in Fig. 2(a). Phase measurementsbetween successive BES channels indicate very long wave-lengths in the poloidal and radial direction, well within thespatial resolution of the ECE diagnostic. The large dis-crepancy between electron density and temperature fluctu-ations is inconsistent with shear Alfvén wave observationsin DIII-D [10]. From kinetic theory, the electrons shouldremain isothermal along the magnetic field lines for lowfrequency modes due to the large electron poloidal transitfrequency (400 kHz for qmin ¼ 3 and Te ¼ 1 keV inFig. 2). Hence, for low frequency shear Alfvén waves itis the dominant radial component of the E Bmotion thatgives rise to comparable electron density and electrontemperature perturbation. In contrast, the data in Fig. 2(a)are consistent with a dominant E B motion tangential tothe flux surfaces (induced by radial electric fields) withnegligible radial displacement. A consequence is a domi-nant compressional contribution to the electron densityfluctuations with relatively weak electron temperatureand poloidal magnetic field fluctuations.The NOVA code [22], which includes geodesic acousticmode (electrostatic) coupling to shear Alfvén waves[23,24], was used to calculate the n ¼ 0 GAM continuum,shown in Fig. 2(c). The GAM continuum is calculatedusing the effective adiabatic index  ¼ ðPe þ 7=4PiÞ=ðPe þ Pi þ PfÞ ’ 0:81 where P= ¼ c, P is the totalplasma pressure, Pi, Pe, Pf are the ion, electron, and fastion pressure,  in the mass density, and c is a constant. Off-axis peaking of the GAM continuum is a requirement forthe existence of the ideal GAM and such conditions may beachieved in JET with strong magnetic shear reversal[14,25]. In contrast, the GAM continuum rarely peaksoff-axis in DIII-D due to weak magnetic shear reversaland monotonic temperature profiles. Extensive NOVA 131879.0425pol)pol)0500.02.0 Te (keV)Ti (keV)ne (1013 cm-3)f (kHz)0.00.51.01.52.034567δTe/Te < 0.2 %1.7 1.8 1.9 2 2.1 2.2131879131877131876Major Radius (m)q-profileδn/n (%)425 ms(a)(b)(c)FIG. 2 (color). Radial profiles of (a) the density fluctuationlevel ~ne=ne and q profile vs major radius Rmeasured using beamemission spectroscopy (BES), taken 6 cm above the plasmamidplane; (b) ion temperature Ti, electron temperature Te,electron density ne vsffiffiffiffippol where pol is the poloidal flux;(c) n ¼ 0 GAM continuum evaluated using the NOVA code andthe observed range of frequency (red band). BT ¼ 2 T, R0 ¼1:7 m.0 200 400 600 8000.00.20.40.60.81.0300 310 320 330 3400.00.1rms Bθ (Gauss)01300 310 320 330 340Time (ms)Time (ms)Time (ms)152025303540f(kHz) 2.5 MW NBII p (MA)Neutrons (au)LogIntensity (a)(b)(c)133067–1.5–1.0–0.50.0)FIG. 1 (color). Evolution of (a) plasma current Ip and 75 keVdeuterium neutral beam power PNBI, (b) edge poloidal magneticfield fluctuations ~B and neutron emission ns, (c) time resolvedpower spectrum of ~B. Bursting and frequency chirping coincidewith 10%–15% drops in the neutron emission. Plasma toroidalmagnetic field BT ¼ 2 T, major radius R0 ¼ 1:7 m, minor ra-dius a ¼ 0:6 m.PRL 101, 185001 (2008) P HY S I CA L R EV I EW LE T T E R Sweek ending31 OCTOBER 2008185001-2analysis confirms that no ideal GAM solution exists forthese DIII-D discharges.However, a newly developed nonperturbative electro-static theory for the energetic-particle-driven GAM, theE-GAM, captures many of the features observed in experi-ment [16]. The analysis shows that a robust n ¼ 0 modewith dominant radial electric field and a GAM-like m ¼ 1density perturbation [14], can be driven well below theideal GAM frequency when the energetic particle pressureis a significant fraction of the thermal plasma pressure. Themode frequency occurs below the poloidal transit fre-quency of the injected beam ions and is driven unstableby beam ion anisotropy. The mode radial width is deter-mined by the drift orbit width of the passing ions, whichincreases with increasing magnetic safety factor. For75 keV counterinjected beam ions with qmin ’ 3:5[Fig. 2(a)], the poloidal transit frequency of the beamions is close to 45 kHz, or about 2 the observed modefrequency. Both the velocity anisotropy and drift orbitwidth are largest for counterpassing particles at high qminin DIII-D [4], consistent with the conditions for the obser-vation of mode activity.The E-GAM is simulated using a hybrid model with afluid description for the thermal plasma and a drift kineticdescription for the fast ions [16]. Linear simulations havebeen carried out using a slowing down distribution for theinjected beam ions for the profiles corresponding to theDIII-D discharge in Fig. 2. Figure 3(a) shows the electrondensity perturbation ~ne=ne calculated using the hybridcode with a beam ion beta on axis, hð0Þ ¼ 0:17%, andfast ion profile corresponding to classical orbit analysisusing the TRANSP code [26]. The fast ion beta is compa-rable to the thermal plasma beta [thð0Þ ¼ 0:13%] within100 ms of the start of beam injection, corresponding to theplasma profiles shown in Fig. 2. The calculated electrondensity perturbation is global, consistent with observationson DIII-D [Fig. 2(a)], and unlike the core localized struc-ture expected for the ideal GAM [14]. Figure 3(b) showsthe simulation results for the mode frequency and growthrate vs hð0Þ. The simulation result in Fig. 3(b) indicatesthat the mode frequency is largely independent of hð0Þnear(’ 20 kHz). This is close to the observed mode frequency(22–28 kHz) and well below the poloidal transit frequencyof the 75 keV counterpassing beam ions (’ 45 kHz). Fromtheory the E-GAM frequency scales with the poloidaltransit frequency of the beam ions which scales inverselywith qmin, consistent with observations. The simulationsalso indicate a very large linear growth rate [Fig. 3(b)] upto =! ’ 30%. The fast ion beta for mode onset extrapo-lates to hð0Þ ’ 0:05%, consistent with the early onset ofthe instability in experiment [Fig. 1(c)]. The elevated qminallows GAM-like modes to arise without substantial ther-mal ion Landau damping, leading to a low hð0Þ thresholdfor the mode onset. The large linear growth rates calculatedover a wide range of fast ion beta suggests the possibility ofvery strong nonlinear interactions, consistent with thebursting, rapid frequency chirping and neutron drops ob-served in experiment. Such a response likely maintains thefast ion distribution close to marginal stability according totheory [19,27].Unlike ideal MHD modes, the E-GAM existence isdetermined by the fast ion distribution which is less wellknown than other equilibrium profiles and is nonlinearlymodified by the instability itself. However, qualitativefeatures of the mode are robust to variations in the fastion distribution such as the low mode frequency and theradially extended m ¼ 1 standing wave pattern.Measurements taken along a vertical array of BES chan-nels intersecting the magnetic axis (cf. Fig. 4) reveal aninversion of the mode parity through the magnetic axisindicative of a standing wave. The location of the modeinversion in Fig. 4 tracks the location of the magnetic axisand a mode null is also observed at the point of phaseinversion. The predicted peak in the mode density is ex-pected to occur well above and below the magnetic axis.From the location of the BES measurements just above the0102030400.05 0.10βh (0)%0.15 0.20010203040Frequency (kHz) (b)Major Radius (m)0.10.50.9-0.9-0.5-0.1(a)1.01.1 1.7 2.3Vertical Height (m)   0.0–1.0FIG. 3 (color). (a) 2D density perturbation (~ne=ne normalizedto unity) from linear hybrid simulation of the E-GAM showingm ¼ 1 standing wave. The dashed horizontal line is the elevationof the linear BES array at the time of interest. (b) Modefrequency (blue) and linear growth rate =!ð%Þ (red) vs centralfast ion beta hð0Þ.PRL 101, 185001 (2008) P HY S I CA L R EV I EW LE T T E R Sweek ending31 OCTOBER 2008185001-3plasma midplane [Fig. 3(a)] we infer that the peak densityfluctuation level could be as large as 10%. Further workwill focus on the measurement of the peak density fluctua-tion level of the E-GAM in the region where the lineareigenfunction is expected to peak.Note that an n ¼ 0 oscillation should not change thecanonical angular momentum of the fast ions so that ionradial diffusion is not expected even with efficient wave-particle energy exchange. What can change is the pitchangle of the particle as it loses energy to the wave. Lossescan then occur by the transit of counterpassing particles tounconfined trapped particle orbits. More speculatively, thereduction in the neutron emission could also be due to thechanneling [28] of the fast ion energy to the backgroundplasma. The combination of large linear growth rate, lowmode frequency, and low radial diffusion makes it possibleto couple the fast ion energy to the thermal plasma throughwave dissipation mechanisms. Future nonlinear simula-tions will address the mechanism of fast ion loss and thepossibility of channeling.In summary, countergoing beam ions in DIII-D excitelarge amplitude n ¼ 0 geodesic acousticlike compres-sional modes in plasmas with elevated central safety factor(qmin  2), relevant to steady state plasma regimes. Thefrequency of the modes, at about half the ideal GAMfrequency, cannot be explained within the context of idealMHD theory. A new electrostatic fluid-kinetic model re-veals a robust n ¼ 0 mode, the E-GAM, which reproducesmany of the features observed in experiment. The largecalculated linear growth rate suggests that the instabilitywill strongly modify the fast ion distribution to keep itclose to marginal stability [19,27]. Rapid drops in theneutron emission are indicative of intense wave-particleinteractions causing beam ion loss and/or energy channel-ing to background plasma. A key goal of future studies is tounderstand the nonlinear dynamics of the instability and toconfirm the predicted mode structure well above and belowthe plasma midplane.This work is supported by the U.S. Department ofEnergy under DE-AC02-76CH03073, DE-FG03-97ER54415, DE-FC02-04ER54698, DE-FG03-01ER5461, DE-FG03-96ER54373, W-7405-ENG-48, andDE-AC05-76OR00033.[1] K. Ikeda, Nucl. Fusion 47, 1213 (2007).[2] T. C. Luce, Nucl. Fusion 45, S86 (2005).[3] A. Fasoli et al., Nucl. Fusion 47, S264 (2007).[4] R. B. White, Theory of Toroidally Confined Plasmas(Imperial College Press, London, 2006), 2nd ed.[5] K. L. Wong et al., Phys. Rev. Lett. 66, 1874 (1991).[6] W.W. Heidbrink et al., Nucl. Fusion 31, 1635 (1991).[7] E. D. Fredrickson et al., Nucl. Fusion 46, S926 (2006).[8] Y. Kusama et al., Nucl. Fusion 39, 1837 (1999).[9] R. Nazikian et al., Phys. Plasmas 15, 056107 (2008).[10] M.A. Van Zeeland et al., Phys. Rev. Lett. 97, 135001(2006).[11] G. J. Kramer et al., Phys. Plasmas 13, 056104 (2006).[12] J. L. Luxon, Nucl. Fusion 42, 614 (2002).[13] P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987).[14] C. J. Boswell et al., Phys. Lett. A 358, 154 (2006).[15] H. L. Berk, C. J. Boswell, and D. Borba et al., Nucl.Fusion 46, S888 (2006).[16] G. Y. Fu, following Letter, Phys. Rev. Lett. 101, 185002(2008).[17] N. Winsor, J. L. Johnson, and J.M. Dawson, Phys. Fluids11, 2448 (1968).[18] H. L. Berk, B. N. Breizman, and N.V. Petvishvili, Phys.Lett. A 234, 213 (1997).[19] H. L. Berk et al., Phys. Plasmas 6, 3102 (1999).[20] G. McKee, K. Burrell, and R. Fonck et al., Phys. Rev. Lett.84, 1922 (2000).[21] C. T. Holcomb et al., Rev. Sci. Instrum. 77, 10E506(2006).[22] C. Z. Cheng and M. S. Chance, Phys. Fluids 29, 3695(1986).[23] N. N. Gorelenkov, H. L. Berk, and R.V. Budny, Nucl.Fusion 45, 226 (2005).[24] G. J. Kramer et al., Phys. Plasmas 13, 056104 (2006).[25] S. E. Sharapov et al., Phys. Rev. Lett. 93, 165001 (2004).[26] R. V. Budny, Nucl. Fusion 42, 1383 (2002).[27] R. G. L. Vann, H. L. Berk, and A. R. Soto-Chavez, Phys.Rev. Lett. 99, 025003 (2007).[28] M. C. Herrmann and N. J. Fisch, Phys. Rev. Lett. 79, 1495(1997).–6 –4 –2 0 2131874Z (cm)–1.00.0Cosine (φ)1.0325 ms375 ms425 ms475 msFIG. 4 (color). Cosine of the phase ( cos) of the n ¼ 0 modevs vertical height (z) measured along a vertical array of BESchannels located at major radius R ¼ 1:9 m. The phase is shownat 4 times in a single discharge (131874), each corresponding toa different vertical height of the magnetic axis (dashed lines:3,4, 5, 6 cm, respectively). The point of phase inversiontracks the motion of the magnetic axis, indicative of an m ¼ 1standing wave.PRL 101, 185001 (2008) P HY S I CA L R EV I EW LE T T E R Sweek ending31 OCTOBER 2008185001-4

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Intense Geodesic Acousticlike Modes Driven by Suprathermal Ions in a Tokamak Plasma

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Intense geodesic acousticlike modes driven by suprathermal ions in a tokamak plasma.

Intense geodesic acousticlike modes driven by suprathermal ions in a tokamak plasma.

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