First evidence of Alfvén wave activity in KSTAR 3 plasmas 1 0 2 n M.J. Hole1, C. M. Ryu2, M.H. Woo2, J. G. Bak3, S E. a Sharapov4, M. Fitzgerald1, and the KSTAR team3 J 0 1 Research School of Physical Sciences and Engineering, Australian National 2 University, Acton 0200, ACT Australia ] 2 POSTECH, Pohang, Korea h 3 National Fusion Research Institute, Daejeon, Korea p 4 EURATOM/CCFE Fusion Assoc., Culham Science Centre,Abingdon, Oxon OX14 - m 3DB, UK s a l Abstract. We reporton firstevidence of waveactivity during neutralbeam heating p . in KSTAR plasmas: 40 kHz magnetic fluctuations with a toroidal mode number of s c n = 1. Our analysis suggests this a beta-induced Alfvén eigenmode resonant with i the q = 1 surface. A kinetic analysis, when coupled with electron temperature s y measurements from electron cyclotron emission and ion/electron temperature ratios h from crystallography, enables calculation of the frequency evolution, which is in p [ agreement with observations. Complementary detailed MHD modelling of the magnetic configuration and wave modes supports the BAE mode conclusion, by 1 locating an n = 1 mode separated from the continuum in the core region. Finally, v 8 we have computed the threshold to marginal stability for a range of ion temperature 0 profiles. These suggest the BAE can be driven unstable by energetic ions when the 7 ion temperature radial gradient is sufficiently large. Our findings suggest that mode 4 . existence could be used as a form of inference for temperature profile consistency in 1 the radial interval of the mode, thereby extending the tools of MHD spectroscopy. 0 3 1 : v PACS numbers: 52.55.Fa, 52.55.-s,52.55.Tn i X r a Submitted to: Plasma Phys. Control. Fusion Beta-induced Alfvén wave activity in KSTAR plasmas 2 1. Introduction Instabilities such as Alfvén eigenmodes, driven by fast particles, are of programmatic concern as they can expel energetic ions from the plasma, thereby preventing heating by thermalisation. [1] In addition, such energetic particles expelled can damage the first wall, and a fusion reactor can only tolerate fast particle losses of a few per cent. [2] Another motivation for the study of Alfvén eigenmodes is their potential use as a diagnostic for the plasma, particularly through the tool of MHD spectroscopy. [3] One such class of fast particle driven instabilities that can occur at relatively low frequency are beta induced Alfvén eigenmodes (BAEs). The characteristic experimental feature of this instability are magnetic fluctuations at a frequency intermediate between the fishbone and the toroidal Alfvén eigenmode (TAE), with angular frequency ωTAE = v /(2qR), with v the Alfvén speed, q the safety factor and R the major radius. [4] A A These modes were first identified in DIII-D, [5] and have since been discovered in other tokamaks in beam, [6] ion cyclotron heated [7] and Ohmically heated discharges in the presence of a magnetic island. [8, 9, 10, 11, 12] More advanced kinetic treatments, which include corrections to kinetic theory for diamagnetic and shaping effects, as well as the inclusion of trapped particles have been used to study BAEs in ASDEX. [13] Radial profile information was measured during sawteeth in Tore Supra. [14] Recently, BAEs driven by electronpopulations have been observed inthe tokamakHL-2A,[15]andthere is some evidence that magnetic oscillations in the H-1 heliac are also driven by energetic electrons. [16] The aim of this paper is to report on first evidence of Alfvénic wave activity during neutral beam heating in KSTAR plasmas. In 2010 and 2011 campaigns KSTAR plasmas included 1.2 MW of neutral beam heating, which provided a source of heating to excite Alfvénic wave activity modes. Data from the 2010 campaign, which was fully analysed during 2011, shows 40-60kHz magnetic fluctuations. We present the first ideal MHD calculation of a core localised mode with toroidal mode number n = 1 for an experimental configuration. The mode is global with very small resonance with continuuum modes. Second, thisworkisthefirst observationofAlfvénic wave activityin KSTAR. With up to 14MW of neutral beam heating and 14MW of RF heating planned, KSTAR plasmas will become a pilot for ITER plasmas, and provide the opportunity to explore the wave-particle-plasma interaction in regimes approaching burning plasmas. Our work builds on preliminary observations of electron fishbones in KSTAR in 2009, [17] and aliased TAE activity in 2011. [18] Finally, as a spin-off, we have developed a new form of MHD spectroscopy for consistency of the temperature profile with the observation of wave activity. The remainder of the work is as follows: in Section 2 we introduce the experiments conducted in KSTAR, and in Sec. 3 present detailed modelling. Finally, Sec. 4 contains concluding remarks and discusses implications for future work. Beta-induced Alfvén wave activity in KSTAR plasmas 3 2. Experiments In 2010 a set of neutral beam injection (NBI) excitation experiments were conducted in KSTAR in an attempt to generate shear Alfvénic wave activity. Subject to operator controls, the choice of plasma conditions were optimised for this purpose: a relatively low toroidal magnetic field of 1.95 T, and maximum available NBI heating: 1.2MW of 80keV NBI. For deuterium plasmas, 80keV NBI would produce fast D neutrals with speedv = 2.8 106 ms−1. Withplasmadensities ofupto5 1019 m−3 expected, the ||,beam × × minimum Alfvén speed is v = 4.4 106 ms−1. While the beam speed is sub-Alfvénic, A × it is greater than the first sideband resonance at v /3, and so it is possible that TAE A modes may excited, as was found during early operation of MAST. [19] Alfvén cascades have also been observed on JET in reverse shear configurations with v /v as low ||,beam A as 0.2. [20] Four NBI heated discharges (#4218-#4220) were produced, with flat top plasma currentI intherange210 < I < 407kA,electroncyclotronresonanceheating (ECRH) p p power up to 200 kW, and core plasma density up to 3 1019 m−3. There was no × discernible impact of ECRH heating on these plasmas. Figure 1 shows the temporal evolution of one such discharge, #4220. For this 4.5s plasma, 2s of NBI was applied from 2s during current flat-top. 500 A) (a) k (p I 0 1.5 W) 1 (b) M0.5 ( −3) 0 m (c) 9 10 2 1 × (e0 n 0 1 2 3 4 5 t (s) Figure 1. Evolution of #4220 showing (a) plasma current I , (b) auxiliary heating p (P in blue, P in red), and (c) line averagedelectron density n . NBI ECRH e Figure 2 shows magnetic oscillations of discharge #4220. The mode activity correlated with NBI heating, and a study of electron cyclotron emission data reveals that the plasma is sawtoothing throughout the heating phase. A study of signal phase versus geometric angle, computed from a toroidal Mirnov array provides weak evidence that the mode has n = 1. Unfortunately, the coils are located flush with the conducting wall, and so the signal to noise ratio is large, and there is significant n = 0 noise present. Information about the poloidal mode number is not available. Similar oscillations were observed in discharges #4218,#4219 and #4221. A simple scoping exercise reveals that the mode activity is unlikely to correspond to a Toroidal Alfvén Eigenmode. The middle of the TAE gap lies at ω = v /(2qR). TAE A Beta-induced Alfvén wave activity in KSTAR plasmas 4 x 104 10 0 8 z] −2 8281[H 6 −4−1T Hz] 48. B| [ = δ z], df 4 −6g |10 H o f [ 2 l −8 0 1 2 3 4 5 t [s], dt=0.02048[s] Figure 2. Magnetic spectrogram of #4220 with ω (red) and BAE mode (black) CAP from Fig. 5(a) overlaid(red). Using n n (0), taking R as the magnetic axis, and using q = q = (2m+ 1)/(2n) i e mn ≈ for m = 1,2,3 gives 160 kHz, 100 kHz and 70 kHz, respectively. Mode activity with frequency of order 150 kHz and m = n = 1 was observed in the 2011 campaign. The observed mode reported here has a frequency of 40 kHz, which would be commensurate with a resonance of q = 5. This is the edge q of these elongated plasmas, and so the TAE frequency will be significantly greater than 40 kHz. Following Gorelenkov et al [21] we have also computed the thermal ion transit frequency ωti = q2kBTi/mi.(qR0), which isthe upper beta-acousticAlfvén Eigenmode (BAAE) gapfrequency. ForKSTAR plasmas, the on-axis frequency ranges from 29kHz, using the central ion temperature inferred from #4229 down to 17kHz. These are below the observed wave frequency, at 40-60 kHz. In contrast, the frequency as well as its time evolution is a closer match to the evolution of the kinetic accumulation frequency ωCAP = 1/R0q2Ti/mi(7/4+Te/Ti)), with R0 the major radius, mi the ion mass, and Ti and Te the ion and electron temperature, respectively. [22]Electron cyclotronemission (ECE) data gives theon-axis value of electron temperature T = 1.2 keV. While not available for discharge #4220, e x-ray imaging crystal spectrometer [23] data providing T ,T is available for nearby i e discharge #4229 with the same level of NBI heating. This pulse also shows evidence of toroidal rotation, with core rotation up to 100 km/s, producing a core Doppler shift of up to 8kHz. Rotation of either a near stationary mode or magnetic island is thus insufficient to describe the observations. Correcting for the offset in neutral beam heating interval for this discharge, we have computed ω and over plotted the evolution in Fig. 2. The frequency match is close, CAP as is the slight frequency drop following beam turn-on at 2 s. The drop in frequency occurs due to the initial drop in T observed in the core ECE channel. Similar BAE e frequency scaling is evident for discharges #4218 and #4219. Beta-induced Alfvén wave activity in KSTAR plasmas 5 3. Detailed Modelling We have undertaken detailed modelling of the plasma at the onset of mode activity at 2 s. By analysing data from a set of 20 electron cyclotron emission (ECE) chords we have been able to identify the inversion radius and locate the q = 1 surface. To correct the q = 1 surface of magnetics-only constrained EFIT to match ECE data we have used CHEASE [24] to remap the current profile as I∗(s) I∗(s) + cI (s) and pressure core → profile with p′(s) λp′(s) so as to match the sawtooth inversion radius and EFIT β , p → respectively. Here, s is the square root of normalised poloidal flux, with s = 0 the core and s = 1 the edge. The core current profile selected is a ramp, I (s) = 1 s. Figure core − 3 shows a cross section of the corrected equilibrium flux surfaces and q profile. 5 (c) 1.5 (a) q 1 0 0.5 Z [m] 0 p [kPa]10 (d) −0.5 00 −1−.51 p’ Pa/Wb]−0.2 (e) M [−0.4 ψ [Wb]0.00.51 (b) I ||[MA] 246 (f) 0 0 1 2 0 0.5 1 R [m] s Figure 3. Equilibrium for #4220 at 2s. Panel (a) shows contours of poloidal flux with the plasma vessel cross section overlaid, and panel (b) is a major radius profile of poloidal flux ψ. Panels (c)-(f) show q,p,p′(ψ) and I as a function of s, the square || root of normalised poloidal flux. Figure 4 shows the Alfvén and ion sound continuum for n = 1, computed using the code CSCAS [25] with adiabatic index γ = 5/3. In Fig. 4(a) the toroidicity and ellipticityinducedgapscanbeidentified. UsingthemostrecentversionoftheidealMHD global stability code MISHKA [26] we have computed TAE gap modes. The TAE gap modeproduced by theq = (2m+1)/2n = 1.5resonance ats = 0.45 hasa frequency of mn 120 kHz, well above the measured 40 kHz oscillation. In Fig. 4(b) we have zoomed into the low frequency part of the continuum and identified different continuum branches. As shown by Gorelenkov et al , [21] the frequency of the ion sound and modified shear Alfvén continuum modes drops to zero at rational surfaces. The accumulation point of the low frequency gap introduced in the shear-Alfvén continuous spectrum because of finite beta is ω /ω = (γβ)0.5, with ω the Alfvén angular frequency at the As,gap A A magnetic axis. To identify a global mode separated from the MHD continuum, we have selected an s interval of 0 < s < 0.3, thereby avoiding the resonance with the m = 3 ion sound branch. The discrete mode identified in Fig. 4(b) is separated from the Beta-induced Alfvén wave activity in KSTAR plasmas 6 continuum above and below, and so forms a gap mode between singular modes. In the limit that the s interval is expanded to the full domain, the eigenfunction retains its global structure. The mode frequency is ω/ω = 0.1371. A single channel millimeter A − wave interferometer system provides a measurement of the time-resolved line integrated electron density, n .[27] Assuming a parabolic profile for the density provides a measure e of on-axis density. If n 0.8n is also assumed, [28] the Alfvén angular frequency i e ≈ can be computed, yielding ω/(2π) 50 kHz at 2s. We have overplotted the frequency ≈ evolution of this estimate in Fig. 2. The mode, which is resonant with the core of the plasma, has similar global mode structure to modes computed in DIII-D by Turnbull et al [29]. In contrast, the BAE mode modelled by Huysmans et al [30] is in the region of greater shear, and posseses more poloidal harmonics. Figure 5 shows the V1 eigenvector, which is the ρ component of the contravariant fluid displacement velocity, for (a) a discrete mode, and (b) a nearby continuum mode. A continuum mode is one that is localised to a resonant surface with poloidal flux ψ, and a solution of the shear Alfvén dispersion relation ω(ψ) = k (ψ)v (ψ), with k = k B/B.[25] The BAE in Fig. 5(a) has a || A || · global mode structure with negligent resonant coupling with continuum modes, whereas the continuum mode in Fig. 5(b) has resonances at crossings of the continuum at s = 0.57,s = 0.66 for m = 2 and s = 0.77,s = 0.84 for m = 3. In contrast to earlier work, [29, 30] the global mode of Fig. 5(a) has significantly reduced coupling to resonances with the continuum, and therefore will exhibit weaker continuum damping. 4 0.4 (a) (b) 4 3 0.3 1 1 2 A A ω 2 ω 0.2 3 ω/ ω/ −1 2 3 3 1 0.1 0 1 1 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 s s Figure 4. Ion sound and Shear Alfvén continuum (shown as black points) for n = 1 modesfor#4220at2s. Alsoshownistheqprofile(solidblackcurve),normalisedmass density profile ρ/ρ0 (solid green curve), TAE frequency (solid blue curve), elliptical Alfvén eigenmode frequency (solid red curve) and accumulation point of the low frequencygapω (solidpinkcurve). Figure(b)focusesonthe BAEregion,which As,gap also shows the BAE mode (red line). Ideal MHD codes such as MISHKA solve for the wave structure in full toroidal geometry, but provide no information about mode drive. The particle-wave resonance condition [31] is n m+l v v ω = 0, (1) || || R − qR − Beta-induced Alfvén wave activity in KSTAR plasmas 7 0.15 (a) (b) 0.1 m=1 m=1 0 V1 0.05 V1 m=−2 m=2 −0.05 m=3 0 m=3 m=2 −0.05 −0.1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 s s Figure 5. Eigenfunctionsfor(a)ann=1BAEwithfrequencyω/ω = 0.1371,and A − (b) an n=1 continuum mode with frequency ω/ω = 0.1380. Both real (solid) and A − imaginary (dashed) components are shown. where l is a Fourier mode number in poloidal angle θ of the particle magnetic drift velocity. The mode peaks at s = 0.16, for which q = 0.89. At this radial location the l = 0 resonance condition requires the unphysical condition v /v = 1.3, while for || ||,beam l 1 the resonance condition can be satisfied for v < v . Thus, the mode can || ||,beam | | ≥ be driven by sidebands, l 1. The mode resonance is broad due to the finite radial | | ≥ region of varying q covered by the mode width. Meanwhile, the mode excitation threshold by energetic ions is reduced by inverse ion Landau damping connected with finite thermal ion temperature gradient. [22] In the limit of vanishing continuum damping, an estimate of the threshold to marginal stability can be made using the kinetic treatment of Zonca [22], which studied the drive due to thermal ion temperature radial gradients, and studied the relationship between kineticballooningmodes(KBM)andBAEs. Inthattreatmentitwasshownthestability conclusions were a function of the frequency range of ω relative to the core-plasma CAP ion diamagnetic frequency ω = kBTi(k b) lnP . Here, k is Boltzman’s constant, ∗pi eiB × ·∇ i B k = m/re +n/Re the wave vector, b = B/ B , and P the thermal ion pressure. If θ φ i | | 2 2 ω ω theKBMaccumulation pointwas always stable, andtheBAE maybecome ∗pi ≪ CAP unstable for values of η = (∂lnT /∂lnn ) greater than a critical value η , given by i i i ic 2 ω ti η , (2) ic ≈ √7+4τ qω ∗ni with ω = kBTi(k b) n /n the ion diamagnetic drift frequency. If ω is ∗ni eiB × · ∇ i i ∗pi increased further, the unstable BAE accumulation point is expected to smoothly connect to an unstable KBM accumulation point with exponentially small growth rate 2 when ω ω . The most unstable BAE/KBM accumulation point occurs when ∗pi ≫ CAP 2 2 ω ω , when the BAE and KBM are strongly coupled. For the plasma conditions ∗pi ≈ CAP 2 2 of KSTAR, we compute ω /(2π) 4 kHz, and so ω ω , and thus plasmas ∗pi ≈ ∗pi ≪ CAP with η > η with η given by Eq. (2) are unstable. In this frequency regime δE 0, ic ic k ≈ consistent with ideal MHD. Indeed, we compute ω /(2π) 60 kHz at the minimum As,gap ≈ of the m = 1 continuum at s = 0.24. This frequency, and the computed BAE gap mode frequency of 50 kHz at 2s, is close to the kinetic accumulation frequency ω . CAP By expanding η = (∂lnT /∂lnn ) = ∂lnTi ∂lnni, as well as (k b) n /n = i i i ∂r . ∂r × · ∇ i i Beta-induced Alfvén wave activity in KSTAR plasmas 8 (k b) ∂lnni, the ratio η /η expands as × r ∂r i ic ∂lnT k T /(e B)(k B) i B i i r η /η = × (3) i ic ∂r 2/(7+4τ)ω /q q ∗i Equation (3) is independent of the ion density profile, and so can be computed for different radial temperature profiles. X-ray crystallography of nearby discharge #4229 measures T (0)/T (0) = 0.75 i e during NBI heating, and we have used this value for #4220. Together with ECE T e data for #4220, this fixes T on-axis. To account for the unknown core localisation of i the ion temperature profile, we have expressed the temperature profile as the sum of profiles T (s) and T (s), with T (s) = T (s)+T (s), and r sa, with a the minor radius. a b i a b ≈ The profile T (s) is an approximation to the Ohmic temperature profile. A constraint a for T (0) is provided by crystallography during the pre-NBI heating phase of #4229: a that is T (0) = 0.25T (0). As a plausible estimate for the Ohmic ion temperature profile a e we have assumed n(s) T (s), and inferred T (s) from the equilibrium pressure profile. a a ∝ Finally, we have modelled the core temperature profile as T (s) = (T (0) T (0))(1 tanh(αs))tanh(10(1 s)), (4) b i a − − − with α varied to control the core radial localisation of T (s), and term tanh(10(1 s)) b − included to force T (s) to zero at s = 1. b Figure 6(a) shows a plot of different candidate modelled ion temperature profiles on the outboard radial chord, and Fig. 6(b) shows the corresponding η /η values. The i ic candidate BAE mode in Fig. 5(a), whose m = 1 Fourier magnitude is also shown in Fig. 6(b), has a peak at radial position r 0.08 m with a radial width of 0.2a = 0.1 m. For ≈ this mode, η /η < 1 for a broad, Ohmic-like ion temperature profile. For sufficiently i ic high radial temperature gradient and/or sufficiently high ion temperature, the Alfvénic ion temperature gradient driven mode [22] instability threshold will be approached, or possibly even exceeded, in the region where the mode amplitude is large, and so the mode can become unstable, due to a combination of energetic and thermal ion kinetic effects [32]. 4. Conclusions We have provided first evidence of beta induced Alfvén eigenmode activity in neutral beamheatedKSTARplasmas. The40kHz, n = 1observed modematches thefrequency of the accumulation point of the Alfvén continuum. By using the radial localisation of sawtooth inversion radius, we have been able to identify the radial position of the q = 1 surface, and using this, constrain the equilibrium. A detailed mode analysis reveals the presence of a core localised beta induced Alfvén eigenmode. Finally, a kinetic treatment of the mode marginal stability threshold shows a range of plausible ion temperature profiles for which the mode exctiation threshold is reduced, and the mode can be driven by energetic ions. This suggests that modeexistence could beused asa formof inference for temperature profile consistency in the radial interval of the mode, once beam drive Beta-induced Alfvén wave activity in KSTAR plasmas 9 1000 (a) V] e 500 T [i 0 0 0.1 0.2 0.3 0.4 r [m] 4 3 ηic (b) η / i 2 1 0 0 0.1 0.2 0.3 0.4 r [m] Figure 6. Variationof η /η threshold with different ion temperature profiles. Panel i ic (a) shows possible ion temperature profiles (solid) with core temperature matching crystallography data from discharge #4229, and panel (b) shows the corresponding profile of η /η . In both panels the dashed line corresponds to a possible ohmic ion i ic temperatureprofile,withτ takenfromdischarge#4229priortoNBIheating. Inpanel (b) the light line is V1 of the BAE in Fig. 5(a). | | and relevant damping contributions have been computed, thereby extending the tools of MHD spectroscopy. Our suggestion is complementary to recent work by Bertram et al ,[16] who suggested mode frequency could be used to infer the temperature at the resonant surface of a BAE mode in the H-1 heliac. Improvements in diagnosis and reliability of KSTAR plasmas will enable further exploration of new physics, in steady state plasma environments of up to 14MW of NBI heating. A priority is the introduction of kinetic and motional Stark effect constraints to EFIT, which will remove uncertainties in detailed modelling. In future work we hope to consolidate mode frequency variation with pressure and magnetic field strength. Judicious phasing of NBI during current ramp-up and ramp-down, together with new electron cyclotron current drive systems also offer the opportunity to influence the magnetic field configuration through co and counter injection. A wider sample set of modes, together with concurrent crystallography data, would enable a more thorough investigation of marginal stability thresholds and a quantitative study of mode drive and damping. Finally, as the position of the resonances are determined by the q profile and the density profile, similarity experiments with different edge q profiles and density profiles would illuminate the level of continuum damping. For instance, as the q profile flattens different m continuum mode branches are removed, and continuum damping is reduced. Alternately, as the density profile in the edge drops the location of the continuum resonance moves inward. In this case the radial separation between the resonances and gap mode decreases, the coupling of the eigenfunction to the continuum becomes stronger, and hence the continuum damping is increased. [33, 34] Beta-induced Alfvén wave activity in KSTAR plasmas 10 Acknowledgments ThisworkwaspartlyfundedbytheAustralianGovernmentthroughAustralianResearch Council grants FT0991899, DP1093797, as well as National Research Foundation of Korea grants NFR 2011-0018742 and NRAF-2012-0000590, and the RCUK Energy Programmeunder grantEP/I501045andtheEuropeanCommunities under thecontract ofAssociationbetweenEURATOMandCCFE.Theviewsandopinionsexpressed herein do not necessarily reflect those of the European Commission. The authors gratefully acknowledge the support of J. Kim from NFRI in assisting with access to KSTAR data, and the support of G. A. Huysmans from CEA Cadarache in the provision of CSCAS, HELENA and MISHKA codes. References [1] B.N.BreizmanandS.E.Sharapov. 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