Supported by. The drift kinetic and rotational effects on determining and predicting the macroscopic MHD instability
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1 NSTX-U Supported by The drift kinetic and rotational effects on determining and predicting the macroscopic MHD instability Coll of Wm & Mary Columbia U CompX General Atomics FIU INL Johns Hopkins U LANL LLNL Lodestar MIT Lehigh U Nova Photonics ORNL PPPL Princeton U Purdue U SNL Think Tank, Inc. UC Davis UC Irvine UCLA UCSD U Colorado U Illinois U Maryland U Rochester U Tennessee U Tulsa U Washington U Wisconsin X Science LLC Z.R. Wang 1, J. E. Menard 1, Y.Q. Liu 2, J.-K. Park 1 1 Princeton Plasma Physics Laboratory 2 Culham Centre for Fusion Energy, Culham Science Centre Integrated Simulations Workshop May 18, 2015 Culham Sci Ctr York U Chubu U Fukui U Hiroshima U Hyogo U Kyoto U Kyushu U Kyushu Tokai U NIFS Niigata U U Tokyo JAEA Inst for Nucl Res, Kiev Ioffe Inst TRINITI Chonbuk Natl U NFRI KAIST POSTECH Seoul Natl U ASIPP CIEMAT FOM Inst DIFFER ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching ASCR, Czech Rep
2 Background Kinetic effects on resistive wall mode, ideal wall mode, plasma response etc. have been extensively studied since fluid MHD approach fails to accurately treat these problems. MARS-K code has been largely upgraded to improve numerical stability and include more kinetic physics e.g. finite orbit width effect and energy dependence of collisionality. Successful benchmark has been carried out among MARS-K, IPEC-PENT, MISK and HAGIS for calculation of kinetic effects. Proposed Research for Reliable Prediction of MHD Instability Explore MHD macroscopic instability through Nyquist contour technique in experiments and compare with numerical simulation. Tearing Instability and NTV Torque in presence of external fields. Further improve kinetic model to include perturbed E and experimental energetic particles distribution function. Study kinetic effects in non-linear MHD simulation. 2
3 Outline Hybrid kinetic-mhd modelling using MARS-K Progress of applying MARS-K to determine and predict MHD instability Kinetic effects on resistive wall mode instability in ITER Kinetic and rotational effects on ideal wall mode instability in NSTX Quantitative validation of hybrid kinetic-mhd theory with DIII-D n=1 plasma response experiment Anticipated MARS application to compare with experiments Summary and future plan of MARS code development 3
4 Drift-kinetic equation: df L 1 MARS-K: Hybrid Drift-Kinetic MHD Formulation MARS-K solves linearized MHD equations with perturbed kinetic pressure, including toroidal flow V f =RW, vacuum, resistive wall and external coils. MHD equations: i ω + nω ξ = v + Inertial term ξ Ω R 2 ϕ iρ ω + nω v = p + j B 0 + J 0 b + ρ 2ΩZ v v Ω R 2 ϕ ρξ ΩZ V 0 i ω + nω b = v B 0 + b Ω R 2 ϕ (ηj) Resistivity i ω + nω p = v P 0 ΓP 0 v Mode eigenvalue j = b dt = f ε 0 H1 t f 0 H1 P φ φ ν 1 efff L H 1 : perturbed Lagrangian replaced by kinetic pressure MARS-K in self-consistent approach: Drift kinetic effects can modify mode eigenfunction. Coriolis force Kinetic pressure p and p couple with MHD equations Resonant operator in f L 1 : Precession drift p = pi + p bb + p Diamagnetic drift I bb p e iωt+inφ = dγmv 2 f L 1 e,i p e iωt+inφ = dγ 1 2 Mv 2 f L 1 e,i Centrifugal force Mode eigenvalue n ω N + εk 3/2 ω T + ω E ω λ ml = nω d + α m + nq + l ω b + nω E ω iν eff Bounce/Transit EXB Crook Collisions Y.Q. Liu et al, PoP 2014 NSTX-U 4
5 MARS-K: First Order Finite Orbit Width (FOW) Correction: Important For Energetic Particles (EPs) Solution of the drift kinetic equation for the perturbed distribution function perturbed kinetic pressures (non-adiabatic part) poloidal Fourier harmonics zero-order term first-order FOW correction terms 2 nd & 3 rd terms come from FOW correction to equilibrium distribution function 4 th term comes from FOW correction to perturbations 2 nd term disappears for trapped particles [Liu et al., PoP 21, (2014)] 5
6 Outline Hybrid kinetic-mhd modelling using MARS-K Progress of applying MARS-K to determine and predict MHD instability Kinetic effects on resistive wall mode instability in ITER Kinetic and rotational effects on ideal wall mode instability in NSTX Quantitative validation of hybrid kinetic-mhd theory with DIII-D n=1 plasma response experiment Anticipated MARS application to compare with experiments Summary and future plan of MARS-K development 6
7 ITER 9MA: Self-Consistent Computations of Hybrid Kinetic MHD: Isotropic Slowing Down Model (Fusion Born a s) Fluid model, w/o plasma flow, predicts unstable RWM between no-wall & ideal-wall beta limits Fluid theory [Liu et al., PoP 21, (2014)] 7
8 ITER 9MA: Self-Consistent Computations of Hybrid Kinetic MHD: Isotropic Slowing Down Model (Fusion Born a s) Kinetic theory, including precessional drift resonance contributions from both thermal & energetic particles, predicts marginal stability for ITER target plasma Fluid theory Precession resonance [Liu et al., PoP 21, (2014)] 8
9 ITER 9MA: Self-Consistent Computations of Hybrid Kinetic MHD: Isotropic Slowing Down Model (Fusion Born a s) Adding bounce & transit resonance contributions (ZOW), from both thermal & energetic ions, further stabilize the mode Fluid theory Precession resonance All resonances w/ ZOW [Liu et al., PoP 21, (2014)] 9
10 ITER 9MA: Self-Consistent Computations of Hybrid Kinetic MHD: Isotropic Slowing Down Model (Fusion Born a s) Further adding 1 st order FOW correction, to bounce & transit resonance contributions of EPs, stabilises the mode at high beta but destabilises the mode at lower beta Kinetic effects significantly reduce growth rates of the RWM Fluid theory Precession resonance All resonances w/ ZOW All resonances w/ FOW [Liu et al., PoP 21, (2014)] 10
11 NSTX: Experimental b N Limit of n=1 Ideal Wall Mode Can Be Predicated by Hybird Kinetic-MHD Calculation Experimental fluid rotation destabilizes plasma and leads to under predication of b N limit in fluid MHD calculation. Kinetic effects stabilize ideal wall mode and agree with experimental b N and mode frequency. NSTX shot , t=610ms Fluid b N limit~5.6 for low Wt A =3% Fluid b N limit~4.2 for experimental W(0)t A =20% b N range Kinetic b N limit~ for expt. W(0)t A =20% Menard, Wang and Liu et al., PRL 113, (2014)] 11
12 NSTX:Eigenfunction of Ideal Wall Mode is Modified by Kinetic Effects and Plasma Rotation The eigenfunctions of radial plasma displacement solved by ideal MHD and hybrid kinetic MHD are compared. The eigenfunctions are modifed in both core and edge by kinetic effects and plasma rotation. Soild: Fluid IWM W(0)t A =0, Dashed: Kinetic IWM W(0)t A =20% Kinetic IWM m=2 m=1 Fluid IWM m=3 m=4 12
13 DIII-D: n=1 Plasma Response Predicted by Kinetic-MHD Agrees with Internal Structure Measurement from Soft X-Ray n=1 Internal response structure comparison Simulated 2D radial displacement Fluid response 1 12 SXR sightline geometry Exp Kinetic response The quantitative agreement between experiment and kinetic plasma response shows validation of hybrid kinetic MHD theory (MARS-K). Wang, Lanctot, Liu et al., PRL 114, (2015) 13
14 Outline Hybrid kinetic-mhd modelling using MARS-K Progress of applying MARS-K to determine and predict MHD instability Kinetic effects on resistive wall mode instability in ITER Kinetic and rotational effects on ideal wall mode instability in NSTX Quantitative validation of hybrid kinetic-mhd theory with DIII-D n=1 plasma response experiment Anticipated MARS application to compare with experiments Summary and future plan of MARS-K development 14
15 Nyquist Contour Significantly Improve Physical Understanding of MHD instability and Plasma Response Nyquist contour can be formed by scanning coil frequency from -infinity to +infinity. Fluid vs. Kinetic cases shows different Nyquist contours. Comparing experimental and simulated Nyquist contour can. Further validate hybrid kinetic-mhd theory; Reveal multi-mode plasma response to n=1 and n=2 perturbation; infer growth/damping rate of (multiple) mode(s) (Padé approximation); MARS simulation of DIII-D n=1 Nyquist contour MARS Nyquist Fluid w/o Rotation Fluid + Rotation Kinetic w/o Rotation Kinetic + Rotation Padé approximation 1 st mode g 1 = (a.u.) 2 nd mode g 2 = (a.u.) 3 rd mode g 3 = (a.u.) 15
16 Summary Kinetic effects with FOW significantly reduce growth rate of RWM in ITER. Strong rotation and kinetic effects substantially modify the ideal-wall limit in ST plasmas with high b. Kinetic IWM calculation reproduce experimental ideal wall b limit and mode frequency that fluid calculations cannot. Validation of hybrid kinetic-mhd theory with DIII-D experiments indicates importance of kinetic modification on response(mode) structure. Future Plan Application of MARS-K to study experimental Nyquist contour and tearing instability Inclusion of the perturbed electrostatic potential in hybrid formulation Implement the experimental EPs distribution function Study kinetic effects in non-linear MHD simulation. Possibility to do real time feedback control with hybrid kinetic-mhd? 16
17 Numerical Study for ITER 9MA Steady State Scenario (340MW and Q=5) ITER target: b N =2.94 Peq safety factor q min =1.58 W 0 =6kHz =2.7%w A P a /P th ~20% 17
18 Adding perturbed electrostatic potential (work in progress) Perturbed electrostatic potential and quasi-neutrality f f a df dt L L f P a f E Ze A c Mv (0) f f P L L t 2 (0) R Zef κ ξ Zef f P (0) f E (0) L B B B (0) f ( B B ) Ze( ) (0) ξ f ξ f ( f f ) Z j j, a j, L dv j 0 18
19 MARS Has Numerical Capability to Study Tearing Instability and NTV Torque in Presence of External Fields MARS-Q can do physical analysis in terms of the small island in the quasi-linear approach. The code can be used to simulate dynamics of tearing mode in the experiments. Plasma rotational effect can be included. The code includes the JxB resonant torque + Neoclassical toroidal viscosity(ntv) torque MAST plasma with n=3 magnetic perturbation Time evolution of (2,1) island width Rotation damping Y.Q. Liu et al, PPCF 2012 G.Z. Hao et al, PoP 2014 MARS-Q will be validated with NSTX-U experiments for tearing instability study. 19
20 Amplitude(Gauss/KA) DIII-D: Plasma Response Predicted by Kinetic-MHD Agrees with Internal Structure Measurement from Soft X-Ray Comparison of n=1 plasma response on ISL magnetic sensor Internal response structure comparison 2D radial displacement Fluid plasma response 1 12 SXR sightline geometry Exp Kinetic plasma response Wang, Lanctot, Liu et al., PRL to be published (2015) The quantitative agreement between experiment and kinetic plasma response shows validation of hybrid kinetic MHD theory. 20
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