Predictions of fusion α-particle transport due to Alfvén eigenmodes in ITER

Transcription

1 Predictions of fusion α-particle transport due to Alfvén eigenmodes in ITER M. Fitzgerald, S.E. Sharapov, P. Rodrigues 2, A. Polevoi 3, D. Borba 2 2 Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal 3 ITER Organization, St Paul-lez-Durance Cedex, France CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority. This work was part-funded by the RCUK Energy Programme [grant number EP/I501045] and the European Union s Horizon 2020 research and innovation programme.

2 Physics exposition MHD shear Alfvén spectrum in tokamaks with focus on TAE mode Wave particle interaction ITER tokamak calculations HAGIS code description Properties of scenario modelled Results Outline Slide 1

3 Stability and the MHD spectrum For tokamaks to operate as fusion devices, sufficiently steady conditions need to be established through macroscopic force balance. The bulk of the plasma is hot and Maxwellian and largely governed by ideal MHD force balance j B = p To assess the stability of the MHD force balance, it is important to consider first the linear response to small perturbations. The self-adjoint linear MHD response F ξ = ρω 2 ξ is directly analogous to the eigenvalue problem of quantum mechanics, yielding a discrete spectrum of real eigenvalues ω 2, corresponding to stable oscillations (waves) ω 2 > 0 or exponentially growing/decaying deformations (instabilities) ω 2 < 0. In addition to the discrete spectrum, a continuum of modes exist corresponding to singularities in the MHD response. Slide 2

4 Cylindrical Shear Alfvén MHD continuum ω = ±k v A = ± B ρ m as labelled n = 3 m r B θ B n 2π L 5 6 B z B 7 8 Axial and angular symmetry mean that m and n are good quantum numbers for labelling the different modes in the shear Alfvén spectrum. Not proper eigenmodes, because their field vector components oscillate in an uncoordinated way. These waves phase mix and are heavily damped. r a Slide 3

5 Toroidal MHD continuum with TAE gap Far from crossing points: ω = k v A = ± B φ qr ρ m nq q = dφ dθ along a field line n = B~ 1 R Δv A~ r R ~O(ε) TAE band gap at Bragg frequency v A 2qR Δω~O(ε) r a Slide 4

6 Defects in the Fibre Bragg grating lead to gap modes Imperfection Gap mode In addition to B modulation between large and small radius, pressure, curvature and magnetic shear lead to an imperfection in periodicity of Alfvén speed. Discrete eigenmodes due to this imperfection known as Toroidal Alfvén Eigenmodes (TAE) exist with frequencies within the forbidden region. TAE band gap at Bragg frequency v A 2qR Because the TAE modes are found in the TAE band gap, TAEs are possible which do not readily damp energy to the Alfvén continuum. The high resonance quality factor/low damping of these modes can be readily seen in the simulated linear MHD response to an external antenna on JET (right). Huysmans, G. T. a. et al. (1995). Modeling the excitation of global Alfve n modes by an external antenna in the Joint European Torus (JET). Physics of Plasmas, 2(5), doi: / Slide 5

7 TAEs with MHD frequencies and mode structure are routinely observed on current experiments DIII-D tokamak [VanZeeland 2006] Can be nasty... DIII-D - TAE modes expelled 50% of beam power TFTR ejected particles burned a hole in a vacuum port. Van Zeeland, M. A. et al. (2006). Physical Review Letters, 97(13), doi: /physrevlett Weller, A. et al. (2001). Physics of Plasmas, 8(3), 931. doi: / Heidbrink, W. W. (2008). Physics of Plasmas, 15(5), doi: / White, R. B. et al. Physics of Plasmas, 2(8), doi: / W7-AS stellarator [Weller 2001] Slide 6

8 MHD modes are destabilised through inverse Landau damping by fast particles In a tokamaks with beam and/or RF heating, a non-maxwellian distribution of fast particles is present in addition to the thermal species. Drive or damping depends on gradients of distribution function (in space and velocity) near resonance The small resonant population is responsible for a perturbation to the fluid response, providing a modification to the (zero in MHD) growth rate The pressure contribution of the fast species is often small when compared to the thermal plasma (β fast β thermal ) Growth rates for TAE modes are typically: γ ω ~ resonance Super Alfvénic fast species Dawson, J. (1961). On Landau Damping. Physics of Fluids, 4(7), 869. doi: / Slide 7 v (or x)

9 Nonlinear wave-particle trapping v [O Neil(1965)] HAGIS deals with nonlinearities produced when fast particles are resonant and trapped in Alfvén modes This approximation is valid for small γ ω, β fast β thermal and where coupling with the continuum is weak (both satisfied well for TAE modes, verified by experiment and gyrokinetic modelling) Such weakly nonlinear modes are expressible in the form E(x, t) = A t E bulk (x, ω bulk )exp( iω bulk t) F [animation courtesy Matt Lilley] v F v x O Neil, T. (1965). Collisionless Damping of Nonlinear Plasma Oscillations. Physics of Fluids, 8(1965), doi: / Slide 8

10 ITER tokamak modelling ITER will pursue burning plasmas where Super Alfvénic alpha particles will be required to provide significant heating TAE modes can be driven unstable by alpha particles and neutral beam heating on ITER In the calculations that follow, we predict how important alpha driven TAEs are to the confinement of alpha particles. We include all relevant TAEs, the most important damping mechanisms, and retain all relevant nonlinear TAE effects (including avalanches). Slide 9

11 Contribution to BEAM RF neutrons Unfinished JET business: alpha driven TAEs in D-T JET time Beam damping other damping time α drive Sharapov, S. E et al. (2008). Burning plasma studies at JET. Fusion Science and Technology, 53(4), Core localised alpha driven modes with amplitudes δb r B 0 ~10 5 seen on TFTR tokamak Nazikian, R et al. (1997). Alpha-particle-driven toroidal Alfven eigenmodes in the tokamak fusion test reactor. Physical Review Letters, 78(15), doi:doi /PhysRevLett Slide 10

12 Main parameters of the ITER Q=10 baseline scenario used ITER baseline scenario: I P = 15 MA, B T = 5.3 T, R 0 = 621 cm, a = 200 cm, P NNBI = 16.5 MW (on-axis) MW (off-axis), E NNBI = 1 MeV, P ECRH = 6 MW at q=3/2 Plasma consists of D, T, He, and Be n D :n T = 50:50, n Be (r) = 0.02 n e (r). Transport code ASTRA was used for plasma parameters and profiles T e 0 = 24.7 kev, T i 0 = 21.5 β α dβ α d r a S. D. Pinches et al. Physics of Plasmas, 22:021807, Polevoi et al. J. Fusion Res. SERIES 5 (2002) 82 Slide 11

13 ITER baseline q-profile, shear and TAE gaps Shear Alfvén continuum q r q dq dr Normalised radius Two very distinct regions evident: core with nearly zero shear and high alpha particle gradient external with finite shear and fewer alpha particles Normalised radius Continuum crossing points. Colour gives m. Black line is β α Slide 12

14 Amplitude (arb.) Amplitude (arb.) ITER baseline TAE modes Amplitude (arb.) Amplitude (arb.) n = 29 m = 30 n = 29 Odd parity m = Normalised radius m = Normalised radius n = 29 m = 30 n = 16 m = 29 m = Even parity Normalised radius Normalised radius Slide 13

15 x R 3 HAGIS code equations Evolving particle phase coordinates [White & Chance (1984)] v R 2 FIXED MHD EIGENMODE STRUCTURE μ = 0 Evolving wave amplitude and phase [Berk & Breizman (1995)] [Candy et al. (1997)] White, R., & Chance, M. (1984). Hamiltonian guiding center drift orbit calculation for plasmas of arbitrary cross section. Physics of Fluids, 27, Berk, H.., Breizman, B.., & Pekker, M.. (1995). Simulation of Alfven-wave-resonant-particle interaction. Nuclear Fusion, 35(12), doi: / /35/12/i36 Candy, J., Borba, D., Berk, H. L., Huysmans, G. T. a., & Kerner, W. (1997). Nonlinear interaction of fast particles with Alfve n waves in toroidal plasmas. Physics of Plasmas, 4(7), doi: / Slide 14

16 Some inputs TAE modes with toroidal mode numbers 1 n 35 were computed with the MISHKA code 129 modes were found, 3-5 different TAEs for each n Kinetic damping effects of the modes due to thermal D and T ions, He ash, and electrons were obtained from linear code CASTOR-K 1 Analytical estimates for radiative damping of lower frequency TAEs gives γ d ω = 1.3% 1 Rodrigues et al. Nuclear Fusion, 55(8), Slide 15

17 Isolated mode linear growth rates from HAGIS CLTAE even: black CLTAE odd: blue External or Global mode: red Slide 16

18 Nonlinear saturation of 88 modes n=15-35, no damping Individual mode simulations Multi-mode simulation All differences between the two figures are due solely to energy coupling of different modes via common alpha particle population Core localised modes are amplified over global modes Slide 17

19 Effects of damping on a single mode γ L ω = 5% γ L ω = 0.6% γ D γ L = 0.5 Rapid modulation of amplitude is characteristic of damping of wave near saturation Saturation is reduced by ~50 for γ D γ L 0.5 γ D γ L = 0.64 Wong, H. V., & Berk, H. L. (1998). Growth and saturation of TAE modes destabilized by ICRF produced tails, 2781(1998), doi: / Slide 18

20 Convective transport of holes and clumps MAST TAEs v JET TAEs [animation courtesy Matt Lilley] x F F HAGIS ITER calculation Berk, H., Breizman, B. et al. (1997). Spontaneous hole-clump pair creation in weakly unstable plasmas. Physics Letters A, 234(3), doi: /s (97) Pinches, S. D. et al.(2004). Spectroscopic determination of the internal amplitude of frequency sweeping TAE. Plasma Physics and Controlled Fusion, 46(7), S47 S57. doi: / /46/7/s04 Slide 19 v v

21 88 modes n=15-35 coupled with Landau damping 10 odd CLTAE modes, γ d ω = 2% < β α > = 0. 8% ( different scenario a factor of ~8 larger), circular geometry Saturation achieved significantly diminished due to Landau damping, much as for the single mode. Saturation here means steady amplitude due to balance of free energy in gradient and damping. When this energy is exhausted, the mode will decay. Candy, J., Borba, D., Berk, H. L., Huysmans, G. T. a., & Kerner, W. (1997). Physics of Plasmas, 4(7), Slide 20

22 88 modes n=15-35 coupled with Landau damping No holes and clumps evident Only CLTAE modes are causing redistribution Flattening of profile will not be complete due to dimensionality, and also happens on very long timescales due to low nonlinear bounce frequency and thus slow phase mixing Candy, J., Borba, D., Berk, H. L., Huysmans, G. T. a., & Kerner, W. (1997). Physics of Plasmas, 4(7), Slide 21

23 108 modes n=10-35 with Landau and radiative damping Simulations including lower n modes and radiative damping, give basically the same results. We use those amplitudes in simulations below δb r B P ζ is related to average radius Three resonant test particle orbits at 980keV are presented above in the presence of the computed TAE activity Widths of stochastic spreading are 7cm for the core orbit, 1cm for the global orbit, and 1mm for the quiet region in between A TAE transport barrier near the quiet region is responsible for suppressing avalanche effects (coupling between core and edge localised modes) Slide 22

24 Artificially increased amplitude by x50 δb r B Mode amplitudes were scaled artificially by a factor of 50 (comparable to the change expected by ignoring Landau damping) and the test particle orbits were followed again Both external and internal regions are stochastic and 50cm wide. BUT transport barrier still evident Slide 23

25 Artificially increased amplitude by x100 δb r B Once phase space islands are large enough to overlap, orbits become chaotic FFT gives ~ 1 f Pink noise Berk, H. L., Breizman, B. N., & Ye, H. (1993). Map model for nonlinear alpha particle interaction with toroidal Alfve n waves. Physics of Fluids B: Plasma Physics, 5(5), doi: / Slide 24

26 129 modes n=1-35 with damping Last completed simulation with all modes found in range n=1-35 NO damping used for modes n=1-10 Rogue n=9 mode has resulted but still negligible Slide 25

27 129 modes n=1-35 with damping No change in radial redistribution from 108 and 88 mode case, or indeed, when considering CLTAE only Slide 26

28 129 modes n=1-35 with damping Quiet region still evident between core and external modes and we conclude that the alpha transport barrier is still present when modes n=1-35 are included Slide 27

29 Summary for alpha driven ITER TAE modes The baseline 15 MA ITER scenario with low shear and q(0)~1 has two distinct regions with very different density of the TAE gaps: Core region, r/a<0.5, where almost all alphas are, but TAE-gaps are scarce and only highly-localised low-shear TAEs could exist, External region, r/a>0.5, where alpha-pressure is low, global TAEs exist For the 129 TAEs found in range 1 n 35, a transport barrier is found to form at r 0. 5 for this q profile which inhibits radial a stochastic alpha transport from core to edge global modes when the amplitudes are below δb r B The amplitudes attained in HAGIS nonlinear simulation of many modes, when including the effects of Landau and radiative damping, were found to be δb r , below the threshold for the transport B 0 barrier to breakdown by at least a factor of 50, thus radial redistribution was limited to a small region where the core modes were found Slide 28