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Pablo Rodriguez-Fernandez1, A. E. White1, N. M. Cao1,
A. J. Creely1, M. J. Greenwald1, N. T. Howard1, A. E. Hubbard1,
J. W. Hughes1, J. H. Irby1, C. C. Petty2, J. E. Rice1
2017 US/EU Transport Task Force Workshop
April 26th 2017 Williamsburg, VA
Work supported by US DoE under grants DE-FC02-99ER54512(C-Mod) and DE- FC02-04ER54698 (DIII-D) and La Caixa Fellowship
1Plasma Science and Fusion Center (MIT), Cambridge MA
2General Atomics, San Diego CA
Perturbative transport studies the response of the plasma
to intentional or spontaneous perturbations
1
• Relationship between transport fluxes and gradients during transient
perturbations ➔ Physics of “pulse” propagation.
• Perturbative experiments are useful to isolate different effects and identify
contributions to transport.
Ion Heat Flux-Matched
Simulation
cGYROpert = 0.4m2 sc Exp
pert = 4.0m2 s
Courtesy of A.J. Creely
𝜒𝑒𝑃𝐵 =
1
𝑛𝑒
𝑄𝑒
𝛻𝑇𝑒≠ 𝜒𝑒
𝑖𝑛𝑐 =1
𝑛𝑒
𝜕𝑄𝑒
𝜕𝛻𝑇𝑒
• Turbulent transport models should
be able to reproduce perturbative
measurements ➔ Validation
Cold-pulse injections via laser blow-off can be used for
impurity and heat transport studies
Edge
Core
2
• Impurities can be injected using laser blow-off (LBO).
• Enhanced radiation causes drop in edge temperature ➔ Cold pulse.
• Cold pulse propagates inwardly from edge to core.
• Impurity and heat transport phenomena can be tested.
Heat-pulse injections via partial sawtooth and modulated
ECH are also used to probe transient heat transport
• Partial sawtooth heat pulses are used in
Alcator C-Mod and ASDEX-U to measure 𝜒𝑒𝐻𝑃.
(see talk: A.J. Creely, Thursday 4.50pm)
• Extended-Time-to-Peak method [Tubbing NF 1987]:
𝜒𝑒𝐻𝑃 = 4.2
𝑎𝑐𝑉𝐻𝑃
𝛼
• Propagation of ECH heat pulses is used in DIII-D
to measure 𝜒𝑒𝐻𝑃.
• Gentle’s ODE method:
−𝜒𝑒𝐻𝑃𝛻2 ෨𝑇𝑒 + 𝑉𝑒
𝐻𝑃𝛻 ෨𝑇𝑒 +1
𝜏𝐻𝑃 + 𝑖3
2𝜔 ෨𝑇𝑒 +
𝜉𝐻𝑃
𝑛𝑒=
ሚ𝑆𝑒
𝑛𝑒
3
Creely NF 2016
DeBoo APS 2011
At low density, edge cold-pulse injections trigger fast
reversed-polarity responses in the core.
• Expected cold-pulse propagation is observed at high-density.
• At low density, core 𝑻𝒆 rapidly rises after edge cold-pulse injection.
• Past work referred to these phenomena as “non-local” transport events.
5
C-Mod
Gentle PoP 1995
Edge
CoreTEXT
• [Rice 2013; Gao 2014] In C-Mod, Non-local
transport (1) and Intrinsic Rotation (2)
abruptly change at the same value of 𝑛𝑒
• [Shi 2016] In KSTAR, correlation is also present
with addition of ECH.
6
(1)
(2)
Rice NF 2013Gao NF 2014
(1)
(2)
Past work on C-Mod and recent results from KSTAR suggest
correlation with intrinsic rotation
LOC SOC
• Absence of 𝑇𝑒 inversion with
reversed rotation at low/medium 𝐼𝑝.
• New parameterization reveals that
𝑻𝒆 inversions persist passed the
reversal density at 1.1 MA.
7
Recent C-Mod work demonstrates that correlation is not
universal ➔ Not present at high current
• Absence of 𝑇𝑒 inversions with peaked co-current rotation with ICRF.
• Contrasts work with ECH plasmas in KSTAR [Shi 2016], where rotation is
counter-current when 𝑇𝑒 inversions disappear.
8
Courtesy of N.M. Cao
𝑷𝑰𝑪𝑯 = 𝟏. 𝟐𝑴𝑾
Also: Absence of temperature inversions is observed with
co-current rotation in ICRF plasmas on C-Mod
• Conclusions from this work:
𝐼𝑝 and 𝑃𝐼𝐶𝑅𝐹 break universality of correlation between 𝑇𝑒 inversions and
intrinsic rotation reversals.
At high plasma current, temperature inversions persist at high density.
Core heating independent of magnitude of edge perturbation.
• This study did not explain why the core 𝑇𝑒 increase appears, but it proves a
de-coupling between the two momentum and heat transport effects.
9
“The Million Dollar Question”:
Can local turbulent transport model explain the fast 𝑇𝑒
inversions and the the trends with plasma parameters?
Summary of Alcator C-Mod results
• P. Rodriguez-Fernandez et al., “On the correlation between non-
local effects and intrinsic rotation reversals in Alcator C-Mod”,
Nuclear Fusion (accepted)
11Name/Conference/Date
Incremental diffusivity and stiffness are measured in heat
pulse experiments at DIII-D using modulated ECH
• Perturbed transport equation:
−𝐷𝐻𝑃𝛻2 ෨𝑇𝑒 + 𝑉𝐻𝑃𝛻 ෨𝑇𝑒 +1
𝜏𝐻𝑃 + 𝑖3
2𝜔 ෨𝑇𝑒 +
𝜉𝐻𝑃
𝑛𝑒=
ሚ𝑆𝑒
𝑛𝑒
• The real power balance diffusivity can be estimated and the pinch term
contribution in steady state can be inferred:
𝐷𝑃𝐵 =1
𝛻𝑇𝑒න
0
𝛻𝑇𝑒
𝐷𝐻𝑃𝑑 𝛻𝑇𝑒 ⟹ 𝑉𝑃𝐵 =𝑄𝑒
𝑃𝐵
𝑛𝑒𝑇𝑒+
1
𝑇𝑒න
0
𝛻𝑇𝑒
𝐷𝐻𝑃𝑑 𝛻𝑇𝑒
DeBoo PoP 12
• This method assumes:
𝑄𝑒 = −𝑛𝑒𝐷𝑒𝛻𝑇𝑒 + 𝑛𝑒𝑉𝑒𝑇𝑒
𝐷𝑒 = 𝐷𝑒(𝜌,𝑇𝑒,𝛻𝑇𝑒,𝑛,𝛻𝑛) 𝑉𝑒 = 𝑉𝑒(𝜌,𝑇𝑒,𝑛,𝛻𝑛)
• It neglects changes in transport due to
perturbations in the ion channel.
r/a
12Name/Conference/Date
The role of the ion channel in the electron transient
transport at DIII-D is studied
• Comparison of 𝜒𝑒𝑖𝑛𝑐 from gyro simulations and experiments depend on our
capability to isolate the effect of different turbulence drives.
• Transport coupling between ions and electrons is not negligible.
• Previous work (M. Gildner, C.C. Petty) showed that collisional coupling is not
enough to explain ෨𝑇𝑖𝑒𝑥𝑝➔ Coupling through transport coefficients needed.
Gildner 05
r/a r/a
13Name/Conference/Date
New laser blow-off system will be installed on DIII-D
➔ Can we predict the cold pulse behavior?
• 𝑇𝑒 inversion phenomenon has never been studied in DIII-D.
• Looking for evidence of non-local transport is of great interest for the
development of predictive transport models.
”Non-local” thresholds [Gao, NF 2014]
DIII-D?
• PhD Thesis: Bring elements together (new LBO / ECH) to determine if local
models can reproduce the transient behavior.
• Local models suggest ion-electron
transport coupling.
• New experiments can be designed with
cold and heat pulses in same plasma.
• Comprehensive multi-field, multi-scale
fluctuation measurements are available.Rmaj [m]
Integrated modeling tools can be used to study cold pulse
and heat pulse propagation
15
Machine Parameters and
Experimental Data (Diagnostics)Transport Fluxes
Diffusivities GYRO GENE TGLF …
But TRANSP can also be used to predict plasma evolution from first principles
Theory-based models:
Heat/particle transport,
pedestal, sawtooth…
P-TRANSP
”Virtual” Tokamak:
Geometry, Magnetics, Heating
Systems, Gas injections…
Budny NF 2008
Profiles, output, performance…
TRANSP
Validation: 𝑇𝑖 offset, 𝑍𝑒𝑓𝑓, dilution…
Not measured quantities: 𝑞(𝑟), 𝐽(𝑟)…
Xingqiu APS 2013
• A new laser blow-off system will be installed on DIII-D in 2017/8.
• Cold and heat pulses can be launched in the same plasma.
• High-resolution Ti profile and fluctuation measurements will enable the study
of propagation physics.
16
Extensive database of cold pulses has been built in Alcator C-Mod:Rice NF 2013Gao NF 2014Rodriguez-Fernandez NF 2017
P-TRANSP
Validation of modeling techniques for cold and heat pulse propagation
Predictions of propagation of pulses in DIII-D will be made
before LBO is available
New LBO in DIII-D will allow the validation of these predictions
“Predict First” approach will be used to design cold/heat
pulse experiments with LBO in DIII-D
17
• Goal: Find combination of plasma parameters (e.g. Τ𝑎 𝐿𝑇) within error bars
for desired “transport state” (e.g. 𝑄𝑒, 𝜒𝑒𝑖𝑛𝑐).
• Initial plasma conditions and fixed parameters are provided to PTRANSP.
• Both input and output
parameters can vary within
experimental error bars.
• Machine learning methods
speed up optimization.
“Perturbative Transport” - based validation tool will be used
to find combination of parameters
• To be presented at IAEA-TM on Fusion Data Processing, Validation and
Analysis (May 30th – June 2nd, Cambridge MA)
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