Nonlinear MHD Modelling of Rotating Plasma Response to Resonant Magnetic Perturbations.


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1 Nonlinear 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. DifPradalier 1, G. Latu 1, C. Passeron 1, E. Nardon 1, V. Grandgirard 1, A. Ratnani 1 1 Association EuratomCEA, CEA/DSM/IRFM, Centre de Cadarache, 13108, SaintPaullezDurance, France. 2 ITER Organization, Route de Vinon,13115 SaintPaullez Durance, France TH/21 (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: HPCFF(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 pumpout (at low ν*)? Rotation braking/acceleration? Fenstermacher, IAEA2010 AUG:Suttrop,PRL 2011 KSTAR, Jeon, IAEA 2012 this session M. Bécoulet, , TH/21, 24 th IAEA, San Diego, California, USA 2/14
3 Outline: RMPs and flows in nonlinear resistive MHD code JOREK : RMPs at the computational boundary (SOL, Xpoint, 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 JETlike 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, quasistatic islands. RMPs in ITER.(IVC,54kAt,n=3). Screening of RMPs (stronger for central islands, penetration at the edge). Boundary deformation, lobes near Xpoint,splitting of strike points. No significant density/temperature transport, modulations near Xpoint. M. Bécoulet, , TH/21, 24 th IAEA, San Diego, California, USA 3/14
4 Nonlinear reduced resistive MHD in torus (Xpoint, 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/21, 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? JETlike: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/21, 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] JETlike 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/21, 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 ) JETlike Similar results in cylinder [Becoulet NF 2012] M. Bécoulet, , TH/21, 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, quasistatic 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] JETlike M. Bécoulet, , TH/21, 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: Hmode,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/21, 24 th IAEA, San Diego, California, USA 9/14
10 Boundary deformation. Lobes near Xpoint (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/21, 24 th IAEA, San Diego, California, USA 10/14
11 Small changes in edge T e, n e profiles, no density pumpout. Maximum T e,n e modulations ~near Xpoint. T e n e RMP off RMP on RMP off T e n e RMP off RMP on ITER RMP on M. Bécoulet, , TH/21, 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/21, 24 th IAEA, San Diego, California, USA 12/14
13 DIIID 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 => vacuumlike 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/21, 24 th IAEA, San Diego, California, USA 13/14
14 Discussion and conclusions. Nonlinear 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. JETlike(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, quasistatic 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 Xpoint. 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/21, 24 th IAEA, San Diego, California, USA 14/14
15 Additional slides M. Bécoulet, , TH/21, 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/21, 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/21, 24 th IAEA, San Diego, California, USA 17/14
18 Equilibrium flows (w/o RMPs) : parallel velocity (central source, SOLsheath 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 JETlike: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/21, 24 th IAEA, San Diego, California, USA 18/14
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