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

Alcator C-Mod

Experiments

4

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)

10

DIII-D

Experiments

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]

14

Modeling

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)

References

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