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Experimental Techniques at ASDEX Upgrade for Validation of Gyrokinetic Simulations
A.J. Creely1 G.D. Conway,2 S.J. Freethy,1,2 T. Görler,2
T. Happel,1 A.E. White,1 and the ASDEX Upgrade Team2
1 MIT PSFC 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 and by the US DOD under the NDSEG Fellowship
1A.J.CreelyTTF2017,Williamsburg,VA
Validation of Gyrokinetic Codes Requires
Detailed Comparison to Experiment
A.J.CreelyTTF2017,Williamsburg,VA 2
n Gyrokinetic simulations must be validated with experimental results before they can be used predictively
n Ion-scale simulations contain reduced physics, but run much faster than multi-scale simulations (~107 CPU hours) [Howard PoP 2016].
n Would like to use ion-scale simulations, but recent results on Alcator C-Mod suggest that ion-scale GYRO simulations are insufficient for some L- and I-mode plasmas [Creely PoP 2017].
n New techniques on ASDEX Upgrade enable further investigation of these discrepancies, as well as cross-machine and cross-code comparisons:
n Long Wavelength Electron Temperature fluctuations (CECE)
n Perturbative Thermal Diffusivity (Partial Sawtooth Heat Pulses)
Ion-Scale Simulations of Alcator C-Mod
L-mode Plasmas Motivate Further Work
A.J.CreelyTTF2017,Williamsburg,VA 3
n Ion Heat Flux (Matched)
[Creely PoP 2017]
A.J.CreelyTTF2017,Williamsburg,VA 4
n Ion Heat Flux (Matched)
n Electron Heat Flux (Under)
[Creely PoP 2017]
Ion-Scale Simulations of Alcator C-Mod
L-mode Plasmas Motivate Further Work
Ion-Scale Simulations of Alcator C-Mod
L-mode Plasmas Motivate Further Work
A.J.CreelyTTF2017,Williamsburg,VA 5
Ion Heat Flux-Matched Simulation
χGYROpert = 0.4m2 sχExp
pert = 4.0m2 s
n Ion Heat Flux (Matched)
n Electron Heat Flux (Under)
n Perturbative Diffusivity (Under)
[Creely PoP 2017]
Ion-Scale Simulations of Alcator C-Mod
L-mode Plasmas Motivate Further Work
A.J.CreelyTTF2017,Williamsburg,VA 6
Ion Heat Flux-Matched Simulation
χGYROpert = 0.4m2 sχExp
pert = 4.0m2 s
n Ion Heat Flux (Matched)
n Electron Heat Flux (Under)
n Perturbative Diffusivity (Under)
n Temperature Fluctuations (Under)
Sensitivity Limit
[Creely PoP 2017]
Ion-Scale Simulations of Alcator C-Mod
L-mode Plasmas Motivate Further Work
A.J.CreelyTTF2017,Williamsburg,VA 7
Ion Heat Flux-Matched Simulation
χGYROpert = 0.4m2 sχExp
pert = 4.0m2 s
n Ion Heat Flux (Matched)
n Electron Heat Flux (Under)
n Perturbative Diffusivity (Under)
n Temperature Fluctuations (Under)
Sensitivity Limit
[Creely PoP 2017]
Ion-Scale Simulations of Alcator C-Mod
L-mode Plasmas Motivate Further Work
A.J.CreelyTTF2017,Williamsburg,VA 8
Ion Heat Flux-Matched Simulation
χGYROpert = 0.4m2 sχExp
pert = 4.0m2 s
n Ion Heat Flux (Matched)
n Electron Heat Flux (Under)
n Perturbative Diffusivity (Under)
n Temperature Fluctuations (Under)
Sensitivity Limit
Done on ASDEX Upgrade Same Result
Done on ASDEX Upgrade Different Results
In Progress on ASDEX Upgrade
In Progress on ASDEX Upgrade
[Told PoP 2013]
[Creely PoP 2017]
[Told PoP 2013]
Perturbative Thermal Diffusivity Governs
the Propagation of Heat Pulses
A.J.CreelyTTF2017,Williamsburg,VA 9
€
χePB =
1ne
Q∇rTe
χepert =
1ne
∂Q∂(∇rTe )
n Standard power balance electron thermal diffusivity, governs steady state diffusion.
n Perturbative, or incremental, thermal diffusivity governs the diffusion of perturbations and is related to stiffness [Tubbing NF 1987].
n Should not be directly compared with one another [Cardozo PPCF 1995].
€
ne∇rTe€
Qe
Perturbative Diffusivity is Measured
Experimentally through Heat Pulses
A.J.CreelyTTF2017,Williamsburg,VA 10
n Heat pulses generated with partial sawteeth [Creely NF 2016], modulated ECH [Ryter PPCF 2010], etc.
n Partial sawteeth avoid non-diffusive ‘ballistic’ transport associated with full sawteeth [Fredrickson PoP 2000].
n Perturbative diffusivity calculated here with Extended-Time-to-Peak Method for partial sawteeth [Tubbing NF 1987, Creely NF 2016].
n Can then compare to gyrokinetics [Smith NF 2015].
χepert ~ VHP
αVelocity of Peak: VHP Pulse Damping: α
Alcator C-Mod Partial Sawtooth Heat Pulse
Perturbative Thermal Diffusivity Found to
Correlate with Various Plasma Parameters
A.J.CreelyTTF2017,Williamsburg,VA 11
n Previous work investigated the correlation between perturbative diffusivity and various plasma parameters (ne, Te, a/LTe, etc.)
C-Mod data from [Creely NF 2016]
Perturbative Thermal Diffusivity Found to
Correlate with Various Plasma Parameters
A.J.CreelyTTF2017,Williamsburg,VA 12
C-Mod data from [Creely NF 2016]
n Previous work investigated the correlation between perturbative diffusivity and various plasma parameters (ne, Te, a/LTe, etc.)
n Initial work on ASDEX Upgrade shows trends consistent with those found on Alcator C-Mod
Future Work Will Compare to Perturbative
Diffusivity Measured with Modulated ECH
A.J.CreelyTTF2017,Williamsburg,VA 13
n All previous work with partial sawteeth has been on Alcator C-Mod, which doesn’t have ECH.
n ASDEX Upgrade can also measure perturbative diffusivity with modulated ECH [Ryter PPCF 2001].
n Allows for cross-machine gyrokinetic validation (GENE and GYRO), and multi-scale simulations
[Adapted from Ryter PPCF 2001]
Modulated ECH on ASDEX Upgrade
Future Work Will Compare to Perturbative
Diffusivity Measured with Modulated ECH
A.J.CreelyTTF2017,Williamsburg,VA 14
n All previous work with partial sawteeth has been on Alcator C-Mod, which doesn’t have ECH.
n ASDEX Upgrade can also measure perturbative diffusivity with modulated ECH [Ryter PPCF 2001].
n Allows for cross-machine gyrokinetic validation (GENE and GYRO), and multi-scale simulations
[Adapted from Ryter PPCF 2001]
Modulated ECH on ASDEX Upgrade
Preliminary Data Falls in this Range
Correlation Electron Cyclotron Emission
(CECE) Measures Temperature Fluctuations
A.J.CreelyTTF2017,Williamsburg,VA 15
n CECE measures low-k (kθρs<0.4) electron temperature fluctuations, key to understanding ITG/TEM turbulence [Freethy RSI 2016, This Conference]
n Correlating two closely spaced ECE radiometer channels allows detection of fluctuations below thermal noise of single channel
n Statistical noise floor depends on length of the measurement time period.
Statistical Noise Floor
ASDEX Upgrade Shot 33995
ρtor= 0.66
New Hardware on ASDEX can Measure
Radial Profiles and Correlation Length
A.J.CreelyTTF2017,Williamsburg,VA 16
n Recent upgrade from 10 channels on two systems to 30 channels on one system
n Allows for fine radial profile measurements
n Preliminary analysis of L-modes shows that temperature fluctuation levels increase with radius
n Future work will look at radial correlation lengths
Conclusions and Future Work
A.J.CreelyTTF2017,Williamsburg,VA 17
n Would like to use ion-scale gyrokinetic simulations, but recent results on Alcator C-Mod suggest that ion-scale GYRO simulations are insufficient for some L- and I-mode plasmas [Creely PoP 2017].
n New techniques on ASDEX Upgrade enable further investigation of these discrepancies, as well as cross-machine and cross-code comparisons:
n New CECE enables fine radial profile and correlation length measurements
n Partial Sawtooth Heat Pulses enable passive measurement of perturbative thermal diffusivity
n Currently in the process of comparing GYRO and GENE on Alcator C-Mod and utilizing new techniques on ASDEX Upgrade for GENE comparisons.
References [1] N.T. Howard et al., Phys. Plasmas 23, 056109 (2016). [2] A.J. Creely et al., Phys. Plasmas, 24, 056104 (2017). [3] Told, D. et al., Physics of Plasmas 20, 122312 (2013). [4] Tubbing, B.J.D. et al., Nucl. Fusion 27, 1843 (1987). [5] Lopes Cardozo, N.J., Plasma Phys. Controlled Fusion 37, 799 (1995). [6] A.J. Creely et al., Nucl. Fusion 56, 036003 (2016). [7] Ryter, F. et al., Plasma Phys. Control. Fusion 52, 124043 (2010). [8] Smith, S.P. et al., Nucl. Fusion 55, 083011 (2015). [9] Fredrickson, E.D., et al., Phys. Plasmas 7, 5051 (2000). [10] Ryter, F. et al., Plasma Phys. Controlled Fusion 43, A323 (2001). [11] S.J. Freethy et al., Rev. Sci. Instum., 87, 11E102 (2016). [12] S.J. Freethy, This Conference. [A1] F. Jenko et al., Phys. Plasmas 7, 1904 (2000). [A2] A. Casati et al., Phys. Rev. Lett. 102, 165005 (2009). [A3] Citrin, J. et al., Nucl. Fusion 54, 023008 (2014).
18A.J.CreelyTTF2017,Williamsburg,VA
19
Backup Slides
A.J.CreelyTTF2017,Williamsburg,VA
Radial Profile Resolution Greatly Expanded
A.J.CreelyTTF2017,Williamsburg,VA 20
n In 2017 – Greater flexibility and increased number of channels to allow finer δTe/Te radial profiles (below) and radial correlation lengths
2015/16 radial profile
2017 radial profile
Perturbative Thermal Diffusivity is Related
to Gyrokinetic Temperature Profile Stiffness
21
n In gyrokinetic simulations, can measure slope of heat flux against a/LTe above the critical gradient [Citrin NF 2014].
n Run gyrokinetics with different a/LTe to map out slope.
n Can compare to experimentally measured perturbative diffusivity [Smith NF 2015]
High and low stiffness plasmas, with same critical gradient.
A.J.CreelyTTF2017,Williamsburg,VA
∂Qe
∂(a / LTe )= χe
HP ⋅neTea
a/LTe
Qe (MW/m2)
Higher Stiffness
Lower Stiffness
LTe =Te∇Te
A.J.CreelyTTF2017,Williamsburg,VA 22
Te Before Sawtooth
A.J.CreelyTTF2017,Williamsburg,VA 23
Te
r Inversion Radius
Mixing Radius
Before Sawtooth
After Full Sawtooth
Ballistic Effect
Partial Sawtooth
A.J.CreelyTTF2017,Williamsburg,VA 24
Te
r Inversion Radius
Mixing Radius
Before Sawtooth
After Partial Sawtooth
Perturbative Diffusivity is Measured
Experimentally through Heat Pulses
A.J.CreelyTTF2017,Williamsburg,VA 25
n Propagation of diffusive heat pulses in plasma can be used to measure perturbative diffusivity.
n Heat pulses generated with partial sawteeth crashes, modulated ECH, etc. [Creely NF 2016, Cardozo PPCF 1995, Ryter PPCF 2010]
n Perturbative diffusivity calculated here with Extended-Time-to-Peak Method for partial sawteeth [Tubbing NF 1987, Creely NF 2016].
χeHP ~ VHP
αVelocity of Peak: VHP Pulse Damping: α
ASDEX Partial Sawtooth Heat Pulse
ECE Radiometer
Perturbative Diffusivity is Measured
Experimentally through Heat Pulses
A.J.CreelyTTF2017,Williamsburg,VA 26
n Propagation of diffusive heat pulses in plasma can be used to measure perturbative diffusivity.
n Heat pulses generated with partial sawteeth crashes, modulated ECH, etc. [Creely NF 2016, Cardozo PPCF 1995, Ryter PPCF 2010]
n Perturbative diffusivity calculated here with Extended-Time-to-Peak Method for partial sawteeth [Tubbing NF 1987, Creely NF 2016].
χeHP ~ VHP
αVelocity of Peak: VHP Pulse Damping: α
ASDEX Partial Sawtooth Heat Pulse
Perturbative Diffusivity is Measured
Experimentally through Heat Pulses
A.J.CreelyTTF2017,Williamsburg,VA 27
n Propagation of diffusive heat pulses in plasma can be used to measure perturbative diffusivity.
n Heat pulses generated with partial sawteeth crashes, modulated ECH, etc. [Creely NF 2016, Cardozo PPCF 1995, Ryter PPCF 2010]
n Perturbative diffusivity calculated here with Extended-Time-to-Peak Method for partial sawteeth [Tubbing NF 1987, Creely NF 2016].
χeHP ~ VHP
αVelocity of Peak: VHP Pulse Damping: α
ASDEX Partial Sawtooth Heat Pulse
Perturbative Diffusivity is Measured
Experimentally through Heat Pulses
A.J.CreelyTTF2017,Williamsburg,VA 28
n Propagation of diffusive heat pulses in plasma can be used to measure perturbative diffusivity.
n Heat pulses generated with partial sawteeth crashes, modulated ECH, etc. [Creely NF 2016, Cardozo PPCF 1995, Ryter PPCF 2010]
n Perturbative diffusivity calculated here with Extended-Time-to-Peak Method for partial sawteeth [Tubbing NF 1987, Creely NF 2016].
χeHP ~ VHP
αVelocity of Peak: VHP Pulse Damping: α
ASDEX Partial Sawtooth Heat Pulse
New Hardware on ASDEX can Measure
Radial Profiles and Correlation Length
A.J.CreelyTTF2017,Williamsburg,VA 29
Waveguide
Local Oscillator
Mixer
Amplifier
Power Divider
Amplifier
Detector
Digitizer
Mirror Bandpass
Filter
Antenna
Plasma
24 Fixed Frequency Channels 6 Tunable Frequency Channels
New Hardware on ASDEX can Measure
Radial Profiles and Correlation Length
A.J.CreelyTTF2017,Williamsburg,VA 30
Sensitivity Limit
Noise
n Recent upgrade from 10 channels on two systems to 30 channels on one system
n Preliminary analysis of L-modes shows that temperature fluctuation levels increase with radius
!TT = 0.48%!TT = 0.63%!TT = 0.80%
Alcator C-Mod GYRO parameters
A.J.CreelyTTF2017,Williamsburg,VA 31
n Will compare experimental Qi , Qe , fluctuations and perturbative diffusivity to global (r/a = 0.65 - 0.9) nonlinear GYRO simulations.
n Simulations exhibit high physics fidelity: n All inputs were obtained from experiment n 3 kinetic species (deuterium, electrons, impurities) n Realistic geometry (Miller parameterization) n Electrostatic turbulence (E&M effects neglected due to low beta) n Rotation effects (ExB shear, etc.) n e-i, and i-i collisions are included
n Simulation box size of approximately 105 x 120 ρs n 28 toroidal modes ; ~500 radial grid points n Captures long wavelength (ITG/TEM) up to kθρs up to ~ 1.35
[Candy PRL 2003]