Overview of Gyrokine.c Studies on Electromagne.c Turbulence P.W. - - PowerPoint PPT Presentation

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Overview of Gyrokine.c Studies on Electromagne.c Turbulence P.W. - - PowerPoint PPT Presentation

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OV/51 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.

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SLIDE 1

Overview of Gyrokine.c Studies on Electromagne.c Turbulence

P.W. Terry1, D. Carmody1, H. Doerk2, W. GuEenfelder3, D.R. Hatch4, C.C. Hegna1, A. Ishizawa5, F. Jenko 2,6, W.M. Nevins7, I. Predebon8, M.J. Pueschel1, J.S. Sarff1, and G.G. Whelan1

1University of Wisconsin‐Madison 2Max Planck Ins:tute for Plasma Physics, Garching, Germany 3Princeton Plasma Physics Laboratory 4Ins:tute for Fusion Studies, University of Texas at Aus:n 5Na:onal Ins:tute for Fusion Science, Japan 6University of California at Los Angeles 7Lawrence Livermore Na:onal Laboratory 8Conzorzio RFX, Padua, Italy

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SLIDE 2

Recent Discoveries from Gyrokine.c Studies of Turbulence and Transport at Finite β

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

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SLIDE 3

Background

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

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  • 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

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SLIDE 4

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

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SLIDE 5

Introduc.on: Gyrokine.cs Gyrokine.cs: eliminate the fast gyrophase from the equa.ons of mo.on ⇒ significant speed up ⇒ gyrokine.c Vlasov, field equa.ons

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Capabili.es used:

  • Nonlinear gyrokine.c equa.ons
  • Radially local simula.ons
  • δf approach
  • Mul.ple geometries and equilibria
  • Electromagne.c, binary collisions
  • Codes: GENE, GYRO, GS2, GKV
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SLIDE 6

Satura.on at Finite β Modeling Scaling Analysis Nonlinearity excites damped modes in unstable k‐space range

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k k k-k k

kx ky Unstable mode Stable mode 1 Stable mode 2 Stable mode 3 Stable mode 4

k k k

Tearing Parity Stable Modes Non Zonal Transi.on Kine.c Ballooning Mode

Energy transfer: • High k modes (tradi.onal cascade)

  • Damped modes at same k

Damped modes: • Thousands excited

  • Significant sink for satura.on

In CBC ITG turbulence: O(104) damped modes excited OV/5‐1 kyρi = 0.2

Makwana 2014

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SLIDE 7

Satura.on at Finite β Modeling Scaling Analysis 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

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Tearing Parity Stable Modes Non Zonal Transi.on Kine.c Ballooning Mode

OV/5‐1 Hatch 2012, 2013

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SLIDE 8

Satura.on at Finite β Modeling Scaling Analysis 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

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Tearing Parity Stable Modes Non Zonal Transi.on Kine.c Ballooning Mode

Away from kyρs = 0.2, flux not aEributable to unstable mode Not captured by quasilinear theory OV/5‐1 Hatch 2013

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SLIDE 9

Satura.on at Finite β Modeling Scaling Analysis

Above a cri.cal β zonal flows are disabled and transport ‘runs away’ to high values

  • Very large fluxes
  • ~ 0.9% Cyclone base case

Zonal flows are disabled through magne.c field stochas.city

  • Allows charge to stream

from flux surfaces

  • Confirmed by residual

flow calcula.on

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Tearing Parity Stable Modes Non Zonal Transi.on Kine.c Ballooning Mode

crit

NZT

OV/5‐1 Pueschel 2013, Terry 2013

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SLIDE 10

Satura.on at Finite β Modeling Scaling Analysis set by a form of overlap criterion

  • When
  • is radial displacement of perturbed

field <Bx> in ½ poloidal turn

  • λBxx is radial correla.on length
  • depends on gradients through <Bx>

=> increases with weaker gradients

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Tearing Parity Stable Modes Non Zonal Transi.on Kine.c Ballooning Mode

crit

NZT

crit

NZT

crit

NZT

crit

KBM

1 T T,crit

( )

/ 2 (0.5 < < 1)

r

1/2 Bxx

r

1/2

r

1/2

T = T r R0 T

where OV/5‐1 Pueschel 2013

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SLIDE 11

Satura.on at Finite β Modeling Scaling Analysis In absence of zonal flows (high β) kine.c ballooning mode saturates by developing par.cular structures

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Tearing Parity Stable Modes Non Zonal Transi.on Kine.c Ballooning Mode

ITG

% 2 . = β

φ

Radial direc.on

Linear Nonlinear KBM (Tokamak) KBM (Helical)

% 7 . 1 = β .% 2 = β

OV/5‐1 Ishizawa 2013

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SLIDE 12

Satura.on at Finite β Modeling Scaling Analysis

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Tearing Parity Stable Modes Non Zonal Transi.on Kine.c Ballooning Mode

  • Tokamak: twisted modes along the field line saturate KBM
  • LHD: most unstable KBM has finite radial wavenumber, kr

=> Satura.on caused by nonlinear interac.ons between oppositely inclined finite kr modes

KBM (beta=1.7%) regulated by oppositely inclined modes ITG (beta=0.2%) regulated by zonal flows KBM (beta=1.7%) regulated by oppositely inclined modes OV/5‐1

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SLIDE 13

Satura.on at Finite β Modeling Scaling Analysis

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Tearing Parity Stable Modes Non Zonal Transi.on Kine.c Ballooning Mode ITG 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

Zonal flow

2 2

/ 5

n i Ti i i

L v T n Q ρ =

2 2

/ 3

n i Ti i i

L v T n Q ρ =

KBM Ishizawa 2014 , IAEA‐FEC TH/P6-40 OV/5‐1

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SLIDE 14

Satura.on at Finite β Modeling Scaling Analysis

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NSTX RFX‐mod MST

  • Transport from magnetic “flutter”

χe,em~v||,eδBr

  • Unclear what sets overall saturation and

scaling of δBr

  • Threshold in ∇Te, or βe
  • γ and χe depend on νe (.me‐

dependent thermal force)

  • χe~νe consistent with global

confinement trends ΩτE~ν*

‐1

NSTX: MTM drives large χe (high β , high ν)

OV/5‐1 GuEenfelder 2013 Gyrokine.c simula.on: MTM in standard tokamaks (Doerk 2011)

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SLIDE 15

Satura.on at Finite β Modeling Scaling Analysis

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NSTX RFX‐mod MST

  • MTM: most unstable mode in transport barriers of helical states (QHS)
  • Quasi‐linear collisionless form of χe~(ρe/LTe) vth,eLc, in good agreement with

experiment

  • Unstable for a/LTe~2.5 – 3 for typical values of β

MTM in the RFP is sensi.ve to grad‐B/ curvature drixs in ωd. Collisionless MTMs exist, even neglec.ng trapped electron dynamics. Retaining δφ is always destabilizing. OV/5‐1 Predebon 2013

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SLIDE 16

Satura.on at Finite β Modeling Scaling Analysis

MTM is unstable in standard MST discharges at low θ Study with toroidal Bessel func.on equilibrium Thresholds: Finite growth rate as collisionality ‐> 0 Requires weak to moderate shear Theory: Start with DKE, take high freq. fluid limit Instability as ν ‐> 0 if φ ≠ 0 Enabled by ωDe (ωDe in RFP is larger than tokamak value by R/a)

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NSTX RFX‐mod MST

OV/5‐1 (low θ => low magne.c shear) β = few % a/LTe = 3 ‐ 4 Carmody 2013

ˆ s = 0.4 ˆ s = 0.7 ˆ s = 1.3

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SLIDE 17

Satura.on at Finite β Modeling Scaling Analysis

MST enhanced‐confinement discharges show surprising absence of electrosta.c turbulence Gyrokine.c modeling (fiyng experimental equilibrium): TEM/ITG

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NSTX RFX‐mod MST

OV/5‐1 Flat current profile (reduce global tearing) High θ (high shear) Instability in outer region (β small)

  • Density gradient driven TEM (frequency in electron direc.on)
  • At β ~ 1 – 2%, discharge is below cri.cal β for MTM, NZT, etc.
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SLIDE 18

Satura.on at Finite β Modeling Scaling Analysis 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
  • χe at experimental level

Key issue:

Despite rela.vely high β, RPF is below cri.cal β for electromagne.c effects Why? OV/5‐1

NSTX RFX‐mod MST

OV/5‐1

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SLIDE 19

Satura.on at Finite β Modeling Scaling Analysis RFP equilibrium has smaller length scales than standard tokamak

Smaller equilibrium scales generally push instability thresholds to higher values Gyrokine.cs: (for both electrosta.c and electromagne.c)

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Preliminaries Cri.cal Thresholds

OV/5‐1 !"#$%$&'$#() *+,%-)./)) 0,'$,1.2) 3.22-+1.2) %-2456) *,/-57)/,+5.')")) 8.9,(,9) : ;;):) <) "<) ");)=) <>?) : )):) ) ') ') ")@)ABC)

1 LcritRFP R r

  • 1

Lcrittok

ITG TEM MTM

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SLIDE 20

Satura.on at Finite β Modeling Scaling Analysis

In RFP all β thresholds for electromagne.c effects pushed to much higher values Primary causes: Shorter magne.c shear scale lengths: Smaller q ITG stabiliza.on NZT KBM Larger shear, smaller q push electromagne.c effects to higher β Higher cri.cal gradients allow steeper gradients in experiment

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Preliminaries Cri.cal thresholds

OV/5‐1 LSTok LSRFP ~ qTokq0RFP R r

  • 2

~ O R r

  • nT

2 2 1+ T / q0

( )

2

  • 1

q0

2 ( + 2n)( +1)+ 2e

  • 1 ~ O R

r

  • critTok

critRFP

NZT

critTok

NZT R0

r

  • 1+/2

q0Tok

critRFP

KBM

~ 0.6 R r

  • q R0

Ln + R0 LTe + R0 Ln + R0 LTi

  • Ti

Te

  • >> critTok

KBM

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SLIDE 21

Conclusions

Microturbulence at finite β subject to new effects

  • Stable tearing parity fluctua.ons excited by ITG => electron heat transport
  • Magne.c fluctua.ons can disable zonal flows => much higher transport
  • New instabili.es arise (microtearing, kine.c ballooning mode)
  • Shorter magne.c scale lengths push these effects to higher gradients, beta

Satura.on of microturbulence at finite β involves complex feedback loops, especially with zonal flows and magne.c fluctua.ons (both stable and unstable) Have demonstrated:

  • How interplay between instability, nonlinearly excited stable modes, zonal flows affects

satura.on and transport (varia.on of β changes balances to reveal physics)

  • Magne.c field scales push cri.cal gradients and β to higher values

OV/5‐1