Effects of Alpha Particle Transport Driven by Alfvénic Instabilities on Proposed Burning Plasma Scenarios on ITER

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1 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 I Frascati, Rome, Italy and M. Schneider Ass. Euratom-CEA, CEA/Cadarache, Saint Paul-lez-Durance, France G. Vlad et al., IT/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 1

2 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/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 2

3 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/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 3

4 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/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 4

5 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 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/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 5

6 Equilibrium profiles and parameters SC2 SC4 SCH a(m) R 0 (m) q B T (T) n e0 (10 20 m -3 ) T e0 (kev) n H0 (10 18 m -3 ) β H0 (%) α H,max = max{-r 0 q 2 β H} r α H,max /a G. Vlad et al., IT/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 6

7 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 γ/ω A n= n=4 n= n H0 /n H0, SC G. Vlad et al., IT/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 7

8 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/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 8

9 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 , for n= γ/ω A n= n=6 n= n H0 /n H0, SC4 G. Vlad et al., IT/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 9

10 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 H n H0, SC4 n=6 n H n H0, SC4 G. Vlad et al., IT/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 10

11 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 A n= n=6 n=4 n= n H0 /n H0, SCH G. Vlad et al., IT/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 11

12 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 H n H0, SCH n H n H0, SCH n H n H0, SCH G. Vlad et al., IT/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 12

13 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/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 13

14 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 r/a rβ H Convective phase r max r/a rβ H Diffusive phase r max r/a G. Vlad et al., IT/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 14

15 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/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 15

16 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 = r y rβ H (r;t)dr rβ H,init (r)dr r 95% /a r 95% /a β H0 SC2, n=4 SC4, n=2 tω A β H0 tω A0 Time behavior of central α-particle beta, β H0 : tω A tω A0 G. Vlad et al., IT/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 16

17 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= r 95% /a r 95% /a 0.67 just-after-convection just-after-convection initial initial 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] (τ diff ω A0 ) -1 τ-1 diff, βη τ -1 diff, 95% β H0 /β H0, SC (τ diff ω A0 ) τ -1 diff, 95% τ -1 diff, βη β H0 /β H0, SC4 G. Vlad et al., IT/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 17

18 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/P th IAEA Fusion Energy Conference (FEC 2004). 1-6/11/2004 Vilamoura, Portugal 18

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