OV/5‐1 Overview of Gyrokine.c Studies on Electromagne.c Turbulence P.W. Terry 1 , D. Carmody 1 , H. Doerk 2 , W. GuEenfelder 3 , D.R. Hatch 4 , C.C. Hegna 1 , A. Ishizawa 5 , F. Jenko 2,6 , W.M. Nevins 7 , I. Predebon 8 , M.J. Pueschel 1 , J.S. Sarff 1 , and G.G. Whelan 1 1 University of Wisconsin‐Madison 2 Max Planck Ins:tute for Plasma Physics, Garching, Germany 3 Princeton Plasma Physics Laboratory 4 Ins:tute for Fusion Studies, University of Texas at Aus:n 5 Na:onal Ins:tute for Fusion Science, Japan 6 University of California at Los Angeles 7 Lawrence Livermore Na:onal Laboratory 8 Conzorzio RFX, Padua, Italy
Recent Discoveries from Gyrokine.c Studies of Turbulence and Transport at Finite β OV/5‐1 This overview describes • Discoveries concerning satura.on of microinstabili.es at finite β –Effect of stable modes –Effect of stable modes on magne.c fluctua.ons –Modifica.ons of zonal flows –Effect magne.c configura.ons with short magne.c field scale lengths • Compara.ve modeling across different magne.c configura.ons –Special focus: RFP <–> Tokamak • Synthesis of satura.on understanding, modeling and theory allow us to determine scaling behavior of cri.cal β values for confinement effects Key conclusions: • Stable modes (nonlinearly excited) change satura.on, transport • Short magne.c length scales push cri.cal β ’s and gradients to higher values
Background OV/5‐1 Finite β opera.on is highly desirable for fusion • Fusion reac.ons rates, bootstrap current benefit from high β Finite β affects confinement as shown in prior gyrokine.c studies •Various instabili.es arise Kine.c ballooning mode (KBM) Microtearing mode (MTM) •Overtake electrosta.c modes Ion temperature gradient (ITG) Trapped electron mode (TEM) •Finite β affects satura.on mechanisms Zonal flows decrease more slowly with β than ITG growth rate • Damped modes saturate ITG What does finite β do to them? Pueschel 2010
Outline OV/5‐1 Satura.on Studies Tearing parity stable mode Non zonal transi.on KBM Modeling MTM in NSTX MTM in RFX MTM in MST TEM/ITG in MST Scaling Analysis
Introduc.on: Gyrokine.cs OV/5‐1 Gyrokine.cs: eliminate Capabili.es used: the fast gyrophase from the equa.ons of mo.on •Nonlinear gyrokine.c equa.ons ⇒ significant speed up •Radially local simula.ons • δ f approach •Mul.ple geometries and equilibria •Electromagne.c, binary collisions •Codes: GENE, GYRO, GS2, GKV ⇒ gyrokine.c Vlasov, field equa.ons
Satura.on at Finite β Tearing Parity Stable Modes Modeling Non Zonal Transi.on Scaling Analysis Kine.c Ballooning Mode OV/5‐1 OV/5‐1 Nonlinearity excites damped modes in unstable k‐space range Energy transfer: • High k modes (tradi.onal cascade) k � • Damped modes at same k k Unstable k y k-k � mode k x Damped modes: • Thousands excited Stable mode 1 • Significant sink for satura.on k � Stable mode 2 k � k y ρ i = 0.2 Stable mode 3 k � Stable mode 4 k � In CBC ITG turbulence: O(10 4 ) damped modes excited Makwana 2014
Satura.on at Finite β Tearing Parity Stable Modes Modeling Non Zonal Transi.on Scaling Analysis Kine.c Ballooning Mode OV/5‐1 OV/5‐1 A significant subset of damped modes have tearing parity • Damped modes sample z, v || • Unstable mode: ballooning parity • Damped modes: ballooning, tearing, mixed pari.es Zonal flows catalyze transfer to tearing parity modes, leading to • Stochas.c field at low β • FluEer‐induced electron heat transport Hatch 2012, 2013
Satura.on at Finite β Tearing Parity Stable Modes Modeling Non Zonal Transi.on Scaling Analysis Kine.c Ballooning Mode OV/5‐1 OV/5‐1 Tearing parity modes: outward magne.c fluctua.on‐induced electron heat flux Unstable (ITG) mode: inward flux (low k) Tearing parity modes: outward flux at lowest k’s and high k Away from k y ρ s = 0.2, flux not aEributable to unstable mode Not captured by quasilinear theory Hatch 2013
Satura.on at Finite β Tearing Parity Stable Modes Modeling Non Zonal Transi.on Scaling Analysis Kine.c Ballooning Mode OV/5‐1 OV/5‐1 Above a cri.cal β zonal flows are disabled and transport ‘runs away’ to high values • Very large fluxes • ~ 0.9% Cyclone base case NZT � crit Zonal flows are disabled through magne.c field stochas.city •Allows charge to stream from flux surfaces •Confirmed by residual flow calcula.on Pueschel 2013, Terry 2013
Satura.on at Finite β Tearing Parity Stable Modes Modeling Non Zonal Transi.on Scaling Analysis Kine.c Ballooning Mode OV/5‐1 OV/5‐1 NZT set by a form of overlap criterion � crit •When � r 1/2 � � Bxx • is radial displacement of perturbed � r 1/2 field <B x > in ½ poloidal turn • λ Bxx is radial correla.on length • depends on gradients through <B x > � r 1/2 => increases with weaker gradients NZT � crit NZT 1 � crit � / 2 (0.5 < � < 1) KBM � ( ) � crit � T � � T ,crit � T = � T R 0 where � r T Pueschel 2013
Satura.on at Finite β Tearing Parity Stable Modes Modeling Non Zonal Transi.on Scaling Analysis Kine.c Ballooning Mode OV/5‐1 OV/5‐1 In absence of zonal flows (high β ) kine.c ballooning mode saturates by developing par.cular structures ITG 0 . 2 % β = KBM (Tokamak) 2 .% KBM (Helical) 1 . 7 % β = β = φ Linear Nonlinear Radial direc.on Ishizawa 2013
Satura.on at Finite β Tearing Parity Stable Modes Modeling Non Zonal Transi.on Scaling Analysis Kine.c Ballooning Mode OV/5‐1 OV/5‐1 • Tokamak: twisted modes along the field line saturate KBM • LHD: most unstable KBM has finite radial wavenumber, k r => Satura.on caused by nonlinear interac.ons between oppositely inclined finite k r modes KBM (beta=1.7%) regulated by oppositely inclined modes ITG (beta=0.2%) KBM (beta=1.7%) regulated regulated by zonal flows by oppositely inclined modes
Satura.on at Finite β Tearing Parity Stable Modes Modeling Non Zonal Transi.on Scaling Analysis Kine.c Ballooning Mode OV/5‐1 OV/5‐1 Transport at finite‐beta • Zonal flow of KBM turbulence is much weaker than that of ITG turbulence KBM turbulence is less effec.ve in driving transport than ITG turbulence • 2 2 ITG Q 5 n T v / L = ρ i 0 i Ti i n 2 2 KBM Q 3 n T v / L = ρ i 0 i Ti i n Zonal flow Ishizawa 2014 , IAEA‐FEC TH/P6-40
Satura.on at Finite β NSTX Modeling RFX‐mod Scaling Analysis MST OV/5‐1 OV/5‐1 Gyrokine.c simula.on: MTM in standard tokamaks (Doerk 2011) NSTX: MTM drives large χ e (high β , high ν ) • Transport from magnetic “flutter” χ e,em ~v ||,e δ B r • Unclear what sets overall saturation and scaling of δ B r •Threshold in ∇ T e , or β e • γ and χ e depend on ν e (.me‐ dependent thermal force) • χ e ~ ν e consistent with global confinement trends Ωτ E ~ ν * ‐1 GuEenfelder 2013
Satura.on at Finite β NSTX Modeling RFX‐mod Scaling Analysis MST OV/5‐1 OV/5‐1 • MTM: most unstable mode in transport barriers of helical states (QHS) • Quasi‐linear collisionless form of χ e ~( ρ e /L Te ) v th,e L c , in good agreement with experiment • Unstable for a/L Te ~2.5 – 3 for typical values of β MTM in the RFP is sensi.ve to grad‐B/ curvature drixs in ω d . Collisionless MTMs exist, even neglec.ng trapped electron dynamics. Retaining δφ is always destabilizing. Predebon 2013
Satura.on at Finite β NSTX Modeling RFX‐mod Scaling Analysis MST OV/5‐1 OV/5‐1 MTM is unstable in standard MST discharges at low θ Study with toroidal Bessel func.on equilibrium (low θ => low magne.c shear) Thresholds: β = few % a/L Te = 3 ‐ 4 ˆ s = � 0.4 Finite growth rate as collisionality ‐> 0 ˆ s = � 0.7 Requires weak to moderate shear ˆ s = � 1.3 Theory: Start with DKE, take high freq. fluid limit Instability as ν ‐> 0 if φ ≠ 0 Enabled by ω De ( ω De in RFP is larger than tokamak value by R/a ) Carmody 2013
Satura.on at Finite β NSTX Modeling RFX‐mod Scaling Analysis MST OV/5‐1 OV/5‐1 MST enhanced‐confinement discharges show surprising absence of electrosta.c turbulence Flat current profile (reduce global tearing) High θ (high shear) Instability in outer region ( β small) Gyrokine.c modeling (fiyng experimental equilibrium): TEM/ITG • Density gradient driven TEM (frequency in electron direc.on) • At β ~ 1 – 2%, discharge is below cri.cal β for MTM, NZT, etc.
Satura.on at Finite β NSTX Modeling RFX‐mod Scaling Analysis MST OV/5‐1 OV/5‐1 Saturated turbulence: Large zonal flows Large Dimits shix Transport rates: weaker than experiment by x10 Mock up tearing mode ac.vity using external magne.c perturba.on at experimental level •Weaker zonal flow •Lower Dimits shix – close to exp. gradient • χ e at experimental level Key issue : Despite rela.vely high β , RPF is below cri.cal β for electromagne.c effects Why?
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