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Gyrokinetic Calculations of Microturbulence and Transport for NSTX and Alcator C-MOD H-modes. Martha Redi Princeton 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, - PowerPoint PPT Presentation
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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).
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