Effects of Alpha Particle Transport Driven by Alfvénic Instabilities on Proposed Burning Plasma Scenarios on ITER G. Vlad, S. Briguglio, G. Fogaccia, F. Zonca Associazione Euratom-ENEA sulla Fusione, C.R. Frascati - C.P. 65 - I-00044 - Frascati, Rome, Italy and M. Schneider Ass. Euratom-CEA, CEA/Cadarache, 13108 Saint Paul-lez-Durance, France G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 1
Introduction Next generation Tokamaks (e.g., ITER), should approach the so called ignition condition: heating due to fusion α-particles (hot particles) able to sustain the burning plasma Good confinement of the α-particles is crucial in getting such condition Fusion α-particles are generated with v Η v A =B/(4πn i m i ) 1/2 and peaked density profile free-energy source for the resonant destabilization of shear Alfvén modes (TAE, EPM, ) Interaction of such modes with energetic-particle can induce outward α-particle transport G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 2
Introduction-cont. Transport codes aimed to define burning-plasma scenarios do not include the possibility of Alfvén mode - α-particle interactions Are the proposed scenarios consistent with the α-particle collective dynamics? Which are the effects on α-particle profiles and confinement? Aim of our investigation: to check the consistency of several ITER scenarios by means of particle simulation techniques If α-particle pressure profile in presence of fully saturated modes is: close to initial one different from initial one scenario is consistent scenario could be inconsistent G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 3
The Model Hybrid MHD-Gyrokinetic Code (HMGC): thermal plasma described by zero pressure reduced O(ε 3 ) Magnetohydrodynamic (MHD) equations (circular shifted magnetic flux surfaces); energetic particles described by nonlinear guiding-center Vlasov equation (k ρ Η <<1) solved by particle-in-cell (PIC) techniques; energetic particles are loaded according to an isotropic slowingdown distribution function, with birth energy E fus =3.52 MeV and critical energy E crit 33.0 T e (r) (Stix); assume n D =n T =n i /2 and n i =n e. energetic particles and thermal plasma are coupled through the α particle pressure tensor, which enters the MHD momentum equation; mode-mode coupling neglected (only particle nonlinearities retained). G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 4
ITER scenarios Three different ITER scenarios have been considered: a) the reference monotonic-q scenario ( scenario 2, SC2, from ITER Joint Work Site): inductive, 15 MA scenario, with 400 MW fusion power and fusion yield Q=10; b) the reversed shear scenario ( scenario 4, SC4, from ITER Joint Work Site): steady-state, 9 MA, weak-negative shear, with about 300 MW fusion power and Q=5; q min 2.4 and r qmin /a 0.68. c) a recently proposed hybrid scenario ( scenario H, SCH, from CRONOS package simulations): 11.3 MA weak-positive shear, with about 400 MW fusion power and Q 5. Simulations are performed retaining on-axis equilibrium magnetic field, major and minor radii, the safety-factor q, the plasma density n e, the electron temperature T e and the α-particle density n H. G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 5
Equilibrium profiles and parameters SC2 SC4 SCH a(m) 2.005 1.859 1.8017 R 0 (m) 6.195 6.34 6.3734 q 95 3.14 5.13 3.22 B T (T) 5.3 5.183 5.3 n e0 (10 20 m -3 ) 1.02 0.73 0.72 T e0 (kev) 24.8 23.9 30.0 n H0 (10 18 m -3 ) 0.78 0.62 0.88 β H0 (%) 1.10 0.92 1.37 α H,max = 0.085 0.600 0.155 max{-r 0 q 2 β H} r α H,max /a 0.25 0.50 0.60 G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 6
Linear dynamics: SC2 Several toroidal mode numbers n are found to be unstable. The mode is located around r α H,max /a in radius, and below the Alfvén continuum in frequency. 0.12 γ/ω A0 0.1 0.08 0.06 0.04 n=2 0.02 n=4 n=6 0 0 0.5 1 1.5 2 n H0 /n H0, SC2 2.5 3 3.5 G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 7
Linear dynamics: SC2-cont. Power spectra of scalar-potential fluctuations in the [r,ω] plane, during the linear phase. Upper and lower Alfvén continuous spectra are also plotted (black). n=2 n=4 n=6 G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 8
Linear dynamics: SC4 Toroidal mode number n=2 is found to be the most unstable. The mode is located close to r qmin /a radius, and close to the tip of the lower Alfvén continuum in frequency. A second weaker mode appear in the toroidal gap around r/a 0.4 0.5, for n=2. 0.2 γ/ω A0 0.15 0.1 n=2 0.05 n=6 n=4 0 0 0.5 1 1.5 2 2.5 3 n H0 /n H0, SC4 G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 9
Linear dynamics: SC4-cont. Power spectra of scalar-potential fluctuations in the [r,ω] plane, during the linear phase. n=2 nominal n H value n=4 n H0 1.17 n H0, SC4 n=6 n H0 2.33 n H0, SC4 G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 10
Linear dynamics: SCH This scenario is stable at nominal n H0 =n H0, SCH value. At higher n H0 the mode appears close to the magnetic axis, for n=2; at r α H,max /a, where the local drive is maximum, for higher n. 0.2 γ/ω A0 0.15 0.1 n=8 0.05 n=6 n=4 n=2 0 0 1 2 3 4 n H0 /n H0, SCH G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 11
Linear dynamics: SCH-cont. Power spectra of scalar-potential fluctuations in the [r,ω] plane, during the linear phase. n=2 n=4 n=8 n H0 3.27 n H0, SCH n H0 3.27 n H0, SCH n H0 2.45 n H0, SCH G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 12
Linear Dynamics: localization Radius: the mode is localized where the local drive α H has its maximum Frequency: expected wave-particle resonances (ε<<1, small orbit width, well circulating/deeply trapped particles): ω = ωt l = 1 transit frequency: precession frequency: precession-bounce frequency: ω = ω d precession-bounce resonance seems to dominate (?). E fus 2m H 1 q(r)r 0 E fus m H R 0 ω ch nq(r) r ω = ω d + lω B,l = ±1 ω = ω d +ω B ω B 1 R 0 q(r) ω = ω d ω B SC2, n=2 SC2, n=4 SC2, n=6 E fus m H ( r ) 1/2 R 0 G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 13
Nonlinear dynamics: phenomenology Maximum gradient of rβ H shifts outward first steepening (convective phase, avalanche) then relaxing (diffusive phase: saturated e.m. fields scatter α-particles) rβ Η r max Linear phase 0.5 0.6 0.7 0.8 r/a rβ H Convective phase r max 0.5 0.6 0.7 0.8 r/a rβ H Diffusive phase r max 0.5 0.6 0.7 0.8 r/a G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 14
Nonlinear dynamics: SC2, SC4 SC2 (n=4): scarcely affected by nonlinear saturation (mode localization close to linear-phase one); continuum damping barrier prevents the mode to displace outwards. at saturation SC4 (n=2): the mode is located around q min ; α particles have larger orbit width (higher q): larger convection and diffusion. G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 15
Nonlinear dynamics: SC2, SC4-cont. Define r y (t) as the radial position of the surface containing a fraction y of the α- particle energy: y = 0 1 0 r y rβ H (r;t)dr rβ H,init (r)dr 0.627 0.8 r 95% /a r 95% /a 0.626 0.625 0.624 0.623 0.622 0 100 200 300 400 500 600 700 0.011 β H0 SC2, n=4 SC4, n=2 tω A0 0.76 0.72 0.68 0.64 0 100 200 300 400 500 600 0.0095 β H0 tω A0 Time behavior of central α-particle beta, β H0 : 0.0105 0.01 0.0095 0.009 0 100 200 300 400 500 600 700 tω A0 0.009 0.0085 0.008 0 100 200 300 400 500 600 tω A0 G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 16
Nonlinear dynamics: SC2, SC4-cont. Increase artificially β H0 to investigate the dependence of convection and diffusion on intensity of energetic particle drive. SC2, n=4 SC4, n=2 0.68 0.85 r 95% /a r 95% /a 0.67 just-after-convection 0.66 0.80 just-after-convection 0.65 0.75 0.64 0.70 0.63 initial initial 0.65 0.62 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 β H0 /β H0, SC2 β H0 /β H0, SC4 Characterize diffusion by: τ diff,95% r 95% [ r 95% / t] -1, τ diff,βh0 β H0 [ β H0 / t] -1 10-3 (τ diff ω A0 ) -1 τ-1 diff, βη0 10-4 10-5 10-6 10-7 τ -1 diff, 95% 0 0.5 1 1.5 2 2.5 3 3.5 β H0 /β H0, SC2 10-2 (τ diff ω A0 ) -1 10-3 10-4 τ -1 diff, 95% τ -1 diff, βη0 0 0.5 1 1.5 2 2.5 3 β H0 /β H0, SC4 G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 17
Conclusions Standard ITER monotonic-q scenario (SC2): unstable w.r.t. α-particle driven Alfvén modes; nonlinear saturation produces negligible modifications to the α- particle radial profile: consistent scenario. Reversed shear scenario (SC4): unstable; appreciable changes to the α-particle radial profile: possibly inconsistent scenario. Hybrid scenario (SCH): stable (safety margin of 1.6 in the central α-particle pressure). Caveat: multiple toroidal-mode-number dynamics could enforce α transport; dynamic approach to the reference α-particle pressure could regulate the stronger energetic particle mode dynamics via nonlinear effects of weaker modes. G. Vlad et al., IT/P3-31 20th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 18