Abstract.
In this work we investigate the influence of low frequency turbulence on Doppler spectral line shapes in magnetized plasmas. Low frequency refers here to fluctuations whose typical time scale is much larger than those characterizing the atomic processes, such as radiative decay, collisions and charge exchange. This ordering is in particular relevant for drift wave turbulence, ubiquitous in edge plasmas of fusion devices. Turbulent fluctuations are found to affect line shapes through both the spatial and time averages introduced by the measurement process. The profile is expressed in terms of the fluid fields describing the plasma. Assuming the spectrometer acquisition time to be much larger than the turbulent time scale, an ordering generally fulfilled in experiments, allows to develop a statistical formalism. We proceed by successively investigating the effects of density, fluid velocity and temperature fluctuations on the Doppler profile of a spectral line emitted by a charge exchange population of neutrals. Line shapes, and especially line wings are found to be affected by ion temperature or fluid velocity fluctuations, and can in some cases exhibit a power-law behavior. These effects are shown to be measurable with existing techniques, and their interpretation in each particular case would rely on already existing tools. From a fundamental point of view, this study gives some insights in the appearance of non-Boltzmann statistics, such as Lévy statistics, when dealing with averaged experimental data.
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References
J.A. Krommes, Phys. Rep. 360, 1 (2002)
X. Garbet, Plasma Phys. Control. Fusion 43, A251 (2001)
W. Horton, Rev. Mod. Phys. 71, 735 (1999)
H.R. Griem, Spectral Line Broadening by Plasmas (Academic Press New York and London, 1974)
E. Oks, Plasma Spectroscopy (Springer-Verlag, Berlin Heidelberg, 1995)
H. Capes, D. Voslamber, Phys. Rev. A 15, 1751 (1977)
C. Deutsch, G. Bekefi, Phys. Rev. A 14, 854 (1976)
M. Baranger, B. Mozer, Phys. Rev. 123, 25 (1961)
H. Kubo, H. Takenaga, T. Sugie, S. Higashijima, S. Suzuki, A. Sakasai, N. Hosogane, Plasma Phys. Control. Fusion 40, 1115 (1998)
D.P. Stotler, C.H. Skinner, R.V. Budny, A.T. Ramsey, D.N. Ruzic, R.B. Turkot Jr, Phys. Plasmas 3, 4084 (1996)
J.D. Hey, C.C. Chu, E. Hintz, J. Phys. B: At. Mol. Opt. Phys. 32, 3555 (1999)
M. Koubiti, Y. Marandet, A. Escarguel, H. Capes, L. Godbert-Mouret, R. Stamm, C. De Michelis, R. Guirlet, M. Mattioli, Plasma Phys. Control. Fusion 44, 261 (2002)
N. Bretz, Rev. Sci. Instrum. 68, 2927 (1997)
H.T. Evensen, R.J. Fonck, S.F. Paul, G. Rewoldt, S.D. Scott, W.M. Tang, M.C. Zarnstorff, Nucl. Fusion 38, 237 (1998)
R. Jha et al., Phys. Plasmas 10, 699 (2003)
G.M. Zaslavsky, M. Edelman, H. Weitzner, B. Carreras, G. McKee, R. Bravenec, R. Fonck, Phys. Plasmas 7, 3691 (2000)
M. Jakubowski, R.J. Fonck, G.R. Mckee, Phys. Rev. Lett. 89, 265003 (2002)
Y. Marandet, P. Genesio, M. Koubiti, L. Godbert-Mouret, B. Felts, R. Stamm, H. Capes, R. Guirlet, Nuc. Fus. 44, S118 (2004)
Y. Marandet, H. Capes, L. Godbert-Mouret, M. Koubiti, R. Stamm, Europhys. Lett. 69, 531 (2005)
Y. Marandet, H. Capes, L.Godbert-Mouret, R. Guirlet, M. Koubiti, R. Stamm, Commun. Non Lin. Sci. Num Simul. 8, 469 (2003)
S.I. Braginskii, Rev. Plasma Phys. 1, 205 (1965)
F. Hinton, R. Hazeltine, Rev. Mod. Phys. 48, 239 (1976)
R.K. Janev, D. Reiter, U. Samm, Collision Processes in Low-Temperature Hydrogen Plasmas, Jül-Bericht 4105, Forschungszentrum Jülich, 2003
F.B. Rosmej, H. Capes, M. Koubiti, V.S. Lisitsa, Y. Marandet, A. Meigs, R. Stamm, Europhys. Conf. Abstr. 27A, 1.176 (2003)
S.G. Rautian, I.I. Sobel'man, Sov. Phys. Usp. 9, 701 (1967)
B.H. Bransden, C.J. Joachain, Physic of atoms and molecules (Longman Scientific and Technical, 1983)
Y. Marandet, H. Capes, L. Godbert-Mouret, M. Koubiti, R. Stamm, R. Guirlet, Spectral Line Shapes, edited by C.A. Back, Vol. 12, AIP, Volume 645, page 60, 2002
U. Frisch, Turbulence (Cambridge University Press, 1995)
A. Das, P. Kaw, Phys. Plasmas 2, 1497 (1995)
S.B. Pope, Turbulent Flows (Cambridge University Press, 2000)
H. Chen, S. Chen, R.H. Kraichnan, Phys. Rev. Lett. 63, 2657 (1989)
Y.G. Sinai, V. Yakhot, Phys. Rev. Lett. 63, 1962 (1989)
R.T. Pierrehumbert, Chaos 10, 61 (2000)
D.R. Fereday, P.H. Haynes, Phys. Fluids 16, 4359 (2004)
C. Tsallis, Chaos 6, 539 (1995)
H.R. Griem, Principles of Plasma Spectroscopy, Cambridge Monographs on Plasma Physics (Cambridge University Press, 1997)
A. Unsöld, Physik des Sternatmosphären (Springer-Verlag, Berlin, 1955)
N.A. Iganov, R.A. Sunyaev, Astron. Lett. 29, 791 (2003)
M.D. Ding et al., Astron. Astrophys. 348, L29 (1999)
Ying Liu, Ming-De Ding, Chin. J. Astron. Astrophys. 2, 277 (2002)
I. Koponen, Phys. Rev. E 52, 1197 (1995)
W. Paul, J. Baschnagel, Stochastic processes, From Physics to finance (Springer-Verlag, 1999)
Charge-Transfer Devices in Spectroscopy, edited by J.V. Sweedler, K.L. Ratzlaff, M.B. Denton (VCH, 1994)
P.M. Epperson, M.B. Denton, Anal. Chem. 61, 1513 (1989)
R. Guirlet et al., Plasma Phys. Control. Fusion 43, 177 (2001)
D. Reiter, M. Baelmans, P. Börner, Fus. Sci. Technol. 47, 172 (2005)
J.D. Hey, C.C. Chu, Ph. Mertens, J. Phys. B:At. Mol. Opt. Phys. 38, 3517 (2005)
S. Brezinsek et al., Fus. Sci. Technol. 47, 209 (2005)
A.J.H. Donné et al. Fus. Sci. Technol. 47, 220 (2005)
S. Jespersen, R. Metzler, H.C. Fogedby, Phys. Rev. E 59, 2736 (1999)
A.V. Chechkin, V. Yu. Gonchar, Phys. Plasmas 9, 78 (2002)
C. Beck, Phys. Rev. Lett. 87, 180601 (2001).
P. Resibois, M. DeLeener, Classical Kinetic Theory of fluids (Wiley-Interscience, 1977)
G. Wilk, Z. Wlodarczyk, Phys. Rev. Lett. 84, 2770 (2000)
C. Beck, E.D.G. Cohen, Physica A 322, 267 (2003)
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Marandet, Y., Capes, H., Godbert-Mouret, L. et al. Spectral line shapes modeling in turbulent plasmas. Eur. Phys. J. D 39, 247–260 (2006). https://doi.org/10.1140/epjd/e2006-00105-4
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DOI: https://doi.org/10.1140/epjd/e2006-00105-4