ANOMALOUS PERTURBATIVE TRANSPORT IN TOKAMAKS DUE TO DRIFT-WAVE TURBULENCE

[en] A new method for calculating the anomalous transport in tokamak plasmas is presented. The renormalized nonlinear plasma response function is derived using the direct-interaction approximation (DIA). A complete calculation for the case of electrostatic drift-wave turbulence is presented. Explicit expressions for all coefficients of the anomalous transport matrix relating particle and heat fluxes to density and temperature gradients in the plasma are obtained. The anomalous transport matrix calculated using the DIA does not have the Onsager symmetry. As an example of application, the parameters of the Texas Experimental Tokamak (TEXT) [Nucl. Technol. Fusion 1, 479 (1981)] are used to evaluate all transport coefficients numerically, as well as the spectrum modulation. The relation between the theoretical results and the experimental data is discussed. Although this paper focuses on electron transport for simplicity, the method can also be used to calculate anomalous transport due to ion instabilities, such as the ion-temperature-gradient instability.

Disciplines :

Physics

Author, co-author :

Thoul, Anne ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Astrophysique stellaire théorique et astérosismologie

SIMILON, P. L.

SUDAN, R. N.

Language :

English

Title :

ANOMALOUS PERTURBATIVE TRANSPORT IN TOKAMAKS DUE TO DRIFT-WAVE TURBULENCE

Publication date :

1994

Journal title :

Physics of Plasmas

ISSN :

1070-664X

eISSN :

1089-7674

Publisher :

American Institute of Physics

Volume :

Issue :

Pages :

579-600

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 08 December 2010

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Bibliography

Braginskii S.I. Transport Processes in Plasma , edited by M. A. Leontovitch (Consultants Bureau, New York); 1965, 205.
Hinton F.L. Collisional Transport in Plasma , edited by A. A. Galeev and R. N. Sudan (North-Holland, New York); 1984, 147.
Rosenbluth M.N., Hazeltine R.D., Hinton F.L. Phys. Fluids 1972, 15:116.
Hinton F.L., Hazeltine R.D. Rev. Mod. Phys. 1976, 48:239.
Furth H.P. Fusion , edited by E. Teller (Academic, London); 1981, 210.
Liewer P.C., Pfeiffer W., Waltz R.E. Phys. Fluids 1983, 26:563.
Hugill J. Nucl. Fusion 1983, 23:331.
Tang W.M. Nucl. Fusion 1978, 18:1089.
Riedel K.S. Comments Plasma Phys. Controlled Fusion 1989, 12:279.
Waltz R.E., DeBoo J.C., Rosenbluth M.N. Phys. Rev. Lett. 1990, 65:2390.
Christiansen J.P., Cordey J.G., Thomsen K. Nucl. Fusion 1990, 30:1183.
Callen J.D. Phys. Fluids B 1990, 2:2869.
Boozer A.H., Baldwin D.E., Horton C.W., Dominguez R.R., Glasser A.H., Krommes J.A., Neilson G.H., Shaing K.-C., Sadowski W.L., Weitzner H. Phys. Fluids B 1990, 2:2870.
Wootton A.J., Carreras B.A., Matsumoto H., McGuire K., Peebles W.A., Ritz C.P., Terry P.W., Zweben S.J. Phys. Fluids B 1990, 2:2879.
Burrel K.H., Gentle K.W., Luhmann N.C., Marmar E.S., Murakami M., Schoenberg K.F., Tang W.M., Zarnstorff M.C. Phys. Fluids B 1990, 2:2904.
Houlberg W.A., Ross D.W., Bateman G., Cowley S.C., Efthimion P.C., Pfeiffer W.W., Porter G.D., Shumaker D.E., Sugiyama L.E., Wiley J.C. Phys. Fluids B 1990, 2:2913.
Kaye S.M., Barnes C.W., Bell M.G., DeBoo J.C., Greenwald M., Riedel K., Sigmar D., Uckan N., Waltz R. Phys. Fluids B 1990, 2:2926.
Horton C.W. Drift Wave Turbulence and Anomalous Transport , edited by A. A. Qaleev and R. N. Sudan (North-Holland, Amsterdam); 1984, 383.
Liewer P.C. Nucl. Fusion 1985, 25:543.
Rudakov L.I., Sagdeev R.Z. Nucl. Fusion Suppl., Part B 1962, 481.
Galeev A.A., Oraevskii V.N., Sagdeev R.Z. Sov. Phys. JETP 1963, 17:615.
Krall N.A., Trivelpiece A.W. Principles of Plasma Physics, (McGraw-Hill, New York); 1973.
Mikhailovsky A.B. Instabilities in Inhomogeneous Plasma , edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam); 1983, 587.
Manheimer W.M., Lashmore-Davies C.N. MHD and Microinstabilities in Confined Plasma, (Hilger, New York); 1989.
Rudakov L.I., Sagdeev R.Z. Sov. Phys. Dokl. 1961, 6:415.
Coppi B., Rosenbluth M.N., Sagdeev R.Z. Phys. Fluids 1967, 10:582.
Lee Y.C., Dong J.Q., Guzdar P.N., Liu C.S. Phys. Fluids 1987, 30:1331.
Gladd N.T., Drake J.F., Chang C.L., Liu C.S. Phys. Fluids 1980, 23:1182.
Mazzucato E. Phys. Rev. Lett. 1976, 36:792.
Mazzucato E. Phys. Rev. Lett. 1982, 48:1828.
Brower D.L., Peebles W.A., Luhmann N.C. Nucl. Fusion 1987, 27:2055.
Yu C.X., Brower D.L., Zhao S.J., Peebles W.A., Luhmann N.C., Bravenec R.V., Chen J.Y., Lin H., Ritz C.P., Schoch P.M., Yang X.Z. Phys. Fluids B 1992, 4:381.
Nicholson D.R. Introduction to Plasma Theory, (Wiley, New York); 1983.
Ejima S. (1982) the Doublet III Group. Nucl. Fusion 22:1627.
Greenwald M., Gwinn D., Milora S., Parker J., Parker R., Wolfe S. Plasma Physics and Controlled Nuclear Fusion Research 1984, Proceedings of the 10th International Conference, London , International Atomic Energy Agency, Vienna; 1985, I:45.
TEXT Group, Nucl. Technol. Fusion 1981, 1:479.
Brower D.L., Peebles W.A., Kim S.K., Luhmann N.C., Tang W.M., Phillips P.E. Phys. Rev. Lett. 1987, 59:49.
Rechester A.B., Rosenbluth M.N. Phys. Rev. Lett. 1978, 40:38.
Waltz R.E., Pfeiffer W., Dominguez R.R. Nucl. Fusion 1980, 20:43.
Waltz R.E. Phys. Fluids 1982, 25:269.
Shaing K.C. Phys. Fluids 1988, 31:2249.
Kadomtsev B.B. Plasma Turbulence, (Academic, New York); 1965.
Sagdeev R.Z., Galeev A.A. Nonlinear Plasma Theory, (Benjamin, New York); 1969.
Dupree T.H. Phys. Fluids 1967, 10:1049.
Dupree T.H. Phys. Fluids 1972, 15:334.
Kraichnan R.H. J. Fluid Mech. 1959, 5:497.
Leslie D.C. Developments in the Theory of Turbulence, (Clarendon, Oxford); 1973.
Krommes J.A. Statistical Description and Plasma Physics , edited by A. A. Galeev and R. N. Sudan (North-Holland, New York); 1984, 183.
Similon P.L., Sudan R.N. Annu. Rev. Fluid Mech. 1990, 22:317.
Kraichnan R.H. J. Math. Phys. 1961, 2:124.
Kraichnan R.H. J. Fluid Mech. 1970, 41:189.
Thoul A.A., Similon P.L., Sudan R.N. Phys. Rev. Lett. 1987, 59:1448.
Strachan J.D., Bretz N., Mazzucato E., Barnes C.W., Boyd D., Cohen S.A., Hovey J., Kaita R., Medley S.S., Schmidt G., Tait G., Voss D. Nucl. Fusion 1982, 22:1145.
Efthimion P.C., Mansfield D.K., Stratton B.C., Synakowski E., Bhattacharjee A., Biglari H., Diamond P.H., Goldston R.J., Hegna C.C., Mc Cune D., Rewoldt G., Scott S., Tang W.M., Taylor G., Waltz R.E., Wieland R.M., Zarnstorff M.C. Phys. Rev. Lett. 1991, 66:421.
Christiansen J.P., Callen J.D., Cordey J.G., Thomsen K. Nucl. Fusion 1988, 28:817.
Fredrickson E.D., Callen J.D., McGuire K., Bell J.D., Colchin R.J., Efthimion P.C., Hill K.W., Izzo R., Mikkelsen D.R., Monticello D.A., Par V., Taylor G., Zamstorff M. Nucl. Fusion 1986, 26:849.
Tubbing B.J.D., Lopes Cardozo N.J., Van der Wiel M.J. Nucl. Fusion 1987, 27:1843.
Kim S.K., Brower D.L., Peebles W.A., Luhmann N.C. Phys. Rev. Lett. 1988, 60:577.
de Haas J.C.M., O'Rourke J., Sips A.C.C., Lopes Cardozo N.J. Joint European Torus JET Report ♯JET-R(90)04, National Technical Information Service, Springfield, VANTIS Document No. DE91616771; 1990.
Brower D.L., Kim S.K., Wenzel K.W. Phys. Rev. Lett. 1990, 65:337.
Gentle K.W., Richards B., Austin M.E., Bravenec R.V., Brower D.L., Gandy R.F., Li W.L., Phillips P.E., Ross D.W., Rowan W.L., Schoch P.M., Valanju P.M., Wootton A.J. Phys. Rev. Lett. 1992, 68:2444.
Thoul A.A., Similon P.L., Sudan R.N. Phys. Plasmas 1994, 1:601.
Kulsrud R.M. Handbook of Plasma Physics , edited by A. A. Galeev and R. N. Sudan (North-Holland, Amsterdam); 1984, 115.
Landau E.M., Pitaevskii L.P. Physical Kinetics , Pergamon, New York; 1981, 255-263.
Miyamoto K. Plasma Physics for Nuclear Fusion , (MIT Press, Cambridge, MA)332-333; 1980, 61-65.
Note that even though the magnetic shear is important in the linear theory of drift waves, where it has a stabilizing effect, it might not be important in the strong turbulence limit., Indeed, in this limit, the mode will lose its energy due to the dissipation mechanism (here the ion viscosity) before it can be stabilized by the magnetic shear; .
Gross R.A. Fusion Energy , (Wiley-Interscience, New York); 1984, 83-114.
Hasegawa A., Mima K. Phys. Rev. Lett. 1977, 9:205.
Hasegawa A., Mima K. Phys. Fluids 1978, 21:87.
In reality, the plasma is not neutral, but only quasineutral., Therefore,there is a mean radial electric potential [formula omitted] However, it only creates a global rotation of the plasma, i.e., a Doppler shift of the frequency, and can therefore be eliminated by going into the frame of the rotating plasma, so that [formula omitted] and [formula omitted]; .
Note that [formula omitted]..
Bhatnagar P.L., Gross E.P., Krook M. Phys. Rev. 1954, 94:511.
Callen J.D., Jahns G.L. Phys. Rev. Lett. 1977, 38:491.
Soler M., Callen J.D. Nucl. Fusion 1979, 19:703.
Wesson J.A. Tokamaks, (Oxford Science Publications, Oxford); 1987.
Gentle K.W. Phys. Fluids 1988, 31:1105.
O'Rourke J., Hogeweij G.M.D., Rimini F., Sips A.C.C., Start D.F.M. Bull. Am. Phys. Soc. 1990, 35:1999.
Hossain M., Kress M., Nien Hu P., Blank A., Grad H. Phys. Rev. Lett. 1987, 58:487.
Wootton A.J. Plasma Phys. Controlled Fusion 1988, 30:1479.
Bravenec R.V., Ross D.W., Schoch P.M., Brower D.L., Heard J.W., Hickok R.L., Yang X.Z. Bull. Am. Phys. Soc. 1990, 35:2026.
Crowley T.P. Rev. Sci. Instrum. 1990, 61:2989.
Ross D.W. Bull. Am. Phys. Soc. 1990, 35:2127.
We need to have dissipation at the long wavelengths in order to satisfy the condition [formula omitted] at all k., The molecular viscosity provides the necessary dissipation at the small scales. Therefore, the eddy viscosity damping [formula omitted] should be written as [formula omitted] where [formula omitted] the molecular viscosity, is a small constant; .
Waltz R.E., Dominguez R.R. Phys. Fluids B 1989, 1:1935.
Onsager L. Phys. Rev. 1931, 37:405.
Onsager L. Phys. Rev. 1931, 38:2265.
Balescu R. Phys. Fluids B 1990, 3:564.
Molvig K., Hizadinis K. Phys. Fluids 1984, 27:2847.
Gentle K.W., (private communication); 1990.
Chen L., Cheng C.Z. Phys. Fluids 1980, 23:2240.
Similon P.L., Diamond P.H. Phys. Fluids 1984, 27:916.
Similon P.L., Ph.D. thesis, Princeton University; 1981.