Alpha Particle Transport Induced by Alfvénic Instabilities in Proposed Burning Plasma Scenarios G. Vlad, S. Briguglio, G. Fogaccia and F. Zonca Associazione Euratom-ENEA sulla Fusione, C.R. Frascati C.P. 65 - I-44 - Frascati, Rome, Italy G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 1
Outline Introduction The numerical model Nonlinear Energetic Particle Modes (EPMs) dynamics: avalanches Burning-plasma devices/scenarios Comparison of different devices/scenarios: linear stability nonlinear energetic particle transport Check of the model Preliminary results on ITER-FEAT Hybrid scenario and comparison with ITER-FEAT Standard and Reversed Shear ones Conclusions G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 2
Introduction Particle simulations have shown that transport and confinement properties of energetic ions in Tokamak plasmas can be significantly affected by shear Alfvén modes driven unstable by pressure gradients of the energetic ions themselves Scenarios for proposed burning-plasma experiments (ITER-FEAT, IGNITOR, FIRE) include alpha-particle b profiles, which do not take into account the effects of shear Alfvén modes Aim of this paper is investigating the consistency of some of these scenarios with shear Alfvén mode-particle interactions: a) stability of shear Alfvén modes (Energetic Particle Modes, EPMs) b) effects of unstable modes on alpha-particle profiles and confinement The investigation is performed by particle-in-cell simulations (HMGC code) G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 3
The numerical model-1 The Hybrid MHD-Gyrokinetic simulation Code (HMGC) solves the set of reduced O(e 3 ) MHD equations, coupled with fully nonlinear gyrokinetic Vlasov equation for energetic ( Hot ) particles Relevant equilibrium profiles retained: q, n i, b H /b H (we keep b H as a free parameter) Large aspect ratio approximation (most of simulations presented refer to R /a=1.): b H rescaled to yield the desired value of a H R q 2 b' H Circular shifted magnetic surfaces Single toroidal mode number dynamics: nonlinear mode-mode coupling among different toroidal mode numbers neglected (scan in n to find most unstable mode) G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 4
The numerical model-2 Isotropic Maxwellian (instead of slowing-down) energetic-particle distribution function Particles are loaded initially in (m, V, y) space, and not in (p f, E, m) space (initial relaxation of assigned radial EP profile are observed). Shear-Alfvén equivalence between simulation (Maxwellian) distribution function and physical one (slowing-down) match respective energetic-particle response: Maxwellian (Maxw): ~a H,Maxw V th,h dw Maxw (w/k V th,h ) Slowing-down (SD): ~a H,SD V SD dw SD (w/k V SD ), with V SD (2E fus /m H ) 1/2 Matching the dominant energetic-particle resonance: V th,h @.37V SD Matching the drive intensity: a H,SD V SD @ 1.66a H,Maxw V th,h fi a H,Maxw @ 1.683a H,SD G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 5
Nonlinear EPM dynamics: overview (strongly unstable RS equilibrium) frequency (r/a,w/w A ) eigenfunction f m,n (r) Energetic particle b H (r) differential local drive da H =a H (r,t)-a H,lin (r) G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 6
Burning-plasma devices/scenarios ITER-FEAT IGNITOR FIRE (a) 3 2 q 1 n i /n i / H Hmax / H H 1..8.6.4.2...2.4 r/a.6.8 1. 3 2 1 (c) n i /n i q H / Hmax H / H 1..8.6.4.2...2.4 r/a.6.8 1. 4 (e) n i /n i 3 2 q 1 / H Hmax / H H 1..8.6.4.2...2.4 r/a.6.8 1. monotonic q (from Budny, Nucl. Fusion 42 (22) 1383) (b) 5 4 3 2 1 n i /n i / H Hmax / H H 1..8 q.6.4.2 (d) 3 2 1 H / Hmax H / H 1..8 q.6.4.2....2.4 r/a.6.8 1...2.4 r/a.6.8 1. n i /n i G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 7 Reversed Shear
Toroidal gap structure ITER-FEAT IGNITOR FIRE Alfvén continuum in (r/a,w/w A ) space (w A V A /R ) for n=4 monotonic q Reversed Shear G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 8
Results Are the proposed scenarios stable w.r.t. shear-alfvén modes? If unstable, which consequences for alpha-particle confinement? fi Are the proposed scenarios consistent with Alfvén modes dynamics? In order to compare different devices/scenarios we normalize the free simulation parameter b H to the scenario value b H,scenario. G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 9
Results: linear stability-1 ITER-FEAT IGNITOR FIRE n=4 mode b H above threshold for EPM instability monotonic q Reversed Shear G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 1
Results: linear stability-2 Toroidal mode number n dependence of toroidal gap structure and real frequency (ITER-FEAT RS).3 w lin /w A.2.1 w gap /w A =1/[2q(r)] 2 4 6 8 n The n dependence of the real frequency is slightly weaker than linear Linear dependence would suggest precession resonance to be the relevant one: w precession µ nq(r)/r For small n, mode could locate itself in a valley of the Alfvén continuum G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 11
Results: linear stability-3 b H,Th threshold in central energetic particle pressure b H (for fixed profiles and other parameters) for destabilization of resonant EPMs All the considered scenarios are stable w.r.t. EPMs, (b H,Th >> b H,scenario ), with the exception of the Reversed Shear ITER-FEAT scenario..5 g lin /w A.4.3.2.1 IGNITOR-RS n=4 ITER-FEAT RS n=2 ITER-FEAT n=8 FIRE n=4 IGNITOR n=4 1 b 1 H /b H,scenario G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 12
Results: nonlinear effects on a confinement-1 ITER-FEAT RS scenario, n=2 (unstable at nominal b H ) Power spectra in the plane (r,w) and b H profiles (b H /b H,scenario @1.22) Linear After avalanche Fully saturated G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 13
rn H Results: nonlinear effects on a confinement-2 r max Convective phase (avalanche): maximum gradient of rn H shifts outward, first steepening and then relaxing Linear phase.5.6.7.8 r rn H r max Convective phase.9 r max.8.7.6 [d(rn H )/dr] max.6.5 5 1 15 2 25 3.5 linear phase convective phase t/t A diffusive phase.5.6.7.8 r rn H Diffusive phase.4.3 5 1 15 2 25 3 r max t/t A.5.6.7.8 r G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 14
Results: nonlinear effects on a confinement-3 Saturation of EPMs takes place via an avalanche mechanism, which produces a macroscopic convective redistribution of the energetic-particle source After the convective displacement has completed, a significant diffusion of energetic particles survives because of the continuous scattering of the energetic particles in the saturated electromagnetic fields Define (r/a) y : the radial position of the surface containing a fraction y of the alpha-particle energy: rb H y = Ú Ú (r /a ) y 1 xb H (x;t)dx xb H ( x;t relax )dx.8 (r/a) y.75.7.65 ~t relax (r/a) 95% (r/a) 9% y=85%.6.55 (r/a) 85%.5 5 1 15 2 25 3..2.4.6.8 1. r/a linear (r/a) t/t diffusive 85% phase A phase convective G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 phase 15
Results: nonlinear effects on a confinement-4 Both convection and diffusion are more pronounced for larger b H (larger saturated field levels) Characterize the convection with r/a 85% at the end of the convection phase Characterize diffusion by t diff,95% (r/a) 95% [ (r/a) 95% / t] -1 (t -1 diff,95% µd).8 1-2 t A /t diff,95% r/a 85%.7.6 ITER-FEAT RS n=2 FIRE n=4 ITER-FEAT n=8 1-3 ITER-FEAT RS n=2 FIRE n=4 IGNITOR-RS n=4 ITER-FEAT n=8.5 IGNITOR n=4 1-4 IGNITOR n=4.4.3 1 b 1 H /b H,scenario IGNITOR-RS n=4 G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 16 1-5 1 b 1 H /b H,scenario
Check of the model (ITER-FEAT RS) Large aspect ratio approximation: a) (R /a) sim = 1. fi (R /a) ITER-FEAT @3.3 b) Rescaling b H to keep local drive (a H ) constant: b H,sim (R /a) sim = (R /a) ITER-FEAT b H,ITER-FEAT R /a@3.3 R /a=1.5 Is a) + b) equivalent to take real configuration: b H,sim = b H,ITER-FEAT (R /a) sim = (R /a) ITER-FEAT? g/w A.4.3.2 R /a=3.3 R /a=1..1 1 2 3 4 5 6 b H /b H,scenario G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 17
ITER-FEAT Hybrid scenario-1 No transport code generated scenario available. Use a simple model: parabolic bulk temperature profiles (T@2KeV) bulk plasma density profiles as for standard ITER-FEAT scenario (n@1 1 2 m -3 ) alpha particle profile from fusion reaction rate (Peres) and slowing down time safety factor: q @1.1, q a @5.2 (q 95% @4.1) with almost zero shear up to r@.6a 6 5 4 3 2 1 a H /a Hmax q T e /T e b H /b H n i /n i.2.4.6.8 1 r/a 1.8.6.4.2 n=4 n=8 n=12 G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 18
ITER-FEAT Hybrid scenario-2 Comparison between Hybrid scenario and Standard and Reversed Shear ones: linear unstable modes. Standard most unstable mode: n=8 Reversed Shear most unstable mode: n=2 Hybrid most unstable mode: n=8 G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 19
ITER-FEAT Hybrid scenario-3 Linear growth rates and radial position of the surface containing y=85% of the alpha particle energy of the three ITER-FEAT scenarios considered (most unstable n) Compare the different scenarios w.r.t. the absolute central energetic particle b H (for the Hybrid one, no reference value is available!) Hybrid scenario looks to be promising: higher b H,Th it supports (in a limited range of b H ) a saturated EPM without displacing appreciably the energetic particle profile: b H,Th-avalanche > b H,Th g lin /w A ITER-RS-n2.3 ITER-n8.8 r/a 85%.75 ITER-RS-n2 ITER-Hybrid-n8.2.7.65.1 ITER-Hybrid-n8.6 ITER-n8.1.2.3.4.5.6.7 b H.55.1.2.3.4.5.6.7 ITER-FEAT ITER-FEAT RS ITER-FEAT Hybrid ITER-FEAT Hybrid b H,scenario b H,scenario b H,Th b H,Th-avalanche G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 2 b H
Conclusions Shear Alfvén dynamics and interactions with energetic particles must be retained in order to determine self-consistent fusionproduct profiles for the reference scenario The Reversed Shear ITER-FEAT proposed scenario, in particular, appears to be unstable w.r.t. Energetic Particle Modes These modes are able to broaden alpha-particle profiles both via convective (avalanche) and diffusive mechanisms Small increase of the alpha-particle energy content (w.r.t. the reference scenario) could produce large thermal loads on the first wall Needs for a transport generated ITER-FEAT Hybrid scenario Future work: general equilibrium code (in progress) G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 21
Fine presentazione G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 22
Most unstable toroidal mode number (ITER-FEAT RS) The n dependence of the real frequency is slightly weaker than linear fi linear dependence would suggest precession resonance to be the relevant one: w precession µ nq(r)/r.25 lin / A.2.15.1.5 n=2 n=4 n=8.5.1.15.2.25 H n=2 n=4 n=8.3 w lin /w A.2 The n=2 linear mode grows in a valley of the Alfvén continuum: it suffers less damping and it is more effective in displacing particles. G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 23.1.7 r/a 85%.65.6.55 w gap /w A =1/[2q(r)] 2 4 n 6 8 n=2 n=8 n=4.5.1.15.2.25 b H
Most unstable n Fixed b H (different value for different devices/scenarios).3 g lin /w A.25 gamma-lin/w-a-iter-sc4 gamma-lin/w-a-iter-budny gamma-lin/w-a-ignitor-rs gamma-lin/w-a-ignitor-budny gamma-lin/w-a-fire-budny gamma-lin/w-a-iter-hybrid-1 all-devides-w-real-gam#28e6.2.15.1.5 2 4 6 8 1 12 n G.Vlad 8th IAEA TM on Energetic Particles - San Diego 6-8 October 23 24