Non-linear MHD Modelling of Rotating Plasma Response to Resonant Magnetic Perturbations.

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1 Non-linear MHD Modelling of Rotating Plasma Response to Resonant Magnetic Perturbations. M. Becoulet 1, F. Orain 1, G.T.A. Huijsmans 2, P. Maget 1, N. Mellet 1, G. Dif-Pradalier 1, G. Latu 1, C. Passeron 1, E. Nardon 1, V. Grandgirard 1, A. Ratnani 1 1 Association Euratom-CEA, CEA/DSM/IRFM, Centre de Cadarache, 13108, Saint-Paul-lez-Durance, France. 2 ITER Organization, Route de Vinon,13115 Saint-Paul-lez- Durance, France TH/2-1 (poster session P4, today,14h) This work has benefitted from financial support from the National French Research Program (ANR): ANEMOS(2011) and E2T2(2010). Supercomputers used: HPC-FF(Julich, Germany), JADE(CINES, France), Mésocentre (Marseille, France).

2 Type I ELM control by RMPs in ITER. Many open questions in physics of ELMs+RMPs still remain. Aim: progress in understanding of RMPs, give reliable predictions for ITER. Idea: RMP coils=> magnetic perturbation =>edge ergodic region=> control of edge transport, MHD. However, at the same edge ergodisation in vacuum => different reaction of ELMs to RMPs in experiment: suppression, mitigation, triggering? RMPs are different from vacuum RMPs in plasma! Rotating plasma response : current perturbations on q=m/n => screening of RMPs. [Fitzpatrick PoP 1998], [Waelbroeck NF2012], [Izzo NF 2008], [Becoulet NF 2009, 2012], [Strauss NF 2009], [Orain EPS2012], [Ferraro APS 2011] etc RMPs /ELMs at high ν*? (Type II ELMs- like events, density, magnetic field fluctuations, no changes in profiles) Density pump-out (at low ν*)? Rotation braking/acceleration? Fenstermacher, IAEA-2010 AUG:Suttrop,PRL 2011 KSTAR, Jeon, IAEA 2012 this session M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 2/14

3 Outline: RMPs and flows in non-linear resistive MHD code JOREK : RMPs at the computational boundary (SOL, X-point, divertor geometry) 2 fluid diamagnetic effects (large in pedestal!), neoclassical poloidal viscosity ( V ~ V neo θ, i θ, i in pedestal), V : toroidal rotation source, SOL flows. equilibrium radial electric field (large ExB in pedestal!). [Huysmans PPCF2009] RMPs in JET-like case. (EFCC,40kAt,n=2). Three regimes depending on resistivity and rotation. Oscillating /rotating islands at high resistivity, low rotation δb r (t), δn e (t),δt e (t)-fluctuations (~khz). Link with Type II ELMs with RMPs at high ν*? Static islands at strong rotation, low resistivity, more screening of RMPs. Intermediate: oscillating, quasi-static islands. RMPs in ITER.(IVC,54kAt,n=3). Screening of RMPs (stronger for central islands, penetration at the edge). Boundary deformation, lobes near X-point,splitting of strike points. No significant density/temperature transport, modulations near X-point. M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 3/14

4 Non-linear reduced resistive MHD in torus (X-point, divertor, SOL) with diamagnetic and neoclassical effects (important in large pedestal gradients region!). JOREK. [Huysmans PPCF2009] 2 V R2 τ = u ϕ i 2 IC R B = F ϕ + ψ ϕ ρ p ϕ + V B τ = m /(2 e F µ ρ ) 0 IC i E B diamagnetic parameter F τ F, , IC F ψ = η ψ u ψ u p p R t R R R ϕ B2 R2 R2 ϕ ψ + + p = ρt Ohm s law: ρ R If this term is ~zero at q=m/n => V dia 0 e, Parallel θ = VE, θ + Ve, θ => no RMP screening V momentum: B ρ = ρ V V ( ρt ) J B S VS ν ( ) V neo Π t V ρ i Poloidal ϕ ρ V = ρ V V ( ρt ) J B S VS ν ( ) V neo Π V i momentum: t ρ ( ρt) = V ( ρt) γρt V + T T (1 γ ) S 1 Κ +Κ + + V 2 Temperature: S t T 2 ρ Mass density: ρ = ρv + ( D ρ ) S t + e = ( R/ ψ ) ψ ϕ ρ θ Πneo µ ρ( B2 / B2 Neoclassical poloidal viscosity [Gianakon PoP2002] )( V V ) e i i, neo θ θ, i θ, neo θ Ion poloidal velocity =>neoclassical V V = k τ ( ψ T )/ B B = ψ / R, i, neo i, neo IC θ Temperature dependent viscosity, resistivity, K : θ θ θ ~ ( T / T ) ; η = ; K / K ~10 ( T / T ) η η 3 / / M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 4/14

5 Plasma flows (w/o RMPs): parallel => central source, on targets ion sound speed. Ion poloidal velocity in pedestal => neoclassical. Large ExB rotation in pedestal => RMPs screening? JET-like:R=3m, τ ~ 2.10 q 95 =3,T 3; µ ~10 0 =5keV,n e = m -3,f 0 =9kHz. 5; k = 1; η = IC neo neo Er ( u, ψ )/ ψ SOL Pedestal center=> <=center Pedestal SOL V V θ,i V = ±C, div s M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 5/14

6 Static RMPs + rotating plasma => response currents on the resonant surfaces=> RMP screening. Vacuum RMP (EFCC, n=2, I coil =40kAt ) are increased in time at JOREK boundary. ψ ( t ) = ψ vacuum f ( t ) n = 2 bnd n = 2, 40kAt ERGOS[Becoulet NF 2008] JET-like Poloidal magnetic flux perturbation (max) with RMPs in plasma with flows. ψ n=2 ERGOS [NF Becoulet 2008] JOREK Toroidal current perturbations on the rational surfaces (q=m/2; m=3,4,5,6) with RMPs. j φ,n=2 M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 6/14 JOREK

7 Stronger RMP screening for lower resistivity and larger poloidal rotation. Ergodic region at the edge. Central islands are screened: (m/n)=3/2; 4/2. Edge ergodic region: (5/2,6/2) penetrate (η~t -3/2 ) JET-like Similar results in cylinder [Becoulet NF 2012] M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 7/14

8 Three regimes depending on rotation & resistivity. high η, low τ IC : rotating oscillating islands f * mv / (2 π r ) ~ 6kHz θ res high τ IC : static islands, more screening of RMPs. low η, low τ IC : intermediateocsillating, quasi-static islands =>fluctuations of magnetic field, density and temperature, no significant transport. Possibly related to RMPs suppression at high ν*? Rutherford regime? [Fitzpatrick PoP 1998], [IzzoNF2008] JET-like M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 8/14

9 RMPs in ITER. W/o RMPs n=3 is stable. With RMPs =>n=3 static perturbations at the edge. Courtesy to E.Day,M.Schaffer IVC, max: I coil =90kAt, n=2,3,4. Used here n=3, 54kAt. Radial electric field τ ~ 5.10 ; µ ~10 5; k = 1; η = IC i, neo i, neo ITER: H-mode,15MA/5.3T, R=6.2m, a=2m,q 95 =3,T 0 =27.8keV,n e = m -3,f 0 =1kHz ψ n=3 j φ, n=3 T e, n=3 ITER M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 9/14

10 Boundary deformation. Lobes near X-point (smaller with rotation). Splitting of strike points (> on outer target) ~6cm w/o flows with all flows - screening ITER wall ITER ~22cm Inner target Outer target M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 10/14

11 Small changes in edge T e, n e profiles, no density pump-out. Maximum T e,n e modulations ~near X-point. T e n e RMP off RMP on RMP off T e n e RMP off RMP on ITER RMP on M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 11/14

12 Comparison JOREK&ERGOS(vacuum)&RMHD(cylinder). JOREK (torus, rotating plasma) : RMPs screening on q=m/n (stronger for central islands). Amplification r<r res in JOREK. Compared to vacuum (ERGOS). RMPs screening by rotating plasma (JOREK), smaller screening for edge RMP harmonics (η~t -3/2 ). Compared to cylinder (RMHD,q=q tor ): Stronger RMPs screening in JOREK. Amplification for r<r res. [RMHD: Becoulet NF 2012] ITER ITER M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 12/14

13 DIII-D like [RMHD: Becoulet NF 2012] Island is not screened if at q~(m/n) electron poloidal velocity => zero. For ITER parameters: V θ Ohm s law=>if electron poloidal velocity=>zero: current perturbation no RMP screening => vacuum-like island. vacuum in plasma V e, θ = 0 ~ / V + E, V e dia q m n θ, θ Jϕ, mn => q ~ m / n V θ, e 0 0 For ITER parameters used here electron poloidal velocity is not zero: =>screening ITER RMP off RMP on e, 0 V dia 0 e, θ = V V E, θ + e V θ,e M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 13/14

14 Discussion and conclusions. Non-linear resistive MHD code JOREK development for RMPs with flows: RMPs - at the boundary, 2 fluid diamagnetic effects, neoclassical poloidal viscosity, toroidal rotation source, SOL flows. JET-like(n=2).Three regimes: high η, small (poloidal) rotation (high ν*?) => oscillating and rotating islands, fluctuations δn e, δt e, δψ (t) (~khz). low η, higher rotation => static islands, more screening of RMPs. Intermediate => oscillating, quasi-static islands. RMPs (n=3) in ITER. Screening of central islands, static edge islands, ergodic edge, splitting of strike points (>outer), modulations of n e,t e near X-point. Future: RMPs interaction with ELMs. Modelling of MAST, JET, AUG experiments. W mag,n=2 (t) n e with RMPs in ITER M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 14/14

15 Additional slides M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 15/14

16 Pressure gradient is 3D, locally is even steeper with RMP. RMP on RMP off M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 16/14

17 Peak heat fluxes on divertor targets are reduced with RMPs on. Heat flux on inner and outer divertor targets. M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 17/14

18 Equilibrium flows (w/o RMPs) : parallel velocity (central source, SOL-sheath conditions on divertor targets). Ion poloidal velocity => neoclassical in the pedestal. Parallel flow. V Central plasma: source V Poloidal flow. = ( ψ, u) τ ( ψ, p) / ρ V B 2 / B θ, i + IC θ θ maintains initial V profile: S = ν V V = ( ψ, u ) + τ ( ψ, p ) / ρ / B V, t = θ, e IC θ 0 SOL: sheath conditions on Pedestal: V V T θ, i θ, i, neo i targets: V = ±C SOL: V V B, div s θ, i θ V V θ V θ,neo JET-like:R=3m, a=1m,q 95 =3,T 0 =5keV,n e = m -3,f 0 =9kHz. τ ~ 2.10 ; µ ~10 5; k = 1.; η = IC i, neo i, neo M. Bécoulet, , TH/2-1, 24 th IAEA, San Diego, California, USA 18/14

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