USBPO Mission Statement:

Advance the scientific understanding of burning plasmas and ensure the greatest benefit from a burning plasma experiment by coordinating relevant U.S. fusion research with broad community participation.

USBPO Topical Group Highlights

[The BPO Modeling and Simulation Topical Group facilitates US efforts to develop and apply numerical codes to the understanding and prediction of fusion device performance (leaders are David Mikkelsen and Xianzhu Tang). This month's Research Highlight by D.R. Mikkelsen, et al., describes recent advances and considerations related to simulating turbulent heat flux in the outer region of tokamaks, where experimental values are typically much larger than simulations show. This highlight demonstrates the broad US expertise in this area, as US-based researchers apply and compare the GYRO and TGLF codes to an international group of fusion devices and turbulence simulation codes. -Ed.]

Transport Shortfall in L-mode Plasmas
D.R. Mikkelsen^1*, C. Holland², F. Jenko³, T. Goerler³, and G.M. Staebler⁴

¹ Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, NJ 08543
² University of California-San Diego, 9500 Gilman Dr., La Jolla, CA 92093
³ Max Planck Institute for Plasma Physics, Garching
⁴ General Atomics, P.O. Box 85608, San Diego, CA 92186
* E-mail: mikk@pppl.gov

In the last several years considerable attention has been devoted to an issue known as ‘transport shortfall’: the inability of some gyrokinetic and gyrofluid models of turbulent plasma transport to generate the observed level of transport and fluctuations in the outer regions of some L-mode plasmas in DIII-D [1-4] and Tore Supra [5]. More recently still, the absence of a shortfall in some NSTX [6] and C-Mod [7] L-mode plasmas, and in other turbulence code simulations of DIII-D and AUG L-mode plasmas [8], and the preliminary identification of the first DIII-D L-modes without a shortfall [9], suggest the issue may be limited to a finite range of parameter space and/or numerical approaches.

In spite of the recent surge of interest, the observation of an inherent inability of gyrokinetic and gyrofluid models of turbulent transport to generate adequate transport in cold plasmas is an old one [10]. A physical means of overcoming this tendency toward low transport was also recognized long ago: the temperature gradients simply rise far above the critical gradient and the turbulent transport eventually reaches a high level [11]. Most theoretically-based ‘reduced’ transport models of the 1990s, however, did not have sufficient complexity to adequately include this and model makers turned to additional sources of turbulent transport (typically invoking resistive ballooning modes) to fill the gap. Transport model testing often sidestepped the problem by making predictions only for r/a≤0.8, thereby pushing the problem ‘out of bounds’. This lead to the notion of the periphery becoming a “no man’s land” which did not receive attention in studies of “core transport” or in studies of the “edge”, which focused on the pedestal and scrape-off layer.

Attention to the shortfall rose dramatically when simulations of current ramp-up in ITER highlighted the need for reliable diffusivities in the plasma periphery, which is the most important part of the plasma for evaluating resistive flux consumption and the evolution of internal inductance during the current ramp [12]. This led to a joint ITPA modeling activity (involving the “Integrated Operating Scenarios” and “Transport and Confinement” topical groups) that tested all popular ‘reduced’ transport models by comparing predictions of temperature and current evolution with measurements from ITER-similar current ramps in C-Mod, DIII-D, and JET. No transport model accurately predicts the electron temperature in the outer half of the plasma in all three tokamaks, but ad hoc additions to supplement TGLF’s transport predictions can work for some tokamaks and should be tested on all three.

Figure 1: Comparison of ONETWO power balance calculations (—) of (top) ion and (bottom) electron energy fluxes Qi and Qe to predictions from TGLF (—), GYRO (●), and GEM (◆). Adapted from Rhodes et al., [18].

A shortfall example is shown in Fig. 1 (adapted from [18]), which compares the experimental heat fluxes calculated via the ONETWO code [13] against predictions from the quasilinear, gyrofluid TGLF model [14,15], the nonlinear continuum gyrokinetic GYRO code [16], and the nonlinear particle-in-cell gyrokinetic GEM code [17]; all the predictions are based on experimentally measured profiles and gradients. It is well-known that turbulent transport can be highly sensitive to the temperature and rotation gradients, so the range of uncertainty for the predictions was evaluated from calculations based on an ensemble of profile fits that were allowed to deviate from the nominal experimental data by amounts consistent with the measurement error (the GYRO ‘error bars’ are based on 40 nonlinear simulations, 10 per radial location).

If the temperature gradients are increased sufficiently it is possible to produce a simulated heat flux that matches the experimental flux. The ratio of the flux-matching temperature gradient scale length to the experimental value forms a useful validation metric:

In Fig. 2 this metric has been applied to TGLF flux-matching predictions for a collection of 13 DIII-D L-mode discharges (8 with neutral beam injection, and 5 with only off-axis electron cyclotron heating); metrics for a smaller number of GYRO calculations yield similar results. The cases with Ε_LΤᵢ>1 are all at outer radii, and their local gyroBohm-normalized heat fluxes are all quite large (where Q_gB = n_eT_ec_s(ρ_s/L_Te)²). While GYRO’s Ε_LΤᵢ will differ from that of TGLF, GYRO also exhibits a shortfall in all cases which have a corresponding GYRO simulation. Note that Q/Q_gB is derived from the experimental analysis alone, and may be a useful predictor of ‘shortfall’.

Figure 2: Visualization of the local ion temperature gradient scale length metric ELTi, calculated using TGLF for 8 DIII-D discharges with NBI heating (●) and 5 DIII-D discharges with only ECH-heating (■).

Based on the standard ordering assumptions (all ‘small’ parameters are of the same order) of gyrokinetic theory (the foundation of GYRO and similar codes), one can argue that the gyroBohm-normalized flux Q/Q_gB should be not larger than O(1). The large Ε_LΤᵢ cases in Fig. 2 have larger values of Q/Q_gB than other cases and are larger than O(1), suggesting to some that the turbulence in the outer regions of these L-modes is outside the validity domain of standard gyrokinetics. Others point out that all the parameters of formally ‘small’ order are indeed <<1 even in heat-flux-matching turbulence simulations; although some small parameters are an order of magnitude larger than other small parameters. This debate should be resolvable by careful re-derivation of the gyrokinetic equations with experimentally appropriate orderings. The correlation of higher Ε_LΤᵢ and Q/Q_gB has motivated a number of searches for alternate transport mechanisms and theoretical formulations [19], but no broadly validated solution to the shortfall problem has emerged. No large values of Ε_LΤᵢ or Q/Q_gB have been observed to date for DIII-D H-mode discharges, however, perhaps because H-mode plasmas have higher densities, temperatures and Q_gB in the periphery.

In 2012 the GENE turbulence code [8,20,21] was used to simulate transport at the r/a=0.75 location in Fig. 1, and with the standard experimental plasma parameters as well as the standard practices used by the GENE group for choice of physics models and for grid domain extent and resolution, it produces 4-5 times higher ion heat flux than GYRO. With only a 15% increase of α/L_Τi, within the measurement uncertainty, GENE can match the ion heat flux from ONETWO analysis (whereas an increase of 85% is needed for GYRO or TGLF to match the ion heat flux). The two turbulence codes have been successfully benchmarked with each other several times so this large difference was unexpected, and considerable effort has been devoted to understanding the sources of the differing predictions in this case. Linear benchmarks with simplified physics models do agree well, but differences are observed in some linear calculations with more complete physics models, e.g. due to the different collision operator models being used by default in each code. Nonlinear benchmarks do not yet agree, even with similar simplified physics models and closely matched grid domains and resolutions. Both groups are seeking an understanding of these results, and additional simulations will soon be made by other turbulence codes. Resolving this matter is crucial for confident prediction and modeling of ITER discharges (particularly in the current ramp-up/down phases), and more broadly for understanding the underlying physics of the L-H transition, which will surely require accurate understanding and predictive capabilities of near-edge L-mode turbulence.

*This work was supported by U.S. Department of Energy Contract Nos. DE-AC02-76CH03073, DE-FG02-06ER54871, DE-SC000695, and DE-FG03-95ER54309.

References

1. A. E. White et al., Phys. Plasmas 15, 056116 (2008)
2. C. Holland et al., Phys. Plasmas 16, 052301 (2009)
3. A. E. White et al., Phys. Plasmas 17, 056103 (2010)
4. C. Holland et al., Phys. Plasmas 18, 056113 (2011)
5. C. Bourdelle et al., Plasma Phys. & Controlled Fusion 54, 115003 (2012)
6. Y. Ren et al., “Electron-scale Turbulence Spectra and Plasma Thermal Transport Responding to Continuous ExB Shear Ramping-up in a Spherical Tokamak”, submitted to Nucl. Fusion (2013)
7. N. T. Howard et al., Phys. Plasmas 20, 032510 (2013)
8. F. Jenko et al., EU-US Transport Task Force, Padova, 3-6 Sep. 2012
9. J. Kinsey et al., US Transport Task Force, Santa Fe, 15-17 April 2013
10. M. A. Beer (1995), Ph.D. thesis, Princeton University
11. M. Kotschenreuther, et al., Phys. Plasmas 2, 2381 (1995)
12. T. Casper et al., Nucl. Fusion 51, 013001 (2011)
13. H. E. St. John et al., in Plasma Phys. Control. Nucl. Fusion Res., (Proc. 15th Int. Conf., Seville, 1994) (IAEA, Vienna, 1995), vol. 3, p. 603
14. G. M. Staebler et al., Phys. Plasmas 14, 055909 (2007)
15. J. E. Kinsey et al., Phys. Plasmas 15, 055908 (2008)
16. J. Candy and R. E. Waltz, J. Comp. Phys. 186, 545 (2003)
17. Y. Chen and S. E. Parker, J. Comp. Phys. 220, 839 (2007)
18. T. L. Rhodes et al., Nucl. Fusion 51, 063022 (2011)
19. G. Staebler et al., EU-US Transport Task Force, Padova, 3-6 Sep. 2012
20. F. Jenko, et al., Phys. Plasmas 7, 1904 (2000)
21. T. Goerler et al., J. Comp. Phys. 230, 7053 (2011)

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ITPA Update

For information on the proposed agenda, see BPO forum link.

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Contact and Contribution Information

This newsletter provides a monthly update on U.S. Burning Plasma Organization activities. Topical Group Highlight articles are selected by the Leader and Deputy Leader of those groups (http://burningplasma.org/groups.html). ITPA Reports are solicited by the Editor based on recently held meetings. Announcements, Upcoming Burning Plasma Events, and all comments may be sent to the Editor. Suggestions for the Image of the Month may be sent to the Editor. The images should be photos, as opposed to data plots, though combined graphics are welcome. The goal is to highlight U.S. fusion resources through interesting visualizations.

Become a member of the U.S. Burning Plasma Organization by signing up for a topical group:
burningplasma.org/jointopical

Editor: David Pace (pacedc@fusion.gat.com)
Assistant Editor: Amadeo Gonzales (agonzales@austin.utexas.edu)

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Schedule of Burning Plasma Events

Click here to visit a list of previously concluded events.

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Image of the Month

Illuminating Divertor Physics

Proof-of-principal experiments conducted on one of the helicon plasma sources at West Virginia University [pictured above and featuring graduate student M. Galante (left) and postdoctoral researcher Dr. R. Magee (right)] have demonstrated confocal two photon absorption laser induced fluorescence (TALIF) spectroscopy is capable of performing absolutely calibrated measurements of neutral deuterium and hydrogen density (inset data figure on left) over four orders of magnitude (from < 10¹⁶ m^-3 to 10²⁰ m^-3 as shown on data figure to right), with a spatial resolution better than 2 mm and a time resolution of 10 ns. The TALIF system is shown in a confocal configuration (lower portion of the figure) in which the laser injection (at 205 nm) and light collection (at 656 nm) is accomplished through a single optical port. The planned optical path for installation on the EAST tokamak (lower right) in Hefei, China in 2014 is to enter through a vertical port outboard of the x-point and by scanning the focusing lens, measure the neutral density profile in the pedestal from above the strike point on the divertor wall up to the last closed flux surfaces (internal photo of the EAST divertor with carbon tiles shown at upper right).

This work is funded by the US Department of Energy (DOE) through Grant No. DE-SC0004736.

Contributed by E. Scime and R. Magee, West Virginia University, Morgantown, WV 26506
WVU Plasma Physics: http://ulysses.phys.wvu.edu/~plasma/

R. M. Magee, M. E. Galante, D. McCarren, E. E. Scime, R. L. Boivin, N. H. Brooks, R. J. Groebner,
D. N. Hill, and G. D. Porter, Rev. Sci. Instrum. 83, 10D701 (2012),
http://rsi.aip.org/resource/1/rsinak/v83/i10/p10D701_s1

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