Page 10 - Suppressed ion-scale turbulence in a hot high-β plasma

ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13860
probed radial wavenumber is krB0 as the beams propagates toroidally near the plasma cutoff layer. The wavenumber ky and the probed radii r in the laboratory frame are calculated using the GENRAY31 ray tracing code. Ray tracing calculations are based on high time resolution (10 ms) radial electron density profiles (Fig. 1(c)) reconstructed from a six channel CO2 laser interferometer53 located in the FRC axial midplane. All calculated DBS probing positions are mapped to the axial FRC midplane. For typical C-2 plasma parameters the X-mode and O-mode cutoff layer positions differ only very slightly as the plasma frequency is much larger than the electron cyclotron frequency.
Fluctuation levels extracted from DBS are calibrated here in an approximate fashion by comparison with (line-integrated) Far Infrared Scattering data54 obtained from an FIR chord traversing the plasma tangentially to the separatrix. FIR measures a perpendicular wavenumber range k>rsB0–4. We make the assumption here that the fluctuation spectrum is isotropic in the toroidal and radial direction. The largest contribution to the measured fluctuation amplitude for this FIR chord will come from the vicinity of the separatrix, where the density (and density gradient) is largest. Choosing a similar wavenumber range for the DBS measurements, a rough calibration for the DBS fluctuation levels can be obtained with a systematic maximum error of þ 40%, 50%.
Data availability. The data that support the findings of this study are available from the corresponding author on request.
References
1. Wesson, J. Tokamaks 4th edn. (Oxford University Press, 2011).
2. Tuszewski, M. Field-reversed configurations. Nucl. Fusion 28, 2033–3093
(1988).
3. Steinhauer, L. C. Review of field-reversed configurations. Phys. Plasmas 18,
070501 (2011).
4. Rostoker, N. et al. Colliding beam fusion reactor. Science 278, 1419–1423
(1997).
5. Balbus, S. A. & Hawley, J. F. Instability, turbulence, and enhanced transport in
accretion disks. Rev. Mod. Phys. 70, 1–53 (1998).
6. Schekochikin, A. A. et al. Astrophysical gyrokinetics: kinetic and fluid turbulent
cascades in magnetized weakly collisional plasmas. Astrophys. J. Suppl. 182,
310–377 (2009).
7. Maehara, H. et al. Superflares on solar-type stars. Nature 485, 478–481 (2012).
8. Hoffman, A. L. & Slough, J. T. Field reversed configuration lifetime scaling
based on measurements from the large s experiment. Nucl. Fusion 33, 27–38
(1993).
9. Naitou, H., Kamimura, T. & Dawson, J. M. Kinetic effects on the convective
plasma diffusion and the heat transport. JPSJ 46, 258–265 (1979).
10. Rosenbluth, M. N., Krall, N. & Rostoker, N. Finite Larmor radius stabilization of ‘weakly’ unstable confined plasmas. Nucl. Fusion. Supplement Pt 1, 143–150
(1962).
11. Rostoker, N. in Physics of High Energy Particles in Toroidal Systems (eds
Tajima, T. & Okamoto, M.) 323 (American Institute of Physics, 1994).
12. Binderbauer, M. & Rostoker, N. Turbulent transport in magnetic confinement:
how to avoid it. J. Plasma Phys. 56, 451–465 (1996).
13. McKenna, K. F. et al. Particle confinement scaling in field-reversed
configurations. Phys. Rev. Lett. 50, 1787–1790 (1983).
14. Carlson, A. W. A search for lower-hybrid-drift fluctuations in a field-reversed
configuration using CO2 heterodyne scattering. Phys. Fluids 30, 1497–1509
(1987).
15. Farengo, R., Guzdar, P. N. & Lee, Y. C. Collisionless electron temperature
gradient-driven instability in field-reversed configurations. Phys. Fluids B1,
2181 (1989).
16. Yu, C. A. & Khvesyuk, V. I. Electromagnetic drift instabilities in high-b plasma
under conditions of a field-reversed configuration. Phys. Plasmas 17, 012105
(2010).
17. Binderbauer, M. et al. Dynamic formation of a hot field reversed configuration
with improved confinement by supersonic merging of two colliding high-b
compact toroids. Phys. Rev. Lett. 105, 045003 (2010).
18. Binderbauer, M. et al. A high performance field-reversed configuration. Phys.
Plasmas 22, 056110 (2015).
19. Gupta, S. et al. Transport studies in high performance field-reversed
configuration plasmas. Phys. Plasmas 23, 052307 (2016).
20. Fulton, D. P., Lau, C., Holod, I., Lin, Z. & Dettrick, S. Gyrokinetic particle
simulation of a field reversed configuration. Phys. Plasmas 23, 012509 (2016).
21. Fulton, D. P. et al. Gyrokinetic simulation of driftwave instability in
field-reversed configuration. Phys. Plasmas 23, 056111 (2016).
22. Mase, A. et al. Ambipolar potential effect on drift-wave mode in a tandem-mirror plasma. Phys. Rev. Lett. 64, 2281–2284 (1990).
23. Guo, H. Y. et al. Formation of a long-lived hot field reversed configuration by dynamically merging two colliding high-b compact toroids. Phys. Plasmas 18, 056110 (2011).
24. Galeotti, L., Barnes, D. C., Ceccherini, F. & Pegoraro, F. Plasma equilibria with multiple ion species: equations and algorithm. Phys. Plasmas 18, 082509 (2011).
25. Akhmetov, T. D. et al. Experiments with dense plasma in the central solenoid of AMBAL-M. Trans. Fusion Sci. Technol. 43, 58–62 (2003).
26. Tuszewski, M. et al. Field reversed configuration confinement enhancement through edge biasing and neutral beam injection. Phys. Rev. Lett. 108, 255008 (2012).
27. Tuszewski, M. et al. A new high performance field reversed configuration operating regime in the C-2 device. Phys. Plasmas 19, 056108 (2012).
28. Peebles, W. A. et al. A novel, multichannel, comb-frequency Doppler
backscatter system. Rev. Sci. Instrum. 81, 10D902 (2010).
29. Hillesheim, J. C. et al. New plasma measurements with a multichannel
millimeter-wave fluctuation diagnostic system in the DIII-D tokamak. Rev. Sci.
Instrum. 81, 10D907 (2010).
30. Schmitz, L. et al. Multi-channel Doppler backscattering measurements in the
C-2 field reversed configuration. Rev. Sci. Instrum. 85, 11D840 (2014). 31. Smirnov, A. P. & Harvey, R. W. The GENRAY ray tracing code. Report
COMPX-2000-01 (COMPX-X, 2001).
32. Hennequin, P. et al. Fluctuation spectra and velocity profile from Doppler
backscattering on Tore Supra. Plasma Phys. Controlled Fusion 46, S771–S779
(2006).
33. Schmitz, L. et al. Reduced electron thermal transport low collisionality H-mode
plasmas and the importance of TEM/ETG-scale turbulence. Nucl. Fusion 52,
023003 (2012).
34. Lin, Z. et al. Turbulent transport reduction by Zonal Flows: massively parallel
simulations. Science 281, 1835–1837 (1998).
35. Lin, Z. et al. Gyrokinetic Toroidal Code BGTC http://phoenix.ps.uci.edu/GTC/
codes.php (2010).
36. Boozer, A. H. Plasma equilibrium with rational magnetic surfaces. Phys. Fluids
24, 1999–2003 (1981).
37. Lin, Z., Ethier, S., Hahm, T. S. & Tang, W. M. Size scaling of turbulent transport
in magnetically confined plasmas. Phys Rev. Lett. 88, 195004-1–195004-4
(2002).
38. Candy, J., Waltz, R. E. & Dorland, W. The local limit of global gyrokinetic
simulations. Phys. Plasmas 11, L25 (2004).
39. McMillan, B. F. et al. System size effects on gyrokinetic turbulence. Phys. Rev.
Lett. 105, 155001 (2010).
40. Deng, B. H., Kinley, J. S. & Schroeder, J. Electron density and temperature
profile diagnostics for C-2 field-reversed configuration plasmas. Rev. Sci.
Instrum. 83, 10E339 (2012).
41. Lau, C. K. et al. in 57th Meeting of the American Physical Society, Division of
Plasma Physics. Available at http://meetings.aps.org/Meeting/DPP16/Session/
CP10.74 (2016).
42. Pastukhov, V. P. Collisional losses of electrons from an adiabatic trap in a
plasma with a positive potential. Nucl. Fusion 14, 3–6 (1974).
43. Lam, K. L. et al. Mirror ratio scaling of axial confinement of a mirror-trapped
collisional plasma. Phys. Fluids 29, 3433–3438 (1986).
44. Steinhauer, L. C. Anomalous transport effects in magnetically-confined plasma
columns. Phys. Fluids 21, 230–236 (1978).
45. Garbet, X. Turbulence in fusion plasmas—key issues and impact on transport
modeling. Plasma Phys. Control. Fusion 43, A251–A266 (2007).
46. Dimits, A. M. et al. Scalings of ion-temperature-gradient-driven anomalous
transport in Tokamaks. Phys. Rev. Lett. 77, 71–74 (1996).
47. Biglari, H., Diamond, P. H. & Terry, P. Influence of sheared poloidal rotation
on edge turbulence. Phys. Fluids B 2, 1–4 (1990).
48. Burrell, K. H. et al. Role of the radial electric field in the transition from L (low)
mode to H (high) mode to VH (very high) mode in the DIII-D tokamak. Phys.
Plasmas 1, 1536–1544 (1994).
49. Kaye, S. M. et al. Confinement and local transport in the National Spherical
Torus Experiment (NSTX). Nucl. Fusion 47, 499 (2007).
50. Valovic, M. et al. Scaling of H-mode energy confinement with Ip and Bt in the
MAST spherical tokamak. Nucl. Fusion 49, 075016 (2009).
51. Kaye, S. M. et al. The dependence of H-mode energy confinement and
transport on collisionality in NSTX. Nucl. Fusion 53, 063005 (2013).
52. Blanco, E. et al. Doppler reflectometry studies using a two-dimensional full
wave code. Plasma Phys. Control. Fusion 48, 699–714 (2006).
53. Gornostaeva, O. et al. Two-color CO2/HeNe laser interferometer for C-2
experiment. Rev. Sci. Instrum. 81, 10D516 (2010).
54. Deng, B. H. et al. Far infrared laser polarimetry and far forward scattering
diagnostics for the C-2 field reversed configuration plasma. Rev. Sci. Instrum. 85, 11D401 (2014).
Acknowledgements
We would like to thank the TAE team and TAE collaborators for their support and contributions. We are also grateful to the TAE shareholders for their continued support. This research used resources of the Oak Ridge Leadership Computing Facility at Oak Ridge National Laboratory (DOE Contract No. DE-AC05-00OR22725), and the National Energy Research Scientific Computing Center (DOE Contract No. DE-AC02- 05CH11231).
10 NATURE COMMUNICATIONS | 7:13860 | DOI: 10.1038/ncomms13860 | www.nature.com/naturecommunications