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Homogenization theory for the effective permittivity of a turbulent tokamak plasma in the scrape-off layer

Part of: PLA 17th European Fusion Theory Conference Focus on Fusion

Published online by Cambridge University Press:  06 September 2018

F. Bairaktaris ,
K. Hizanidis ,
A. K. Ram ,
P. Papagiannis ,
C. Tsironis ,
Y. Kominis ,
E. Glytsis ,
O. Chellai ,
S. Alberti  and
I. Furno
F. Bairaktaris*
Affiliation:
National Technical University of Athens, Ir. Politechniou 9, 15780 Athens, Greece
K. Hizanidis
Affiliation:
National Technical University of Athens, Ir. Politechniou 9, 15780 Athens, Greece
A. K. Ram
Affiliation:
Plasma Science and Fusion Center, MIT, 167 Albany St, Cambridge, MA 02139, USA
P. Papagiannis
Affiliation:
National Technical University of Athens, Ir. Politechniou 9, 15780 Athens, Greece
C. Tsironis
Affiliation:
National Technical University of Athens, Ir. Politechniou 9, 15780 Athens, Greece
Y. Kominis
Affiliation:
National Technical University of Athens, Ir. Politechniou 9, 15780 Athens, Greece
E. Glytsis
Affiliation:
National Technical University of Athens, Ir. Politechniou 9, 15780 Athens, Greece
O. Chellai
Affiliation:
Swiss Plasma Center, Ecole Polytechnique Fédérale de Lausanne, Route Cantonale, 1015 Lausanne, Switzerland
S. Alberti
Affiliation:
Swiss Plasma Center, Ecole Polytechnique Fédérale de Lausanne, Route Cantonale, 1015 Lausanne, Switzerland
I. Furno
Affiliation:
Swiss Plasma Center, Ecole Polytechnique Fédérale de Lausanne, Route Cantonale, 1015 Lausanne, Switzerland
*
†Email address for correspondence: fotisb@mail.ntua.gr
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Abstract

There has been a growing interest, over the past few years, on understanding the effect on radio frequency waves due to turbulence in the scrape-off layer of tokamak plasmas. While the far scrape-off layer density width is of the order of centimetres in contemporary tokamaks, in ITER (International Thermonuclear Experimental Reactor), and in future fusion reactors, the corresponding width will be of the order of tens of centimetres. As such, this could impact the spectral properties of the waves and, consequently, the transport of wave energy and momentum to the core plasma. The turbulence in the scrape-off layer spans a broad range of spatial scales and includes blobs and filaments that are elongated along the magnetic field lines. The propagation of radio frequency waves through this tenuous plasma is given by Maxwell’s equations. The characteristic properties of the plasma appear as a permittivity tensor in the expression for the current in Ampere’s equation. This paper develops a formalism for expressing the permittivity of a turbulent plasma using the homogenization technique. This technique has been extensively used to express the dielectric properties of composite materials that are spatially inhomogeneous, for example, due to the presence of micro-structures. In a similar vein, the turbulent plasma in the scrape-off layer is spatially inhomogeneous and can be considered as a composite material in which the micro-structures are filaments and blobs. The classical homogenization technique is not appropriate for the magnetized plasma in the scrape-off layer, as the radio frequency waves span a broad range of wavelengths and frequencies – from tens of megahertz to hundreds of gigahertz. The formalism in this paper makes use of the Fourier space components of the electric and magnetic fields of the radio frequency waves for the scattered fields and fields inside the filaments and blobs. These are the eigenvectors of the dispersion matrix which, using the Green’s function approach, lead to a homogenized dielectric tensor.

Keywords

fusion plasmaplasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 5 , October 2018 , 745840501
Copyright
© Cambridge University Press 2018 

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References

Berreman, D. W. 1972 Optics in stratified and anisotropic media: $4\times 4$ -matrix formulation. J. Opt. Soc. Am. 62 (4), 502.Google Scholar
Chellai, O., Alberti, S., Baquero-Ruiz, M., Furno, I., Goodman, T., Manke, F., Plyushchev, G., Guidi, L., Koehn, A., Maj, O. et al. 2018 Millimeter-wave beam scattering by field-aligned blobs in simple magnetized toroidal plasmas. Phys. Rev. Lett. 120, 105001.Google Scholar
Grulke, O., Terry, J. L., LaBombard, B. & Zweben, S. J. 2006 Radially propagating fluctuation structures in the scrape-off layer of alcator c-mod. Phys. Plasmas 13, 012306.Google Scholar
Krasheninnikov, S. I. 2001 On scrape-off layer plasma transport. Phys. Lett. A 283, 368–370.Google Scholar
Mackay, T. G. & Lakhtakia, A. 2015 Modern Analytical Electromagnetic Homogenization. Morgan & Claypool Publishers.Google Scholar
Myra, J. R., D’Ippolito, D. A., Stotler, D. P., Zweben, S. J., Leblanc, B. P., Menard, J. E., Maqueda, E. J. & Boedo, J. 2006a Blob birth and transport in the tokamak edge plasma: analysis of imaging data. Phys. Plasmas 13, 092509.Google Scholar
Myra, J. R., Russell, D. A. & D’Ippolito, D. A. 2006b Collisionality and magnetic geometry effects on tokamak edge turbulent transport. I. A two-region model with application to blobs. Phys. Plasmas 13, 112502.Google Scholar
Pigarov, A. Y., Krasheninnikov, S. I. & Rognlien, T. D. 2012 Time-dependent 2-d modeling of edge plasma transport with high intermittency due to blobs. Phys. Plasmas 19, 072516.Google Scholar
Sihvola, A.1996 Homogenization of a dielectric mixture with anisotropic spheres in anisotropic background. Tech. Rep. 7050. Lund University.Google Scholar
Snicker, A., Guidi, L., Kohn, A., Maj, O., Weber, H. & Poli, E. 2016 The effect of density fluctuations on ECRH beam broadening and implications to NTM mitigation on ITER. In APS Meeting Abstracts, p. PO6.005.Google Scholar
Valvis, S. I., Papagiannis, P., Papadopoulos, A., Hizanidis, K., Glytsis, E., Bairaktaris, F., Zisis, A., Tigelis, I. & Ram, A. K. 2017 Propagation of radio frequency waves through density fluctuations. In 59th Meeting of the APS Plasma Physics Division.Google Scholar
Zweben, S. J., Boedo, J. A., Grulke, O., Hidalgo, C., Labombard, B., Maqueda, R. J., Scarin, P. & Terry, J. L. 2007 Edge turbulence measurements in toroidal fusion devices. Plasma Phys. Control. Fusion 49, S1–S23.Google Scholar