Energetic-Ion Driven Alfvén Eigenmodes in Large Helical Device Plasmas with Three-Dimensional Structure and Their Impact on Energetic Ion Transport K. Toi, S. Yamamoto 1), N. Nakajima, S. Ohdachi, S. Sakakibara, C. Nührenberg 2), M. Osakabe, S. Murakami, K.Y. Watanabe, M. Goto, K. Kawahata, Ya.I. Kolesnichenko 3), S. Masuzaki, S. Morita, K. Narihara, Y. Narushima, Y. Takeiri, K. Tanaka, T. Tokuzawa, H. Yamada, I. Yamada, K. Yamazaki and LHD Experimental Group National Institute for Fusion Science, Toki 59-5292, Japan 1) Nagoya University, Nagoya 464-863, Japan 2) Max-Planck-Institut fur Plasmaphysik, Greifswald, Germany 3) Institute of Nuclear Research, Kiev 368, Ukraine 8th IAEA TCM on Energetic Particles in Magnetic
Outline 1. Introduction & Motivation 2. Exciation of Alfvén Eigenmodes(AEs) 2.1 Core-localized TAE with even & odd parity 2.2 Transition of the core-localized TAE to global AEs(GAEs) 2.3 Observation of helicity-induced Alfvén eigenmodes(haes) 3. Impacts of AEs on Transport of Energetic Particles & Bulk Plasma 3.1 Enhanced radial transport of energetic ions by TAEs 3.2 Formation of internal transport barrier induced by TAEs 4. Summary
Introduction & Motivation Interaction between energetic ions and MHD perturbations is intensively being studied in major tokamaks because of importance of alpha particle confinement in a burning plasma. Significant progress of Alfvén eigenmode (AE) physics has been made. However, the stability of AEs and impacts of AEs on transport of energetic ion & bulk plasma are still important issues to be clarified toward burning plasma experiments (BPXs). Studies of energetic ion driven AEs are also important for helical systems. These studies in three-dimensional toroidal plasmas such as LHD plasmas would provide powerful knobs to clarify the above issues in Alfvén eigenmode physics for BPXs.
Magnetic Configuration of LHD Rotational Transform ι/2π ( =1/q ) 1.6 1.4 1.2 1.8.6.4.2.%-beta 1.12%-beta 1.61%-beta 2.12%-beta 2.66%-beta.2.4.6.8 1 1.2 ρ 3D-configuration: The field strength on the magnetic surface is nonuniform in both poloidal & toroidal directions. q-profile: Negative shear configuration in the edge, and change to positive shear in the core with the increase in the toroidal beta.
Shear Alfvén Spectra in 3D-Configuration Shear Alfvén spectral gaps in toroidal 3D-plasmas: Magnetic field strength for LHD with l=2 & N=1 is dominated with the component of cos(2θ-nφ ). two cylindrical Alfvén branches intersect and generate gaps: ω= k //m,n V A = - k //m+µ,n+νn V A µ=1,ν=: TAE; µ=2,ν=: EAE; µ=2,ν=1: HAE21 etc. gap frequency : f (µ,ν) = Nνq* - µ V A /(4πRq*)~Nq*f TAE gap position : B/ B o=1+ µ,ν ε B µ,ν (ψ)cos(µθ νnφ) q*=(2m+µ)/(2n+νn) /2 f(µ,ν) gap half-width : f~ ε (µν) B -ε(µν) g resonance condition : V b// /V A =1/[1±2/(νNq*-µ)] N. Nakajima, C.Z. Cheng & M. Okamoto, Phys. Plasma B(1992)
Excitation of Energetic-Ion- Driven Alfvén Eigenmodes
Wide Parameter Scan for AEs-studies in LHD NSTX Excitation of energetic ion driven AEs depends upon characteristic parameters <β b// > and V b// /V A. <β b// > (%) LHD 1 DIII-D ITER.1 JT-6U JET TFTR CHS W7-AS.1.5 1 1.5 2 2.5 3 V b// /V A In LHD, these parameters are scanned over very wide range including ITER parameters, without suffering from current disruption, where E in 18 kev hydrogen beam.
Excitation Range of TAEs & R-TAEs TAEs are excited via fundamental and sideband excitations V b// /V A ( 1/3). R-TAEs ( or EPMs ) are excited from slightly lower V b// /V A (.2). Threshold for <β b// > :.1 % for TAEs and.1 % for R-TAEs (EPMs)
Observation of Core Localized & Global TAEs In the phase before t=1.8s, n=1 and n=2 TAEs are observed. From comparison with shear Alfvén spectra, n=1 TAE: core localized type n=2 TAE: global type n=1 mode consists of a low frequency mode and a slightly higher frequency one whose amplitude is fairly low.
Comparison of Observed TAEs with a Full 3D- Code CAS3D3 Results (1) n=1 C-TAEC Shear Alfvén spectra for n=1 mode at t=1.8 s For f exp = 61 khz: odd parity s~ρ 2 Preliminary! D Case: polidal mode coupling alone 3D Case: including of toroidal mode coupling Global mode calculation by CAS3D3 : Eexistence of core-localized TAEs (C-TAEs) inside the m~2,3/n=1 TAE gap. The observed mode is C-TAEs. Damping by high-n continuum is very week. For f exp = 52 khz: even parit s~ρ 2 Preliminary!
Comparison of Observed TAEs with CAS3D3 Results (2) n=2 G-TAEG Shear Alfvén spectra for n=2 mode at t=1.8 s CAS3D3: global TAE (G-TAE) composed a few Fourier modes around the m~3,4/n=2 TAE gap. The observed n=2 mode is thought to be G-TAEs at the m~3,4/n=2 TAE gap. Preliminary! (n = -2,2 γ ~ )
Eigenmode transition from TAE to GAE during time evolution of ι-profile When the minimum ι() goes through.4, m~2,3/n=1 TAE is converted to m=3/n=1 GAE and m=2/n=1 mode. m=2/n=1 mode will suffer from strong continuum damping, and it is consistent with exp. Results. This phenomenon is similar to RS-AEs in a RS-plasma of JT-6U.
Observation of new AEs in 3D-configuration (Helicity-Induced Alfvén Eigenmodes) At low Bt.7T, coherent magnetic fluctuations less than 5 khz in LHD are observed. Its frequency is about 8 times higher than TAE gap frequency. They will be Helicity induced Alfvén Eigenmode (HAE) whose frequency is by about Nq-times higher than TAE-frequency.
Characters of HAEs The frequencies of these modes are scaled with the Alfvén velocity. Alfvén eigenmode
Comparison with Shear Alfvén Spectra including Toroidal Mode Coupling Shear Alfvén continuum (N f = 2) Expanded view HAE gap is generated by the toroidal mode coupling in addition to poloidal mode coupling. New continua are generated inside HAE gap by the lack of helical symmetry. The observed frequency lies inside the HAE gap in the edge (ρ>.7). HAE and TAE are excited in the edge where the energetic ion pressure gradient will be steep.
Excitation Condition of HAEs The threshold of HAEs : <β b// > is.5 % HAEs were detected in the range of 1.5 < v b// /v A < 2.4. Magnetic shear may be important for the excitation of HAEs in LHD.
Effects of energetic ion driven AEs on energetic ion & bulk plasma transport
54 Effects of energetic ion driven AEs on energetic ion confinement wp@27233-hf-linfit 4 1-5 Wp (kj) 53 52 51 5 Wp 2 1-5 49-21 -5 1.1 1.2 1.3 1.4 time (s) b θ b θ (a.u.) - D Energy Balance of Beam & Bulk Plasma dwb// W W + b// + b// = P dt τs τc dwp Wp + = Wb// dt τe τs The bulk stored energy (diamagnetic signal) is depressed slightly by each TAE burst.
55 Effects of energetic ion driven AEs on energetic ion confinement τ * τ ( τ - τ ) t τe( τs τ ) t Wp/ Wp() = * s * exp(- ) + * exp(- τs τs ( τe τ* ) τ* τs ( τe τ* ) τ where = τ* δt = 1 ms, τ c = 3 ms (during Burst) =1 s ( between Burst) τ s = 37 ms, τ E = 16 ms TAE burst ττ s c τs+ τc Experimental ( during TAE burst : t t TAE) t ttae Wb// / Wb// () 1-exp(- ) for τc= τ τ* τc ttae 1 ms, τc 2 3 ms E Wp (kj) 5 45 Calculation 4.1.2.3.4.5 t' = t - 1.216 ( s ) Bursting TAEs transiently enhance energetic ion loss, and the loss rate~3-5%
Change of Charge-Exchange Neutral Flux across a TAE Burst ( M. Osakabe: this conf.) Neutral Flux Intensity Ratio Neutral Flux [a.u.] 1.8 1.6 1.4 1.2 1.8.6 5 1 15 2 2 1 6 1.5 1 6 1 1 6 5 1 5 Energy[keV] 5 1 15 2 Energy[keV].941 [s].945 [s] Neutral Flux [a.u.] Neutral Flux [a.u.] Mirnov [a.u.] 1.5 -.5-1 2 1 6 67keV 1.5 1 6 1 1 6 5 1 5 2 1 6 1.5 1 6 1 1 6 5 1 5 42keV 27keV 13keV B θ RMS 151keV 138keV 86keV LHD#31221.925.93.935.94.945.95.955 Time [sec] The CX Flux in 1 < E(keV) < E in decreases by about 2% by the burst, and that in 4 < E(keV) < 1 increases up to about 7 %.
Temperature Rise in Divertor Region in a Plasma with TAE bursts ( M. Osakabe: this conf.) The right hand side diverter region indicates larger temperature rise than that in the left-hand side. This tendency agrees with the fastion loss calculation by T. Watanabe. The temperature rise rate during TAE-burst (4[K/s]) is 8 times larger than that between the burst (5[K/s]). IR-measurement in diverter region shows the temperature rise by TAE bursts, which will indicate the loss of fast ions.
Effects of energetic ion driven AEs on bulk plasma confinement(1) δt = 1 ms; τ c = 3 ms (during Burst) Wp (kj) 54 53 52 51 5 W p ρ=.1 ρ=.36 ρ= +.41 ρ= +.65 ρ=.71 ρ= +.89 49 1 1 1.1 1.2 1.3 1.4 time (s) wp@27233 16:54:18 23/1/7 n e L 2.5 2 1.5 n e L (1 19 m -2 ) Wp(kJ) 4.1.2.3.4.5 t' = t - 1.216 ( s ) Every TAE burst Wp transiently increases. This suggests a possibility of global confinement improvement. FIR data indicate the transient formation of internal transport barrier. The Wp increase is thought to be due to increase in core plasma energy. 55 5 45 τ s = 37 ms; τ E = 16 ms TAE Burst Wp(exp) W tail (cal) Wp(cal) 14 12 1 8 6 W tail (kj)
Effects of energetic ion driven AEs on bulk plasma confinement(2) 62 wp@27233-hf-linfit 6 Wp (kj) 58 56 54 52 W p b θ 1.7 1.8 1.9 2 2.1 1 1-5 -1 1-5 b θ (T) [2< f < 1 khz] time (s) A possible candidate mechanism is flow shear generation caused by non-ambipolar energetic ion loss. Frequent TAE burst leads to continuous rise in Wp.
Summary Alfvén eigenmodes are studied over the very wide parameter range including ITER parameter range. Core-localized type (C-) and global type (G-)TAEs are observed. Moreover, C-TAEs with odd parity as well as even parity are observed. Results obtained with CAS3D3 code show good agreement with these data. Eigenmode transition from C-TAEs to two GAEs was observed, which is very similar to the phenomenon takes place in a negative shear tokamak. Helicity induced AE (HAE) was detected for the first time. This discovery would contribute to compact stellarator researches and also AE physics in a tokamak plasma. Bursting TAEs induce appreciable amount of energetic ion loss (~3 %-4%) at low Bt<.75T. TAE-induced loss triggers the formation of transport barrier,
Appendices
Basic Study of External Excitation of TAEs in Low Temperature Plasma of CHS Example of plasma responses to imposed magnetic perturbations with sweeping frequency G. Matsunaga et al., Submitted to PRL Plasma antenna technique for excitation of shear Alfven wave perturbations
Detection of Eigenfrequency and Damping rate of Excited TAE Observed frequencies agree well with the TAE gap frequency. Measure radial profile of the excited n=2 mode has a peak at
Energy of NPA channel [kev] Mirnov [a.u.] 1.5 -.5-1 15 1 5 Effect of a TAE burst on CX Neutral Flux ( M. Osakabe: this conf.) B θ RMS LHD#31221 Peak Position of Increased Neutral Flux Fitted Curve to Exponential Function.925.93.935.94.945.95.955 Time [s] Decay Time = ~4.3ms Radial Distribution Probability Density of Particles Circulating at <ρ> =.55 [1/ ρ] orbit Slowing Down Time of Passing- Particleson NPA Sight Line: τ (86->54keV) [s] s 3 2.5 2 1.5 1.5.6 3.5 LHD#31221 at t=.94s The particle s orbit has higher probability of staying around the n=2/m=3~4 TAE gap. Frequency (khz).5.4.3.2.1 15 1 5 τ s (86->54keV) n=2/m=3~4 n=2/m=2~3.2.4.6.8 1 ρ, <ρ > orbit τ =2.1ms exp. ( τ =4.3m s) decay f TAE (m /n~2/2)
Particle Orbit Classes in CHS (LHD) Guiding center orbit Banana orbit in a tokamak does not exist in CHS ( LHD) configuration. Usual fishbones observed in tokamaks would not be excited. In CHS (LHD), the initial pitch angle of most ions will be in the range of χ=2-5 because of tangential injection.
Hit Points of Lost Energetic Ions on the Vacuum Vessel Surface in CHS Transient loss of fast ions was detected only in the outwardshifted plasmas. Orbit calculations have revealed that energetic ions are lost in poloidally and toroidally localized zone for both inward and outward shifted configurations. Detectors of lost ions should be placed at this narrow zone where lost fast ions would arrive. 36 27 18 9 R ax =.92 m; ρ start =.3 &.5; E=4 kev ρ=.3 ρ=.5-18 -9 9 18 toroidal angle φ
Dependence of energetic ion loss flux on fluctuation amplitude (CHS) Relation between ion loss flux and fluctuation level: δγ i (b fluc ) s s=1: Resonant convec. loss s=2: Diffusive transport s>2: Destruction of magnetic surface For fast ions in χ=4-5 deg. s > 5 or δγ i u(b θ -b crit ): threshold This may link to loss cone. b θ (T) 2 1-5 1 1-5 -1 1-5 -2 1-5 δγ i (a.u.) 4 3 2 1 #6998 Rax=99.5 cm, Bt=.88 T χ = 4-5 deg. 8 85 9 95 1 15 11 115 12 Time(ms) Step function like δγ i ~ (b θ_rms ) 5 2 15 1 5-1 5 1-6 1 1-5 1.5 1-5 2 1-5 (T) b θ_rms