Gyrokinetic Calculations of Microturbulence and Transport for NSTX

and Alcator C-MOD H-modes

Martha RediPrinceton Plasma Physics Laboratory

NSTX Physics Meeting

March 17, 2003

Princeton Plasma Physics Laboratory

Acknowledgement:R. Bell, D. Gates, K. Hill, S. Kaye, B. LeBlanc, J. Menard,

D. R. Mikkelsen, G. Rewoldt (PPPL),

C. Fiore, P. Bonoli, D. Ernst, J. Rice, S. Wukitch (MIT)

W. Dorland (U. Maryland)

J. Candy, R. Waltz (General Atomics)

C. Bourdelle (Association Euratom-CEA, France)

Motivation- Investigate microinstabilities in NSTX and CMOD H-mode plasmas

exhibiting unusual plasma transport

- High e, low i, resilient Te profiles on NSTX; ITB formation on CMOD- Identify underlying key plasma parameters for control of plasma performance

METHOD- GS2 and GYRO flux tube simulations- Complete electron dynamics. 3 radii, 4 species. - Linear electromagnetic; nonlinear, electrostatic calculations (CMOD)

RESULTS:

- Gyrokinetics connection with transport: Questions remaining on NSTXConsistent with transportanalysis on CMOD

GS2 criterion H-mode plasmas:

•GS2: Linear, fully electromagnetic, 4 species•Criteria: /L<<1 for GS2,

but profile effects can mix different wavelengths=> * stabilization (GYRO)

•NSTX zone, rho-star, # ion gyroradii across plasma 0.25r/a *=0.0185/0.6= 0.031 32 0.65r/a 0.014 71 0.80r/a 0.0064 157CMOD

0.25r/a 0.008 1220.45r/a 0.008 1220.65r/a 0.006 167

NSTX: NBI in MHD Quiescent Discharge:

Ti > Te, Resilient Te Profiles

LeBlanc-APS-02

Ip = 0.8 MA

BT = 0.5 T

PNBI = 4 MW

ENBI= 90 keV

T = 16%

W = 0.23 MJ

108730

Two Distinct Plasma Conditions: Resilient Te Profiles during Flattop Period

Overlay of 8 consecutive time points: 0.38 - 0. 49 s.

Overlay of 11 consecutive time points: 0.53 - 0.69 s.

Shoulders at 65 and 125 cm disappear during the later phaseLeBlanc-APS-02

NSTX H-mode: Electron Temperature Profile Resiliency

During H-modeTe(r) remains resilientelectron density increasesion temperature decreases

Examine microinstability Growth rates at 3 zones

What clampsElectron temperature profile?

0 0.5 1.0

5

10

15

0 0.5 1.0

2

4

6

0 0.5 1.0

1.0

0.5

0 0.5 1.0

1.5

1.0

0.5

Gyrokinetic Model Equations

Kotschenreuther, et al Comp. Phys. Comm. 88, 128 (1995)

€

˜ Φ (r,θ,ζ , t) = exp[inζ − inq(r)θ] ˜ φ (θ − 2πp,r, t)exp[inq(r)2πp]p=−∞

p=∞

∑Perturbed electrostatic potential:

Linearized gyrokinetic equation in the ballooning representation, Using the “s-” model MHD equilibrium:

€

∂∂t

˜ g s + v//

qR

∂

∂θ˜ g s + iωds ˜ g s + C( ˜ g s) =

es

Ts

FmsJ0(∂

∂t+ iω*s

T )[ ˜ φ (θ) −v //

c˜ A //(θ)]

Where

€

˜ g s ≡ ˜ f s + (es

Ts

)Fms˜ φ (θ),

ωds = ω*s(Lns R)(E Ts)(1+ v //2 v 2){cosθ + [˜ s θ −α cosθ]sinθ}

kθ = −nq /r,k⊥ = kθ {1+ [˜ s θ −α sinθ]2}1 2

˜ s ≡ (r /q)(dq dr),α ≡ −q2R(dβ dr)

ω*sT ≡ ω*s{[1+ η s[E Ts) − 3 2]},J0 ≡ J0(k⊥v⊥ Ωs)

GS2 Evolution of Linear Growth Rates for kI = 0.1 to 0.8 Some stable, some unstable

NSTX r/a=0.8: ITG Range of FrequenciesOutside Core, ITG Range of FrequenciesGrowth Rates and Eigenfunction at Most Unstable Wavelength

kperp-rho-i

kperp-rho-i

Growth rate (10^4/s)

Real Frequency (10^4/s)Ion diamagnetic drift direction

Θ

NSTX r/a=0.8: ETG Range of Frequencies

Outside core, r/a=0.8, ETG modes unstableGrowth rates and eigenfunction at most unstable wavelengthkperp-rho-i ~60

Θ

Growth rate (10^4/s)

Real frequency (10^4/s)electron diamagnetic drift direction

kperp-rho-i

NSTX r/a=0.65: ITG Range of Frequencies

Growth Rates and Eigenfunction of Most Unstable Mode - Tearing Parity

Growth rate (10^4/sec)

Real frequency (10^4/sec)electron diagmagnetic drift direction

kperp-rho-i

kperp-rho-i

Θ

NSTX Core: ITG Range of Frequencies ITG Range of Frequencies at r/a=0.25 - weak instability Growth Rates and Eigenfunctions at Most Unstable Wavelength

Growth rate (10^4/sec)

Real frequency (10^4/sec)Electron diamagnetic drift direction

kperp-rho-i

kperp-rho-i

Θ

NSTX: Examine Microinstability Growth Rates at 3 Zones

0

5 104

1 105

1.5 105

2 105

2.5 105

3 105

0 0.2 0.4 0.6 0.8 1

ITG Range of WavelengthsStronger growth near plasma edge

Weak instabilities insideMicrotearing modes observedLater plasma has stronger ITG

r/a

NSTX 108730ITG-TEM range of frequenciesH-mode

t=0.6 sec

t=0.4 sec

classicitg g(aky)andeven parityeigenfunction

microtearing g(aky)tearing parityeigenfunction

stable

numerical?

Circles denote ExB shearing rate ITG may be stabilized by shearing at all radii

0

5 105

1 106

1.5 106

2 106

0 0.2 0.4 0.6 0.8 1

ETG Range of WavelengthsStronger growth near plasma edge

Weak or stable modes insideLater plasma has weaker ETG

r/a

NSTX 108730ETG range of frequenciesH-mode

stable

t=0.4 sec

t=0.6 sec

classic etg g(aky)even parity eigenfunction

Circles denote ExB shearing rateETG stabilized by shearing rateexcept near edge at r/a=0.8

Experimental Ti < ITG Critical Gradient

r/a=0.25 RTi/Ti < RcTi/Ti

r/a=0.65 RTi/Ti ~ RcTi/Ti

r/a=0.80 RTi/Ti < RcTi/Ti

Stable ITG drift modes are consistent with the

Kotschenreuther Criterion

NSTX: Critical Gradient Below or At Marginal Stability for ITG

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 5 10 15 20

Drift Modes far below Marginal Stability when ExB Shearing Rate (1.9 - GS2 units) Subtracted

Hybrid root changes from ITG to TEM characterbelow experimental a(grad Te)/Te.

Fastest Growing ITG Drift Mode WavelengthsChange little as grad Te/Te is reduced

a(grad Te)/Te

NSTX 108730t=0.4 sec, r/a=0.8

Maximum ITG growth rate

TEM Criticalvalue

kperp rho-ifor fastest growingITG-TEM drift mode

Measured value

ExB Shearing Rate= 1.9 in GS2 units

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 5 10 15 20

Experimental Temperature Gradient is near Marginal Stability for ITG

and above Marginal Stability for TEM Drift Modes.Drift mode with maximum growth rate

changes from ITG to TEM as grad Te/a/Te decreased.Find two critical gradients, for distinct ITG and TEM roots.

a(grad Te)/Te

NSTX 108730t=0.6, r/a=0.8

Maximum growth rate

kperp rho-ifor fastest growingITG-TEM drift mode

TEM ModeCritical value

Measuredvalue

ITG ModeCritical Gradientvalue

ExB Shearing Rate ~ Maximum Growth Rate

NSTX:Above Critical Gradient for ETG Modes

0

20

40

60

80

100

120

0 5 10 15 20

Experimental Temperature Gradient far above Marginal Stability for ETG

ExB Shearing Rate << Maximum Growth RateFastest Growing ETG Drift Mode Wavelengths

and Growth Rates Decrease as grad Te/Te is ReducedHigher Critical Gradient for ETG than ITG

a(grad Te)/Te

MaximumETG growth rate

Kperp-rho-i for fastest growing ETG drift mode

NSTX 108730t=0.4 sec, r/a=0.8

Measured ValueETG

Critical Gradientvalue

ExB Shearing Rate ~1/10 Maximum Growth Rate

0

20

40

60

80

100

120

0 5 10 15 20

Experimental Temperature Gradient far above Marginal Stability for ETG

ExB Shearing Rate <<Maximum growth RateFastest Growing ETG Drift Mode Wavelengths

and Growth Rates Decrease as grad Te/Te is Reduced

a(grad Te)/Te

ETG CriticalGradientValue

MeasuredValue

MaximumETG Growth Rate

kperp rho-ifor fastest growingETG drift mode

NSTX 108730t=0.6, r/a=0.8

ExB Shearing Rate~1/4 Maximum Growth Rate

Summary: Comparison of NSTX H-modeTransport Coefficients to Gyrokinetic Stability

Why is e so large and i so small? Does ETG maintain resilient Te profiles?Need nonlinear and global calculations; MSE and fluctuation diagnostics

0.25

r/a

0.80

0.65

i eITG ETG

< neo stable stable

Likely ExB stabilized

stable

< neo

ExB stabilized Likely ExB stabilized

ExB stabilized stable

< neo ExB stabilized unstable

Likely ExB stabilized

unstable

>> it=0.4s

t=0.6s

t=0.4s

t=0.6s

t=0.4s

t=0.6s

>> i

>> i

Trigger: CMOD Internal Transport BarrierExamine Microinstability Growth Rates at 3 Zones

Ne Te

Ni(deut) Ti

CMOD -Microturbulent Eigenfunctions: Ballooning Structure along field line

Real and imaginaryParts of electrostaticEigenfunction outside ITB region

ki=0.1 to 0.8

Highest growth rates at 0.4-0.5

“Classic” Ion Temperature Gradient Drift Mode

ITB Trigger Time:Linear, Electromagnetic Gyrokinetic Calculations with GS2:Drift wave Microturbulence at ki = 0.1 to 80.Low kI: ITG => I

anomalous outside ITB TEM and ITG: already stabilized at and within ITBHigh ki: ETG driven by strong Te => e

anomalous at and outside ITB

-25

-20

-15

-10

-5

0

5

0.1 1 10

Real frequencies (~10**6/sec)zones 5,9,13

kperp rho-i from 0.1 through 80

kperp rho-i

Plasma core

At ITB

Outside ITB

-1

0

1

2

3

4

0.1 1 10 100

Growth rates at zones 5,9,13for kperp rho-i from 0.1 to 80

ITG stabilized in plasma core and near ITBeta-i small, TE drive weak; ITG and TEM stable

~10**6/sec

kperp rho-i

Outside ITB

At ITB

Plasma core

Electron drift direction

Ion drift direction

NONLINEAR GS2 Simulations confirm linear results

ITB TRIGGER: Before ne peaks, region of reduced transport and stable ITG microturbulence is established without ExB shear

Quiescent, microturbulence in ITB regionModerate microturbulence in plasma coreHigh microturbulence level outside half-radius

Just inside ITB

Outside ITB

In plasma core

dV2

-Strongest driving force: grad Te/Te

Heat Pulse Propagation(Wukitch, Phys. Plas 9 (2002) 2149)

Sawtooth heat pulse propagation measurements of similar experiments:

Effective heatpulse reduced (by factor~10) in a narrow radial region of ~1 cm, located near the foot of the particle barrier, not necessarily within the barrier

GS2 => drops to neoclassical in core and by 1/2 at the barrier

Rmajor -Raxis [m]

ModelData

modelhp( )r

TRANSP analysis indicates barrier in eff (r,t)

persists after density rise is arrested (1.25 - 1.45 sec) ITB phase has been “controlled”

eff = (ne Te e + ni Ti i) (ne Te + ni Ti )

Bonoli, APS 2001

CMOD H-mode GS2 ResultsITB TRIGGER: Before ne peaks, region of reduced transport and

stable microturbulence is established without ExB shear

• ITG, toroidal ion temperature gradient mode => I

anomalous, unstable outside ITBstabilized at & within the ITB, e drops within ITB

At ITB, stabilized by steep density profile and moderate Te

• ETG at higher values of kI => eanomalous

outside and at ITBPrimary contribution to D: from small values of kI, long

Expect neoclassical e, i in core, as found with TRANSP

• Nonlinear simulations confirm quiescent microturbulence at ITBSensitivity studies => ITB observed with off-axis but not on-axis RF is due to weaker (Te)/Te at the barrier, low q(r), 3% BoronITB also occurs spontaneously in ohmic H-mode, Full story will require detailed comparative study of experiments.Need: Ti(r) and reflectometry fluctuation measurements at ITB

SUMMARY:

GS2 linear calculations of drift wave instabilities in the ion temperature gradient and electron temperature gradient range of frequencies, and ExB shear rate:

Roughly consistent with improved ion confinement in NSTX andimproved confinement within and at ITB in CMOD H-mode plasmas

Remarkably good ion transport in NSTX H-mode (Gates, PoP 2002) would be expected from stable ITG throughout plasma

Profile effects (GYRO) via * stabilization may stabilize ITG everywhere. Electron transport => q monotonic so unstable ETG at all r…need MSE

Resilient temperature profiles on NSTX may be maintained through ETG instabilities, Nonlinear calculations needed. Tearing parity microturbulence found - in

contrast to tokamaks - effects on transport to be determined.

Internal transport Barrier on CMOD appears after off-axis RF heating, where microstabilities are quiescent. Nonlinear calculations in ~ agreement with linear. Sawtooth propagation measurements confirm low transport in the region at the trigger time (Wukitch, PoP, 2002).