Greenwald, M.J.

Hutchinson, I.H.

Lee, W.D.

Marmar, E.S.

Rice, J.E.

Snipes, J.A.

DSpace@MIT

Observations of Anomalous Momentum Transport in TokamakPlasmas with No Momentum InputW. D. Lee, J. E. Rice, E. S. Marmar, M. J. Greenwald, I. H. Hutchinson and J. A. SnipesPlasma Science and Fusion Center, MIT, Cambridge, MA 02139-4307AbstractAnomalous momentum transport has been observed in Alcator C-Mod tokamakplasmas. The time evolution of core impurity toroidal rotation velocity profiles hasbeen measured with a crystal x-ray spectrometer array. Following the L-mode to EDA(enhanced Dα) H-mode transition in both Ohmic and ICRF heated discharges, the en-suing co-current toroidal rotation velocity, which is generated in the absence of anyexternal momentum source, is observed to propagate in from the edge plasma to thecore with a time scale of order of the observed energy confinement time, but muchless than the neo-classical momentum confinement time. The steady state toroidal ro-tation velocity profiles in EDA H-mode plasmas are relatively flat and the momentumtransport can be simulated with a simple diffusion model. Assuming the L-H transitionproduces an instantaneous edge velocity source (which disappears at the H- to L-modetransition), the momentum transport may be characterized by a diffusivity, with val-ues of ∼ 0.07 m2/s during EDA H-mode and ∼ 0.2 m2/s in L-mode. These valuesare large compared to the calculated neo-classical momentum diffusivities. Velocityprofiles during ELM-free H-modes are centrally peaked, which suggests inward mo-mentum convection; the observed profiles are matched with simulations including aninward convection velocity of ∼ 10 m/s. In EDA H-mode discharges which developinternal transport barriers, the velocity profiles become hollow in the center indicatingthe presence of a negative radial electric field well in the vicinity of the barrier foot.1Rotation and velocity shear play important roles in the transition to high confine-ment mode (H-mode) [1-4] and in the formation of internal transport barriers (ITBs) [5]in tokamak discharges. Compared to energy and particle transport, however, there hasbeen considerably less effort addressing momentum transport. In a majority of toka-mak plasmas, the observed toroidal rotation is generated externally by neutral beaminjection. By measuring the rotation profiles from the associated beam diagnostics,and calculating the input torque profiles from the beam injection, momentum transportmay be characterized [6-13]. Momentum confinement is generally found to be anoma-lous, with a diffusivity, χφ, similar to the ion thermal conductivity,χi [6-13], but muchlarger than the neo-classical diffusivity (viscosity). The reliability of this type of analy-sis relies on the accuracy of the input torque calculations, and the inherent assumptionthat there is no additional source of momentum when the plasma enters H-mode. Alca-tor C-Mod ICRF [14] and Ohmic [15] H-mode discharges are found to have substantialspontaneous co-current toroidal impurity rotation (as high as 100 km/s, Mach number0.3) in spite of the fact that there is no momentum input. Similar observations havebeen made on other devices such as JET [16], COMPASS [17] and Tore Supra [18].Several attempts to explain the observed rotation in C-Mod have been made, basedon ICRF wave driven fast particle orbit shift mechanisms [19-20], turbulence [21-22]and sub-neo-classical [23] effects. The similarity of the rotation observed in ICRF andpurely Ohmic plasmas suggests that it is not due to ICRF wave or fast particle effects.The prediction of reversal of the rotation direction with high magnetic field side (HFS)off-axis ICRF absorption [19-20] has not been observed in the experiments [24]. Forthe turbulence driven theories [21-22], the sign of the rotation is correct, but the mag-nitude cannot be tested because the turbulence fluctuation levels are not measured. Thepredictions of the rotation magnitude and direction from the sub-neo-classical theoryagree with the measurements [23], but the calculated momentum diffusion time scaleis two orders of magnitude longer than what is observed. In order to gain a betterunderstanding of the mechanism generating the rotation in the absence of an externalsource, and in general to characterize momentum transport, temporally resolved veloc-ity profiles are needed. Previous off-axis measurements of the doppler shifts of argonx-ray lines on Alcator C-Mod were along sightlines with only a slight toroidal com-ponent [14], so only large rotation velocities could be seen, and only then with poortime resolution. The Alcator C-Mod x-ray crystal spectrometer system has now beenmodified with three fully tangential views, at r/a = 0.0, 0.3 and 0.6. These three rota-tion measurements are augmented by the velocity of magnetic perturbations associatedwith sawtooth oscillations recorded with an array of fast pickup coils [15].The rotation observations were obtained from the Alcator C-Mod tokamak, a com-pact (major radius 0.67 m, minor radius 0.22 m), high magnetic field (B T ≤ 8 T) devicewith strong shaping capabilities and all metal plasma facing components. Auxilliaryheating is available with up to 4 MW of ICRF heating power at 80 MHz. For theplasmas described here, the hydrogen minority heating was with 0 − π phasing, andthere was no momentum input. Shown in Fig.1 are the time histories of the (impurity)toroidal rotation velocities at three radii and the rotation of magnetic perturbations inpre- and post-cursors of sawtooth oscillations, for a 2.0 MW ICRF heated EDA H-mode [25] plasma. This 0.8 MA, 5.3 T discharge entered EDA H-mode at 0.655 s,2as indicated by the drop in the Dα signal, with a subsequent increase in the plasmastored energy and toroidal rotation velocity [14]. The velocity increase was first seen0.6 0.7 0.8 0.9-2024V Tor (104  m/s)r/a0.60.30.20.00.6 0.7 0.8 0.9t (s)01234(arb)Dα0.6 0.7 0.8 0.9020406080100WP (kJ)Figure 1: The plasma stored energy, impurity toroidal rotation velocity at three radii(red dots, green asterisks and purple diamonds for r/a = 0.0, 0.3 and 0.6, respectively),magnetic perturbation rotation (×s) at the sawtooth inversion radius (r/a ∼ 0.2), andthe edge Dα brightness for an ICRF heated EDA H-mode discharge.on the outermost spectrometer (r/a = 0.6), sequentially moving inside, suggesting anedge source of toroidal momentum which propagated in towards the center, with a timescale somewhat longer than τE, the energy confinement time. After about 150 ms (0.8s), the rotation settled to a value of ∼50 km/s (in the co-current direction), with a flatprofile. The fact that the rotation velocities for argon ions and m=1 perturbations arethe same in steady state bolsters arguments from collisional coupling calculations thatit is the bulk plasma rotation being measured [15]. During this steady phase of thedischarge, the central electron density was 2.8× 1020/m3 and the central electron tem-perature was 2.1 keV. Similar velocity profile evolution has been seen in purely OhmicEDA H-mode plasmas without ICRF heating. This time evolution and flat steady staterotation profile suggest that the momentum transport in EDA H-mode plasmas may becharacterized by a purely diffusive process. The situation is different in ELM-free H-mode plasmas, as can be seen in Fig.2. This 0.8 MA, 4.6 T discharge entered ELM-freeH-mode at 0.624 s, reverted to L-mode at 0.834 s, then re-entered ELM-free H-modeat 0.871 s. Following both L-H transitions, there was a rapid increase in the corerotation velocity and stored energy. In contrast to the EDA H-mode case, these rota-tion profiles are highly peaked [14], reaching ∼70 km/s in the core, in the absence of3external momentum input, and ∼15 km/s at r/a=0.6. This demonstrates momentumtransport up the velocity gradient and suggests the presence of an inward momentumpinch [11]. During the first ELM-free period, the central electron temperature was rel-0.6 0.7 0.8 0.9 1.0-20246V Tor (104  m/s)0.6 0.7 0.8 0.9 1.0t (s)0246(arb)Dα0.6 0.7 0.8 0.9 1.0020406080WP (kJ)Figure 2: The plasma stored energy, impurity toroidal rotation velocity at three radii(red dots, green asterisks and purple diamonds for r/a = 0.0, 0.3 and 0.6, respectively),magnetic perturbation rotation (×s) at the sawtooth inversion radius (r/a ∼ 0.2), andthe edge Dα brightness for an ICRF heated ELM-free H-mode discharge.atively constant at 1750 eV, while the electron density rose continuously from 1.1 to2.9× 1020/m3, maintaining a flat profile. Improved particle and impurity confinementis a characteristic of ELM-free discharges; whether this momentum peaking is relatedis an open question. In contrast to these peaked rotation profiles are the hollow profileswhich develop in internal transport barrier (ITB) plasmas. ITB discharges can be pro-duced with off-axis ICRF heating [24,26], provided the resonance location is outside ofr/a = 0.5, and that the plasma first enters EDA H-mode. These ITBs are characterizedby a strong peaking of the core electron density which evolves in conjunction with adecrease and reversal of the core toroidal rotation velocity [24,26]. Shown in Fig.3 arethe rotation time histories for a 4.5 T, 0.8 MA EDA H-mode plasma produced with 2.2MW of off-axis ICRF heating power at 80 MHz. Up until 0.85 s, this plasma exhibitedthe normal EDA H-mode rotation characteristics (Fig.1) with the velocity propagatingin from the outside, and the profile becoming flat across most of the plasma. After0.85 s, the core rotation inside r/a=0.5 (the location of the barrier foot) dropped andreversed direction simultaneously with a strong peaking of the electron density profilealso inside of r/a=0.5. The rotation at r/a=0.6, outside of the barrier foot, decreased40.6 0.8 1.0 1.2-10123V Tor (104  m/s) 0.60.30.00.6 0.8 1.0 1.2t (s)0.00.51.01.52.02.5Dα0.6 0.8 1.0 1.2020406080WP (kJ)Figure 3: The plasma stored energy, impurity toroidal rotation velocity at three radiiand the edge Dα brightness for an off-axis ICRF heated ITB discharge.more slowly and not so far, indicating a positive velocity gradient in the vicinity ofthe ITB foot. The radial electric field, Er, determined from the force balance equationand from calculations of the poloidal magnetic field, assuming neo-classical poloidalvelocity, was found to be -10 kV/m at r/a=0.3 (inside of the ITB foot) and +5 kV/m atr/a=0.6 (outside of the foot), and a lower limit of the E r gradient is ∼250 kV/m2 at 1.1s.The evolution of the velocity profile has been simulated using a simple source-freemomentum transport model∂∂tP +∇ · (−Dφ ∂∂rP − vcraP ) = 0 (1)with P = nimiVφ, where a is the minor radius and where the momentum diffusivity,Dφ, and the momentum convection velocity, v c, are free parameters to be determined.In cylindrical coordinates and subject to the boundary conditions of an edge rotation,V0, during H-modeVφ(a, t) =0, t < tL→HV0, tL→H ≤ t ≤ tH→L0, t > tH→L(2)and with the assumptions (observed in the electrons) of a flat ion density profile, and5spatially and temporally constant Dφ and vc, the toroidal rotation velocity, Vφ, profileevolution may be determined from a solution to∂∂tVφ −Dφ[∂2∂r2Vφ +(1r+vcraDφ)∂∂rVφ +2vcaDφVφ]= 0 (3)via an expansion in confluent hypergeometric functions.An example of a comparison of this model to the observed velocity time evolu-tion in an EDA H-mode plasma similar to that presented in Fig.1 is shown in the topframe of Fig.4. The time of the L- to H-mode transition was 1.11 s. The three curves1.00 1.10 1.20 1.30 1.40 1.50 1.60-20246V Tor (104  m/s)r/a0.60.30.0EDA0.4 0.5 0.6 0.7 0.8 0.9 1.0t (s)-202468V Tor (104  m/s) ELM-freeFigure 4: Comparison of model calculations (solid lines) with observed rotation timehistories for an EDA H-mode plasma (top frame) and an ELM-free H-mode plasma(bottom frame).represent the simulated rotation velocities at the radii of the three spectrometer views.For this case, Dφ was spatially constant with a value of 0.05 m2/s, and vc ≈ 0, whichcorresponds to a momentum confinement time, τ φ, of 150 ms. This momentum dif-fusivity is much greater than the neo-classical viscosity, χφ∼ρi2/τ ii∼0.003 m2/s forthis case, and the momentum transport may be characterized as anomalous. The mo-mentum diffusivity may also be determined for L-mode from the decay of the rotationvelocity after the H- to L-mode transition at 1.53 s; Dφ for the L-mode portion of thisdischarge was 0.20 m2/s, with τφ∼35 ms. From modeling of several ICRF and OhmicEDA H-mode plasmas, Dφ was found to be in the range from 0.05 to 0.10 m 2/s, with vc≈ 0. The simulations for the ELM-free discharge from Fig.2 are shown in the bottomframe of Fig.4, which is on the same time scale as the top frame for comparison. In this6instance Dφ was 0.40 m2/s with vc = 12 m/s, and τφ∼70 ms. This value of the pinchvelocity was necessary to match the quasi-steady peaked profile shape at 0.8 s, with a‘peaking factor’, S ≡ avc/2Dφ = 3.2, along with the overall rise time of the rotation.From the rotation decay after the H- to L-mode transition, a value of D φ∼0.25 m2/swas determined. From the rotation decays in many discharges after the H- to L-modetransition, Dφ for L-mode was determined to be in the range from 0.20-0.25 m 2/s, withvc = 0.The model of Eq.(3) cannot be strictly applied to the ITB case in Fig.3 because theelectron (ion) and argon density profiles [26] were peaking in the core during the barrierevolution. However, along with the negative rotation velocity inside of the barrier foot,this implies a negative momentum density in the core, which would require an outwardmomentum convection in the core during the ITB phase.In the progression from L-mode to EDA H-mode to ELM-free H-mode to ITBdischarges, the particle diffusivity steadily drops (particle confinement increases), ap-proaching neo-classical levels in the core in ITB plasmas. EDA H-mode plasmas havetemporally and spatially constant electron density profiles, ELM-free H-mode plasmasexhibit steadily rising electron density profiles which maintain a flat shape and ITBdischarges show a central peaking of the density profile [24,26] consistent with theneo-classical Ware pinch velocity. The same sequence of impurity confinement maybe characterized as highly anomalous in L-mode, with an impurity diffusivity D I ∼0.5 m2/s (τI ∼ 15-25 ms) and DI ∼ 0.1-0.3 m2/s in EDA H-mode with τ I ∼ 50-150ms [27]. For ELM-free H-mode plasmas, the impurity confinement is long (τ I ∼ 1 s)with reduced DI (∼ 0.05 m2/s) and substantial inward convection (10-100 m/s) at theedge [27]. In ITB discharges there is strong core impurity accumulation [26] with D I(∼ 0.02 m2/s) and vI (∼ 100 ms inward) close to the neo-classical values in the coreplasma. Energy confinement exhibits a somewhat similar progression with χ eff drop-ping from ∼1 m2/s in L-mode, to ∼0.5 m2/s in H-mode [25] and then as far as ∼0.1m2/s (near the neo-classical level) in the core plasma during ITB [26] operation. Mo-mentum confinement demonstrates some similarities in behavior; there is a decreasein the momentum diffusivity from 0.20-0.25 m 2/s in L-mode to the range 0.05-0.10m2/s in EDA H-mode. Also, in ELM-free H-mode there is a strong momentum pinch,with vc ∼10 m/s, analogous to the observations of impurity transport. In ITB dis-charges, particle, impurity and energy confinement may be characterized by transportcoefficients with values similar to neo-classical levels in the core. For these discharges,however, the momentum seems to be expelled from the plasma center, rather than hav-ing increased confinement. The reason that the momentum transport in ITB dischargesdoesn’t follow the behavior of particle and energy confinement may be because theseplasmas have a negative Er well in the core, and may be influenced by the fact thatmomentum is an odd moment of the distribution function, having directionality.The momentum transport in C-Mod has been found to be anomalous, with mo-mentum diffusivities much larger than neo-classical levels. The cause of the toroidalrotation, generated in the absence of a momentum source, as well as the varying veloc-ity profile shapes, remains unexplained.The authors thank A. Hubbard for Te measurements, S. Wolfe for magnetic equi-7librium calculations, J. Terry for Dα measurements, P. Bonoli and S. Scott for usefuldiscussions, S. Wukitch and Y. Lin for operation of the ICRF systems and J. Irby andthe Alcator C-Mod operations group for expert running of the tokamak. Work sup-ported at MIT by DoE Contract No. DE-FC02-99ER54512.References[1] K.C.Shaing and E.C.Crume, Phys. Rev. Lett. 63 (1989) 2369.[2] H.Biglari et al., Phys. Fluids B2 (1990) 1.[3] R.J.Groebner et al., Phys. Rev. Lett. 64 (1990) 3015.[4] K.Ida et al., Phys. Rev. Lett. 65 (1990) 1364.[5] K.Burrell, Phys. Plasmas 4 (1997) 1499.[6] S.Suckewer et al., Nucl. Fusion 21 (1981) 1301.[7] K.H.Burrell et al., Nucl. Fusion 28 (1988) 3.[8] S.D.Scott et al., Phys. Rev. Lett 64 (1990) 531.[9] A.Kallenbach et al., Plasma Phys. Contr. Fusion 33 (1991) 595.[10] N.Asakura et al., Nucl. Fusion 33 (1993) 1165.[11] K.Nagashima et al., Nucl. Fusion 34 (1994) 449.[12] K.-D.Zastrow et al., Nucl. Fusion 38 (1998) 257.[13] J.S.deGrassie et al., Nucl. Fusion 43 (2003) 142.[14] J.E.Rice et al., Nucl. Fusion 38 (1998) 75.[15] I.H.Hutchinson et al., Phys. Rev. Lett. 84 (2000) 3330.[16] L.-G.Eriksson et al., Plasma Phys. Contr. Fusion 39 (1997) 27.[17] I.H. Coffey, R. Barnsley, F.P. Keenan et al., in Proceedings of the 11th Colloquiumon UV and X-ray Spectroscopy of Astrophysical and Laboratory Plasmas, Nagoya,Japan, 1995, p.431, Frontiers Science Series No.15 (Editors: K. Yamashita and T.Watanabe), Universal Academy Press, Tokyo, Japan, 1996[18] G.T.Hoang et al., Nucl. Fusion 40 (1999) 913.[19] F.W.Perkins, et al., Phys. Plasmas 8 (2001) 2181.[20] L.-G.Eriksson and F.Porcelli, Nucl. Fusion 42 (2002) 959.[21] K.C.Shaing, Phys. Rev. Lett. 86 (2001) 640.[22] B.Coppi, Nucl. Fusion 42 (2002) 1.[23] A.L.Rogister, et al., Nucl. Fusion 42 (2002) 1144.[24] J.E.Rice et al., Nucl. Fusion 41 (2001) 277.[25] M.Greenwald et al., Nucl. Fusion 37 (1997) 793.[26] J.E.Rice et al., Nucl. Fusion 42 (2002) 510.[27] J.E.Rice et al., Phys. Plasmas 4 (1997) 1605.8

Observations of Anomalous Momentum Transport in Tokamak Plasmas with No Momentum Input

http://dspace.mit.edu/bitstream/1721.1/94042/1/03ja011_full.pdf

Observations of Anomalous Momentum Transport in Tokamak Plasmas with No Momentum Input

Abstract

Similar works

Full text

Available Versions

DSpace@MIT