electron temperature fluctuations and profile stiffness in alcator … · 2016-05-13 · electron...

Electron Temperature Fluctuations and Profile Stiffness in Alcator C-Mod L-mode and I-mode Plasmas

A.J. Creely1 A.E. White,1 G. Conway,2 S. Freethy,2

N.T. Howard,1 A.E. Hubbard1

1 MIT 2 Max Plank Institute for Plasma Physics – Garching This work is supported by the US DOE under Grants DE-SC0006419 and DE-FC02-99ER54512-CMOD

1A.J.Creely,TTF,Denver,CO 30.3.16

Abstract

30.3.16A.J.Creely,TTF,Denver,CO 2

Experimentally measured core electron temperature fluctuations and perturbative electron thermal diffusivity in Alcator C-Mod I-mode plasmas are compared to gyrokinetic simulations using the GYRO code. I-mode plasmas are characterized by high energy confinement, similar to H-mode, but with L-mode-like particle confinement, making I-mode very favorable for reactors due to the natural absence of Edge Localized Modes (ELMs), but with no impurity accumulation [D.G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. Previous work has revealed that core electron temperature fluctuations measured with a Correlation Electron Cyclotron Emission (CECE) diagnostic are reduced in I-mode [A.E. White et al., Nucl. Fusion 54, 083019 (2014)]. Gyrokinetic simulations with the GYRO code underestimate this reduction in temperature fluctuations, but do predict stiffer temperature profiles [A.E. White et al., Phys. Plasmas 22, 056109 (2015)]. In this work, a new method of measuring perturbative thermal diffusivity (which is related to profile stiffness) [A.J. Creely et al., Nucl. Fusion 56, 036003 (2016)] is applied to these same I-mode plasmas in order to relate changes in temperature fluctuations to changes in perturbative thermal transport. Preliminary results with L-mode plasmas reveal that ion-scale simulations under-predict profile stiffness, but that multi-scale simulations agree quantitatively with experimental measurements.

Transport Quantities for Comparison with

Nonlinear Gyrokinetic Codes


n  To validate gyrokinetic codes, must compare as many experimental quantities as possible to the code output.

n  In this work, concerned primarily with energy transport, not with particle transport.

n  Will measure and compare the following quantities:

n  Ion and Electron Heat Fluxes (power balance diffusivity)

n  Long Wavelength Temperature Fluctuations

n  Perturbative Diffusivity

n  New method utilized here for perturbative measurements

n  Standard power balance electron thermal diffusivity governs steady state diffusion.

n  Perturbative, or heat pulse, thermal diffusivity, governs the diffusion of perturbations [Tubbing NF 1987].

n  Should not be directly compared with one another.

n  Same only if heat flux and temperature gradient are linearly related with no offset [Cardozo PPCF 1995].

Perturbative Thermal Diffusivity Governs

the Propagation of Heat Pulses

4

χePB =

1ne

Qe

∇Te

χeHP =

1ne

∂Qe

∂(∇Te )

€

ne∇rTe€

Qe

A.J.Creely,TTF,Denver,CO 30.3.16

Heat Pulse Thermal Diffusivity is Related to

Gyrokinetic Temperature Profile Stiffness

5

a/LTe

Qe (MW/m2)

Higher Stiffness

Lower Stiffness

n  In gyrokinetic simulations, define temperature profile stiffness as slope of heat flux against a/LTe above the critical gradient [Citrin NF 2014].

n  Can use perturbative diffusivity measurements to validate new multi-scale gyrokinetic simulations [Howard PoP 2014].

n  Can also investigate high confinement regimes, which tend to have higher temperature stiffness [White PoP 2015].

High and low stiffness plasmas, with same critical gradient.


Stiffness = ∂Qe

∂(a / LTe )= χe

HP ⋅neTea

LTe =Te∇Te

Time (s)0.91 0.92 0.93 0.94 0.95 0.96

Tem

pera

ture

(keV

)

0

1

2

3

4

5

6Alcator C-Mod Shot 1101209029

r/a = 0.09r/a = 0.22r/a = 0.35r/a = 0.47r/a = 0.59r/a = 0.70r/a = 0.79r/a = 0.88r/a = 0.97

Partial Sawteeth Generated Heat Pulses Used

to Calculate Perturbative Diffusivity

6

n  Modeling showed partial sawtooth heat pulses consistent with diffusive transport [Fredrickson 2000].

n  C-Mod partial sawteeth exhibit diffusive characteristics [Creely NF 2016].

n  Can be measured with Extended-Time-to-Peak Method [Tubbing NF 1987].

Velocity of Peak: VHP Pulse Damping: α Minor Radius: ac

Diffusive Pulse Shape

A.J.Creely,TTF,Denver,CO 30.3.16€

χeHP = 4.2 acVHP

α

Partial Sawtooth

1101209029

Core

Edge

[Creely NF 2016]

Correlation ECE Radiometer Measures

Temperature Fluctuations on C-Mod


[Sung RSI 2012]

Lens

Antenna

Local Oscillator

Mixer

Amplifier

Bandpass Filter

Amplifier

Detector

Digitizer

Not to Scale

Heat Pulse Thermal Diffusivity in L-Mode and

I-Mode Confinement Will be Compared n  I-Mode is a high confinement regime

n  Steep Te pedestal, no ne pedestal n  Ti pedestals are similar n  High Te, Ti and rotation across profile

n  Energy confinement comparable to or exceeding H-mode [Whyte 2010].

n  L-mode density profile n  Impurity confinement like L-mode

n  I-mode observed on C-Mod, ASDEX Upgrade and DIII-D [Hubbard 2012].

8

Alcator C-Mod Shot 1120907028


Goal: Compare TRANSP, CECE, in L-

and I-mode on C-Mod to Gyrokinetics

Confinement Quantity Experiment Ion-Scale

GYRO Multi-Scale

GYRO

L-Mode

Heat Flux X X X

Fluctuations X X (not yet

compared)

Perturbative Diffusivity X

X X

I-Mode

Heat Flux X X

Fluctuations X X

Perturbative Diffusivity X X


TRANSP Power Balance: Consistency

Checks and L- and I-Mode Comparisons


n  Experimental Comparisons Between L-mode and I-mode:

n  Temperature Profiles

n  Stored Energy

n  Power Balance Thermal Diffusivities

n  Power Balance Heat Fluxes

n  Consistency Checks:

n  Measured and Calculated Total Stored Energy

n  Measured and Calculated Neutron Rate

n  Measured and Calculated Plasma Current

TRANSP L/I Comparison: Fitted

Experimental Temperature Profiles


L-mode: I-mode:

1120917021

[TRANSP Code]

TRANSP L/I Comparison: Stored Energy


L-mode: I-mode:

1120917021

[TRANSP Code]

TRANSP L/I Comparison: Power Balance

Thermal Diffusivities


L-mode: I-mode:

1120917021

[TRANSP Code]

TRANSP L/I Comparison: Power Balance

Heat Flux


L-mode: I-mode:

1120917021

[TRANSP Code]

TRANSP Checks: Total Stored Eenrgy


1120917021

[TRANSP Code]

TRANSP Checks: Neutron Count


1120917021

[TRANSP Code]

TRANSP Checks: Plasma Current


1120917021

[TRANSP Code]

Ion-Scale GYRO Matches TRANSP in I-mode,

Underpredicts L-Mode Electron Heat Flux


[White PoP 2015]

Multi-Scale GYRO Matches TRANSP in L-

Mode, Not Yet Performed in I-Mode


[Howard NF 2016]

CECE on C-Mod Measures Reduction in

Temperature Fluctuations in I-Mode


L-mode: I-mode:

γ γr/a = .74 T/T = 0.8% r/a = .76 T/T = 1.1% r/a = .81 T/T = 1.3%

r/a = .74 r/a = .76 r/a = .81 1120921008

Temperature Fluctuation Reduction

Observed at Various Radial Locations


[White NF 2014]

1120917023 - 1120917027

GYRO Underpredicts Reduction in

Temperature Fluctuations at L-I Transition


[White PoP 2015]

Heat Pulse Diffusivity is Generally Higher in

I-Mode than in L-Mode Within the Same Shot


I-Mode is High Confinement with temperature but no density pedestal [Hubbard NF 2012] Ip = 0.9-1.3 MA ne = 0.4-1.3 1020/m3 All Unfavorable Grad B Drift Bt = 5.4 T 0.6 < r/a < 0.9 L- and I-mode diffusivities from same shot

χeHP

χeHP

x=y Line

[Creely NF 2016]

Stiffness from GYRO Simulations Can Be

Compared to Experimental Diffusivity

n  Non-linear GYRO simulations (input a/LTe scan) used to extract incremental diffusivity as slope of Qe/ne versus Grad Te [Smith NF 2015].

n  Have used ion-scale simulations (ITG/TEM only) to model L-mode and I-mode plasmas [White PoP 2015].


10 20 30 40 T (keV/m)

0

5

10

15

Q /n

(k

eV

m

/s)

-∆

I-mode

L-mode

ee

e

.

GY

RO

sca

ns a

rou

nd

Qi m

atc

he

d sim

ula

tion

s (Wh

ite P

oP

20

15

)

Ion-scale only GYRO Stiffness

χGYROHP = 0.3m

2

sχexpHP =1.7m

2

s

χGYROHP = 0.8m

2

sχexpHP = 2.0m

2

s

L-mode: I-mode:

Stiffness from Multi-Scale Gyrokinetic

Simulations Can Match L-Mode Experiment


χexpHP =1.6± 0.4m

2

sχMultiHP =1.4m

2

sχ IonHP = 0.2m

2

s

n  Ion-scale simulations under-predict stiffness for L-mode plasma [White PoP 2015].

n  New multi-scale simulations match experimental values [Howard PoP 2014].

n  Perturbative diffusivities extracted from partial sawtooth heat pulses provide a validation constraint for gyrokinetic simulations.

1120221012

TRANSP, CECE, and Comparisons to

Gyrokinetic Simulations


n  TRANSP Power Balance:

n  Ion-scale GYRO reproduces experimental ion heat fluxes within uncertainties, electron heat fluxes underpredicted in L-mode.

n  Multi-scale GYRO correctly predicts L-mode, not yet performed for I-mode.

n  CECE Temperature Fluctuations:

n  Significant reduction of fluctuations observed in I-mode

n  Reduction underpredicted by ion-scale GYRO simulations

n  Perturbative Thermal Diffusivity:

n  Increased in I-mode compared to L-mode

n  Underpredicted by ion-scale GYRO, quantitative agreement with multi-scale GYRO simulations

Expansion to ASDEX Upgrade: Hardware


[Freethy RSI Submitted]

Expansion to ASDEX Upgrade:

Fluctuations Observed in Helium L-Modes

30.3.16A.J.Creely,TTF,Denver,CO 29[Freethy RSI Submitted]

The Partial Sawtooth Technique Will Be

Applied on ASDEX Upgrade


n  Partial Sawteeth have been identified on ASDEX Upgrade.

n  Allows for comparison to modulated ECH heat pulses [Ryter PPCF 2001].

n  Allows for cross-machine gyrokinetic validation, and investigation of multi-scale simulations.

[Ryter PPCF 2001]

Modulated ECH on ASDEX Upgrade

Conclusions


n  TRANSP Power Balance:

n  Experimental ion heat fluxes reproduced within uncertainties, electron heat fluxes underpredicted in L-mode.

n  Additional TRANSP runs will be performed for other shots.

n  CECE Temperature Fluctuations:

n  Significant reduction of fluctuations observed in I-mode

n  Reduction underpredicted by ion-scale GYRO simulations

n  Perturbative Thermal Diffusivity:

n  Increased in I-mode compared to L-mode

n  Quantitative agreement with multi-scale GYRO simulations

Future Work


n  Additional TRANSP runs of L-I Transitions

n  Comparison of all quantities above in the same shot, at multiple radial locations

n  Comparison to multi-scale I-mode GYRO runs

n  Additional analysis of ASDEX plasmas

n  Comparison of ASDEX measurements to gyrokinetics (GYRO or GENE)

References

[1] Tubbing, B.J.D. et al., Nucl. Fusion 27, 1843 (1987). [2] Lopes Cardozo, N.J., Plasma Phys. Controlled Fusion 37, 799 (1995). [3] Citrin, J. et al., Nucl. Fusion 54, 023008 (2014). [4] Howard, N.T. et al., Phys. Plasmas 21, 112510 (2014). [5] White, A.E. et al., Phys. Plasmas 22, 056109 (2015). [6] Fredrickson, E.D., et al., Phys. Plasmas 7, 5051 (2000). [7] Creely, A.J. et al., Nucl. Fusion 56, 036003 (2016). [8] Sung, C. et al., Rev. Sci. Instrum. 83, 10E311 (2012). [9] Whyte, D.G. et al., Nucl. Fusion 50, 105005 (2010). [10] Hubbard, A.E. et al., Nucl. Fusion 52, 114009 (2012). [11] See http://w3.pppl.gov/transp, the official homepage of TRANSP for

information concerning the models and methods employed in addition to usage documentation.

[12] Howard, N.T. et al., Nucl. Fusion 56 014004 (2016). [13] White, A.E. et al., Nucl. Fusion 54, 083019 (2014). [14] Smith, S.P. et al., Nucl. Fusion 55, 083011 (2015). [15] Freethy, S.J. et al., Rev. Sci. Instrum., Submitted. [16] Ryter, F. et al., Plasma Phys. Controlled Fusion 43, A323 (2001).


electron temperature fluctuations and profile stiffness in alcator … · 2016-05-13 · electron...

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