TH/1-1 Multi-Scale ITG/TEM/ETG Turbulence Simulations with Real Mass Ratio and β Value S. Maeyama, Y. Idomura, M. Nakata, M. Yagi, N. Miyato Japan Atomic Energy Agency Collaborators ： T.-H. Watanabe (Nagoya Univ.), M. Nunami, A. Ishizawa (NIFS) 25th IAEA FEC, 15 Oct. 2014 This work is supported by HPCI Strategic Program Field No. 4 and MEXT KAKENHI Grant No. 26800283.
Introduction One of the critical issues in ITER is electron heat transport, which is inherently multi-scale physics. “Streamers” in ETG turbulence 2000 [Jenko00PoP] direction A candidate is electron Poloidal temperature gradient modes ( ETG ). Radial direction 2007 [Candy07PPCF,Waltz08PoP,Görler08PRL] ETGs give small transport if there are ion temperature gradient and trapped electron modes ( ITG/TEM ). However, these multi-scale simulations were limited: • Reduced mass ratio (m i /m e =400, 900) • Electrostatic approximation ( β =0) 2
Motivation & Outline Following points are not Linear instabilities from yet clarified: electron to ion scales (i) Are there multi-scale Scale separation with real mass ratio interactions even with Linear growth rate γ R/v ti the real mass ratio 10 and β value? Ion-scale stabilization 1 with real β β =0.04% (ii) If yes, how do the 0.1 β =2.0% interactions occur? 0.1 1 10 Poloidal wave number k y ρ ti 3
Motivation & Outline Following points are not Linear instabilities from yet clarified: electron to ion scales (i) Are there multi-scale Scale separation with real mass ratio interactions even with Linear growth rate γ R/v ti the real mass ratio 10 and β value? Multi-scale simulation Ion-scale demonstrates cross- stabilization 1 with real β scale interactions. β =0.04% (ii) If yes, how do the 0.1 β =2.0% interactions occur? Nonlinear interaction 0.1 1 10 analysis reveals their Poloidal wave number k y ρ ti mechanisms. 3
The GKV code [Watanabe06NF,Maeyama13CPC] • Solve gyrokinetic ions and electrons with electromagnetic fluctuations in a flux-tube geometry. • Validation with experiments. [Posters:Nakata,Ishizawa,Nunami] • High scalability allows ITG/TEM/ETG simulations with ~100k CPU cores in ~100 hours. [Maeyama13SC] 5 Plasma parameters are Cyclone base case 2.5 ITG/TEM parameters [Dimits00PoP] 0 • R/L Ti =R/L Te =6.82, -2.5 R/L n =2.2, T e =T i , -5 r/R=0.18, q=1.4, s=0.786 • Real mass ratio: m i /m e =1836 • Real β value: β =2.0% ETG (below NZT [Pueschel13PRL]) 4
Multi-scale turbulence simulation （ β =2.0% ） Time evolution of the electrostatic potential fluctuations (at mid-plane of the flux tube) 5
Energy Spectra spectrum （ β =2.0% ） 2 ) 10 2 Field energy W k R 2 /(n 0 T i ρ ti ITG Linear growth rate R/v ti ITG/TEM (k y ρ ti <1) 10 10 1 Zonal (k y ρ ti =0) 1 ETG/ Med. (1<k y ρ ti <4) 1 ITG/ Strea ETG/Streamers 10 -1 TEM mers (4<k y ρ ti ) 0.1 10 -2 Med. 0.1 1 10 10 -3 Poloidal wave 0 20 40 60 80 Time t v ti /R number k y ρ ti 6
Energy Spectra spectrum （ β =2.0% ） 2 ) 10 2 Field energy W k R 2 /(n 0 T i ρ ti ITG Linear growth rate R/v ti ITG/TEM (k y ρ ti <1) 10 10 1 Zonal (k y ρ ti =0) 1 ETG/ Med. (1<k y ρ ti <4) 1 ITG/ Strea ETG/Streamers 10 -1 TEM mers (4<k y ρ ti ) 0.1 10 -2 Med. 0.1 1 10 10 -3 Poloidal wave 0 20 40 60 80 Time t v ti /R number k y ρ ti 10 W k 10 -6 6 0.1 10 k y
Energy Spectra spectrum （ β =2.0% ） 2 ) 10 2 Field energy W k R 2 /(n 0 T i ρ ti ITG Linear growth rate R/v ti ITG/TEM (k y ρ ti <1) 10 10 1 Zonal (k y ρ ti =0) 1 ETG/ Med. (1<k y ρ ti <4) 1 ITG/ Strea ETG/Streamers 10 -1 TEM mers (4<k y ρ ti ) 0.1 10 -2 Med. 0.1 1 10 10 -3 Poloidal wave 0 20 40 60 80 Time t v ti /R number k y ρ ti 10 10 W k W k 10 -6 10 -6 6 0.1 10 0.1 10 k y k y
Energy Spectra 10 W k spectrum （ β =2.0% ） 10 -6 0.1 10 k y 2 ) 10 2 Field energy W k R 2 /(n 0 T i ρ ti ITG Linear growth rate R/v ti ITG/TEM (k y ρ ti <1) 10 10 1 Zonal (k y ρ ti =0) 1 ETG/ Med. (1<k y ρ ti <4) 1 ITG/ Strea ETG/Streamers 10 -1 TEM mers (4<k y ρ ti ) 0.1 10 -2 Med. 0.1 1 10 10 -3 Poloidal wave 0 20 40 60 80 Time t v ti /R number k y ρ ti 10 10 W k W k 10 -6 10 -6 6 0.1 10 0.1 10 k y k y
Energy Spectra 10 10 W k W k spectrum （ β =2.0% ） 10 -6 10 -6 0.1 10 0.1 10 k y k y 2 ) 10 2 Field energy W k R 2 /(n 0 T i ρ ti ITG Linear growth rate R/v ti ITG/TEM (k y ρ ti <1) 10 10 1 Zonal (k y ρ ti =0) 1 ETG/ Med. (1<k y ρ ti <4) 1 ITG/ Strea ETG/Streamers 10 -1 TEM mers (4<k y ρ ti ) 0.1 10 -2 Med. 0.1 1 10 10 -3 Poloidal wave 0 20 40 60 80 Time t v ti /R number k y ρ ti 10 10 W k W k 10 -6 10 -6 6 0.1 10 0.1 10 k y k y
Energy Spectra 10 10 10 W k W k W k spectrum （ β =2.0% ） 10 -6 10 -6 10 -6 0.1 10 0.1 10 0.1 10 k y k y k y 2 ) 10 2 Field energy W k R 2 /(n 0 T i ρ ti ITG Linear growth rate R/v ti ITG/TEM (k y ρ ti <1) 10 10 1 Zonal (k y ρ ti =0) 1 ETG/ Med. (1<k y ρ ti <4) 1 ITG/ Strea ETG/Streamers 10 -1 TEM mers (4<k y ρ ti ) 0.1 10 -2 Med. 0.1 1 10 10 -3 Poloidal wave 0 20 40 60 80 Time t v ti /R number k y ρ ti 10 10 W k W k 10 -6 10 -6 6 0.1 10 0.1 10 k y k y
Electron energy diffusion spectrum in multi-scale turbulence is NOT a sum of single-scale ones. In zero- β case, due to strong electron-scale suppression, ion-scale simulations give a good estimate. In finite- β case , electron-scale suppression is weak. Ion-scale transport is enhanced in multi-scale analysis. Zero- β case ( β =0.04%) Finite β case ( β =2.0%) Electron thermal diffusion Electron thermal diffusion 10 2 10 2 100 100 Electron- Electron- scale sim. scale sim. e =7.2 gB e =5.4 gB coefficient ek / gB coefficient ek / gB 1 1 1 1 Ion-scale Ion-scale sim. e =6.4 gB sim. 10 -2 10 -2 e =1.2 gB 0.01 0.01 Multi-scale Multi-scale sim. e =4.5 gB sim. e =6.3 gB 10 -4 10 -4 0.0001 0.0001 0.1 1 10 0.1 1 10 Poloidal wave number k y ρ ti Poloidal wave number k y ρ ti * Ion energy diffusion is similar (see proceedings). 7
Analysis of nonlinear interactions Poloidal wave number q y ρ ti Gyrokinetic triad transfer - Mode-to-mode nonlinear k transfer of perturbed entropy [Nakata12PoP] 𝒒,𝒓 𝐽 𝑡𝒍 = 𝐾 𝑡𝒍 𝒒 𝒓 𝒄 ⋅ 𝒒 × 𝒓 𝒒,𝒓 = 𝜀 𝒍+𝒒+𝒓,𝟏 p 𝐾 𝑡𝒍 2𝐶 𝑈 𝑡 𝑡𝒍 q 𝑒𝑤 3 𝜓 𝑡𝒒 𝑡𝒓 − 𝜓 𝑡𝒓 𝑡𝒒 × Re 𝐺 𝑡𝑁 k + p + q = 0 𝒍 − 𝑤 ∥ 𝐵 ∥𝒍 、 （ Generalized potential 𝜓 𝑡𝒍 = 𝜚 𝑓 𝑡 𝐺 𝑡𝑁 𝒍 ） Nonadiabatic distribution 𝑡𝒍 = 𝑔 𝑡𝒍 + 𝜚 Radial wave number q x ρ ti 𝑈 𝑡 Electron-scale suppression mechanism: • Ion-scale ZF shearing? Or, Another structures? Ion-scale enhancement mechanism: • Inverse cascade to ion-scale turbulence? Or, Damping of ion-scale ZFs? 8
Suppression of electron-scale streamers by high-k x ITG/TEM structures. 𝒒,𝒓 Triad transfer 𝐾 𝑡𝒍 for a streamer 𝑡 (k x ρ ti ,k y ρ ti )=(0,4.4) at t=20-30R/v ti Poloidal wave number q y ρ ti 6 [a.u.] 2 × 10 -5 4 k (Streamer) 1 × 10 -5 2 0 0 -1 × 10 -5 -2 -2 × 10 -5 -4 -6 -6 -4 -2 0 2 4 6 Radial wave number q x ρ ti 9
Suppression of electron-scale streamers by high-k x ITG/TEM structures. Kinetic electrons create 𝒒,𝒓 Triad transfer 𝐾 𝑡𝒍 for a streamer 𝑡 fine radial structures (k x ρ ti ,k y ρ ti )=(0,4.4) at t=20-30R/v ti [Dominski12JPCS, (k x ρ ti >1). Maeyama14PoP] Poloidal wave number q y ρ ti 6 [a.u.] 2 × 10 -5 4 k (Streamer) 1 × 10 -5 2 0 0 p (~1.6 ρ ti -1 ) -1 × 10 -5 -2 -2 × 10 -5 -4 -6 -6 -4 -2 0 2 4 6 Radial wave number q x ρ ti 9
Suppression of electron-scale streamers by high-k x ITG/TEM structures. Kinetic electrons create 𝒒,𝒓 Triad transfer 𝐾 𝑡𝒍 for a streamer 𝑡 fine radial structures (k x ρ ti ,k y ρ ti )=(0,4.4) at t=20-30R/v ti [Dominski12JPCS, (k x ρ ti >1). Maeyama14PoP] Poloidal wave number q y ρ ti 6 [a.u.] At the reduction phase, 2 × 10 -5 4 these radial structures k (Streamer) suppress streamers. 1 × 10 -5 2 0 0 p (~1.6 ρ ti -1 ) -1 × 10 -5 -2 -2 × 10 -5 -4 -6 -6 -4 -2 0 2 4 6 Radial wave number q x ρ ti 9
Suppression of electron-scale streamers by high-k x ITG/TEM structures. Kinetic electrons create 𝒒,𝒓 Triad transfer 𝐾 𝑡𝒍 for a streamer 𝑡 fine radial structures (k x ρ ti ,k y ρ ti )=(0,4.4) at t=20-30R/v ti [Dominski12JPCS, (k x ρ ti >1). Maeyama14PoP] Poloidal wave number q y ρ ti 6 [a.u.] At the reduction phase, 2 × 10 -5 4 these radial structures k (Streamer) suppress streamers. 1 × 10 -5 2 0 0 p (~1.6 ρ ti -1 ) -1 × 10 -5 -2 q (Finer mode) -2 × 10 -5 -4 -6 -6 -4 -2 0 2 4 6 Radial wave number q x ρ ti 9
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