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DIFFER is part of andDIFFER huisstijl presentatie 10/7/15

Fast ion enhanced nonlinear electromagnetic stabilization of tokamak microturbulence

J. Citrin1,2, J. Garcia2, T. Görler3, F. Jenko4, P. Mantica5, D. Told4, C. Bourdelle2, H. Doerk3 D.R. Hatch6, G.M.D. Hogeweij1, T. Johnson7, M.J. Pueschel8, M. Schneider2, and JET

contributors*

1 FOM Institute DIFFER – Dutch Institute for Fundamental Energy Research, Nieuwegein, The Netherlands2 CEA, IRFM, F-13108 Saint Paul Lez Durance, France 3 Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany4 Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA5 Istituto di Fisica del Plasma P. Caldirola, Milan6 Institute for Fusion Studies, University of Texas at Austin, Austin, Texas 78712, USA7 School of Electrical Engineering, Royal Institute of Technology, Euratom-VR Association, Stockholm, Sweden 8 Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA* See the Appendix of F. Romanelli et al., Proc. of the 25th IAEA Fusion Energy Conference 2014, St. Petersburg, Russia

DIFFER is part of andDIFFER huisstijl presentatie 10/7/15Jonathan Citrin

IAEA-TM Frascati, March 2015 2

Outline

Direct numerical simulation of ion-temperature-gradient (ITG) driven microturbulence and comparison with experimental power balance



Motivation: mystery in JET ion heat transport experiments

[1] P. Mantica et al., Phys. Rev. Lett. 102, 175002 (2009); [2] P. Mantica et al., Phys. Rev. Lett. 107, 135004 (2011)[3] F. Jenko, W. Dorland, M. Kotschenreuther, and B.N. Rogers, Phys. Plasmas 7, 1904 (2000); see http://genecode.org. for code details and access

JET data-set in L-mode has challenged theoretical understanding of ion temperature gradient (ITG) turbulence, primarily responsible for ion heat transport [1,2]

Main observation: Significant reduction of ion heat transport “stiffness” defined here as the local normalized qi gradient with respect to R/LTi

We report on an intensive investigation of this phenomenon with the nonlinear gyrokinetic code GENE [3]. We focus on the encircled discharges.

Ion heat flux (qi) vs logarithmic ion gradient (R/LTi) at ρ=0.33

(ICRH only)(NBI or NBI+ICRH)

Heat flux normalising factor

http://genecode.org/


IAEA-TM Frascati, March 2015

The bottom line

Observations could be explained by nonlinear electromagnetic stabilization of ITG turbulence, enhanced by fast ion pressure gradients

Major computational effort: 400 nonlinear simulations, about 8 million CPU hours!

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Note: As pointed out in this meeting, rotational flow shear at low magnetic shear may still play a role in reducing non-local effects. But not responsible for actual low level of flux by itself



•We include: kinetic electrons, experimental geometry, electromagnetic effects, active C species, active fast ions (D from NBI, 3He minority from ICRH)

•Local (flux tube) approximation (1/* ~ 500)

•Only δB┴ fluctuations kept due to low βe≈0.4%. Lack of sensitivity to δB║ verified

•Caveat: fast ions approximated by hot Maxwellians

[4] J.F. Artaud et al., Nucl. Fusion 50, 034001 (2010)[5] M. Schneider et al., Nucl. Fusion 51, 063019 (2011)[6] J. Hedin, T. Hellsten, L.-G. Eriksson and T. Johnson Nucl. Fusion 51, 063019 (2011)

WorkflowFits of raw data fed into CRONOS [4] integrated modelling suite. Interpretative run carried out.

• Current diffusion. HELENA for magnetic equilibrium

• NEMO/SPOT [5] for NBI fast ion calculation

• SELFO [6] for ICRH fast ion calculation

Defines input into GENE simulations

Choice of assumptions and workflow



• With PVG, stiffness only slightly reduced near threshold. Experimental observations cannot be explained by flow shear

• With no PVG, classic “Waltz-rule” threshold shift recovered

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Flow shear does not explain observations

•Compare stiffness for variousγE, with and without PVG term

•Experimental “high rotation”value is γE = 0.3 cs/R

Stabilizing perpendicular flow shear rate (toroidal rotation)

Simulation of low rotation JET discharge 70084 at =0.33Increase flow shear and see if low stiffness can be reached



Electromagnetic-stabilization (1/4): Linear ITG stabilization below EM-branch limit

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ITGEM-branch (e.g. KBM)



Nonlinear EM-stabilization stronger than the linear stabilization!This has been linked with an increase in zonal flow pumping(GK ITG: Pueschel et al., PoP 2008, 2010, 2013,Fluid ITG: Anderson et al., PoP 2011)

Collisional, EM, simulations based on ‘low stiffness’ JET discharge 66404, at =0.33

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M.J. Pueschel et al.,PoP 2013

Zonal flow growth rate:

Cyclone Base Case

Electromagnetic-stabilization (2/4): Nonlinear stabilization stronger than linear



Electromagnetic-stabilization (3/4): Including fast ions increases EM-stabilization



(GENE nonlinear simulations based on 66404 base parameters: 2 species, Ti/Te=1, circular geometry)

s=0.2s=0.7

s=1

s=2

s=0.45

Electromagnetic-stabilization (4/4): Magnetic shear dependence in line with observed trend



Fast ions can stabilise ITG turbulence through 3 general mechanisms

• Dilution of main ion species (e.g. Tardini et al NF 2007)

• Geometric effects: Increased Shafranov shift due to suprathermal pressure Alteration of drift frequency: stabilises ITG at low magnetic shear

(e.g. Bourdelle et al NF 2005)

The 3rd stabilizing effect is key in these discharges

• Stabilization by “electromagnetic effects”. Suprathermal pressure gradients adds to the total ’ . Observed in simulations to significantly stabilize turbulence. Has been analyzed linearly for JET discharges (M.Romanelli et al PPCF 2011).

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Other (non-EM) fast ion stabilization mechanisms of ITG are not important here

These 2 effects do not dominate in these discharges following dedicated checks

As in the thermal case, the nonlinear electromagnetic stabilization is greater than the linear stabilization!



Experimental ion heat flux reached when including fast ions in EM simulations

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Inclusion of fast ions yields strongly reduced fluxes and low stiffness, but only in nonlinear electromagnetic simulations!

Result also consistent with GYRO modelling of DIII-D QH mode (C. Holland et al., Nucl. Fusion 2012)

Simulations with flow shear, EM, and fast ions (D from NBI & ICRH 3He minority), carbon impurities



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J. Citrin et al., Phys. Rev. Lett. 111, 155001 (2013)J. Citrin et al., Nucl. Fusion 54 023008 (2014)

Resolution of open question on JET L-mode ‘low-stiffness’ regime



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Linear study in inner half-radius:EM and fast ion stabilization is important

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Nonlinear study in inner half-radius:EM-stabilization of critical importance

J. Citrin et al, PPCF 2015J. Garcia et al, NF 2015



Flow shear stabilization ineffective at inner half-radius

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When including fast ion mode in NL simulation, fluxes far above power balance levels

Phase 1: With 30% reduced fast ion pressure (no BAE-like mode) Phase 2: increase to nominal fast ion pressure and restart simulation

• System with fast ion mode has fluxes clearly above power balance values. Limit cycles? Robustly maintained below limit? Needs further study.

• Supports use of a “stiff” fast ion transport model in reduced modelling frameworks

Phase 1 Phase 2

What happens nonlinearly if we allow the BAE-like modes to be unstable?

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At outer half-radius, situation reverses:EM effects not important, flow shear is important



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J. Garcia et al NF 2015



JET hybrid scenario power scans vs IPB98 expected scaling

C. Challis et al. NF 2015



JET ILW hybrid scenario power scan trendsrecovered in gyrokinetic nonlinear simulations

J. Garcia et al. NF 2015



Extrapolation to ITER: significant boost in fusion power expected

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Part 3 summary: implications for power scaling and extrapolation



Open theory questions



Final take home messages

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Thank you for your attention!



JET ‘low-stiffness’ discharge 66404: Pressure and -profiles

Location of -boost coincides with location of experimental

R/LTi far above threshold

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Location of fast ion α-boost coincides with location of steep experimental Ti peaking. Suggests increase in EM-stabilization.

High R/LTi zone

High R/LTi zone

Through which other mechanisms can fast ions impact ITG transport?



Fast ion pressure gradients increase the Shafranov shift

Nonlinear simulations with varying equilibria input show that here, the Shafranov shift has only a minor effect



•No separation of branches (low flux 70084 and high flux 66130/404), as in experiment

•Good agreement of fluxes – full agreement easily obtained within reasonable variations of input parameters within confidence intervals

• Electromagnetic stabilization was seen to be negligible here

GENE runs at ρ = 0.64, including all effects (but no fast ions – due to low gradients)



1. At low rotation, Dimits shift (nonlinear R/LTi threshold shift) from modelling did not agree with the extrapolated measured R/LTi threshold

2. At low rotation, the observed stiffness was significantly higher than the nonlinear modelling

This has also been resolved in the new investigation (within the confidence interval of the q-profile)

1. Updated data processing methodology for MSE led to increased q by ~30%. Critical threshold decreased, Dimits shift now consistent

2. Recalibration of the Te measurement now shows an increased Te / Ti of the high flux discharges compared with the low flux discharges. The sets of points thus do not “sit on the same stiffness curve”

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Previous modelling assumed a nominal q≈1.3 for the low flux discharges.Revised MSE processing suggests that q≈1.7 is more accurate (which also

agrees better with interpretative modelling with CRONOS)

The ITG threshold decrease due to this 30% increase in q is sufficient to “reverse” the previous conclusions

Dimits shift < 25% of R/Lticrit. Weaker with kinetic electrons compared with adiabatic (see D.R. Mikkelsen and W. Dorland 2008 Phys. Rev. Lett. 101 135003.)

Strength of conclusion depends on hard-to-pin-down q-profile confidence interval.

However, we can conclude that there is no clear inconsistency

GENE nonlinear simulations. s and q sensitivity scan of ITG

threshold and stiffness.

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Comparison of ion heat flux from GENE simulations of low and high flux discharges in the “high-stiffness-branch”.

Simulations with Zeff = 1.4, electromagnetic, collisions.

Assuming same q-profile as low-flux case, agreement reached between GENE and EXP. Increased Te / Ti decreases the critical threshold. Strong impact on the flux due to high stiffness.

Increased Te/Ti in high flux case compensated by lower q when assuming the q-profile from interpretative modelling

Increased Te / Ti now leads to consistency between power balance and simulations, within q-profile confidence intervals.

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Extra slide: excitation of fast ion modes

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Extra slide: evidence for increased ZF drive

Reduced fluxes in EM cases correlated with increased proportion of zonal flow energy in system

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•Tearing parity dominates as seen by POD analysis (D. Hatch et al., PRL 2011, POP 2012)

•Linearly stable MTM coupled in system with BAE-like mode??•Still an open question. However, not experimentally relevant here

Phase 2: Electron heat flux spectrum

Extra slide: Nonlinear ITG-BAE turbulence

Curious observation of strong electromagnetic electron heat flux when BAE mode unstable

ES fluxEM flux

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