Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

Calculation of the Neoclassical Conductivity of Plasma and Fraction of Trapped Particles for Elongated Damavand Tokamak

Document Type : Research Paper

Authors

F Dini
S Khorasani
Abstract
Configuration of Tokamak plasma has a dominant effect on its parameters. In the calculation of transport, there are some transport coefficients and quantities, where the knowledge of their precise values, according to the system of equations, is essential to be realized. Tokamak has a toroidal configuration, in addition to classical effects, it is necessary to study the neoclassical effects due to the field curvature. The trapped particles in strong electromagnetic fields oscillate on banana-shaped orbits which in turn affect many other collisional transport parameters. Here, a precise estimation of trapped particles based on the standard equilibrium model for an elliptical shape of Tokamak plasma has been carried out using Lin-Liu model. It should be added that in this calculation, the profile of the averaged magnetic field on the flux surfaces has been derived using analytical integration and consideration of an elliptic shape for ellipticity function in the limit of large aspect ratio and zero shift of magnetic flux surfaces. Having the fraction of the trapped particles, by following the formulation and using an appropriate model in various collisional regimes, the neoclassical conductivity of plasma in Damavand Tokamak is obtained and the respective variations have been found. The presented results can exploit the computation of transport and other quantities of Damavand Tokamak.

Highlights

  1. 1.    J. Wesson, ed, “Tokamaks,” 3rd edition, Clarendon Press, Oxford, (2004).

 

  1. 2.    T.J. Dolan, “Fusion Research,” rev. ed, Pergamon Press, (2001).

 

  1. 3.    S. Dean, “Fifty years of U.S. fusion research, an overview of programs,” Nuclear News, 34-40 (2002).

 

  1. 4.    N.B. Morley, M.A. Abdou, M. Anderson, P. Calderoni, R.J. Kurtz, R. Nygren, R. Raffray, M. Sawan, P. Sharpe, S. Smolentsev, S. Willms, A.Y. Ying, “Overview of fusion nuclear technology in the US,” Fusion Engineering and Design, 81, 33-43 (2006).

 

  1. 5.    S. Tanaka, “Overview of research and development activities on fusion nuclear technologies in Japan,” Fusion Engineering and Design, 81, 13-24 (2006).

 

  1. 6.    Y. Strebkov and V. Belyakov, “Review of the activity in Russia in the area of fusion nuclear technology,” Fusion Engineering and Design, 81, 45-58 (2006).

 

  1. 7.    R. Andreani, E. Diegele, W. Gulden, R. Lässer, D. Maisonnier, D. Murdoch, M. Pick, Y. Poitevin and The ITER-EFDA team at Garching, “Overview of the European Union fusion nuclear technologies development and essential elements on the way to DEMO,” Fusion Engineering and Design, 81, 25-32 (2006).

 

  1. 8.    Y. Shimomura and for the ITER International Team and Participant Teams, “Preparation of ITER construction and operation,” Fusion Engineering and Design, 81, 3-11 (2006).

 

  1. 9.    L.S. Soloveev, Soviet Physics JETP, Vol. 26, 400 (1968).

 

  1. 10.              H. Maaberg and C.D. Beidler, “Self-consistent neoclassical transport coefficients for elongated Tokamaks,” Proceedings of 31st EPS Conference on Plasma Physics, London, 28G, 1.100 (28 June-2 July 2004).

 

  1. 11.              ف. دینی، «شبیه‌سازی ترابرد در حوزه زمان در توکامک دماوند،» پایان‌نامه دکتری، دانشکده مهندسی هسته‌ای، دانشگاه صنعتی امیرکبیر، تهران (دی 1382).                                                       
  2. 12.              ر. امراللهی، ف. دینی، س. خراسانی، «شبیه‌سازی تعادل پلاسمای کشیده در توکامک دماوند،» مجموعه مقالات اولین کنفرانس کاربردهای فیزیک و علوم هسته‎ای، دانشگاه صنعتی امیرکبیر، تهران، 259- 261 (بهمن 1378).                                                  

 

 

  1. 13.              S.P. Hirshman and D.J. Sigmar, “Neoclassical transport of impurities in Tokamak plasmas,” Nuclear Fusion, 21, 1079-1180 (1981)

 

  1. 14.              S.P. Hirshman, “Finite-aspect-ratio effects on the bootstrap current in Tokamaks,” Physics of Fluids, 31, 3150-3152 (1988).

 

  1. 15.              M.C.R. Andrade and G.O. Ludwig, “Comparison of bootstrap current and plasma conductivity models applied in a self-consistent equilibrium calculation for Tokamak plasmas,” Nuclear Fusion, 45, 48-64 (2005).

 

  1. 16.              Y.R. Lin-Liu and R.L. Miller, “Upper and lower bounds of the effective trapped particle fraction in general Tokamak equilibria,” Physics of Plasmas, 2, 1666-1668 (1995).

 

  1. 17.              A.A. Galeev and R.Z. Sagdeev, “Transport phenomena in a collisionless plasma in a toroidal magnetic system,” Soviet Physics JETP, 26, 233-240 (1968).

 

  1. 18.              S.P. Hirshman, R.J. Hawryluk, B. Birge, “Neoclassical conductivity of a Tokamak plasma,” Nuclear Fusion, 17, 611-614 (1977).

 

  1. 19.              O. Sauter, C. Angioni, Y.R. Lin-Liu, “Neoclassical conductivity and bootstrap current formulas for general axisymmetric equilibria and arbitrary collisionality regime,” Physics of Plasmas, 6, 2834-2839 (1999); Erratum: 9, 5140 (2002).

 

  1. 20.              J.P.H.E. Ongena, M. Evard, D. McCune, “Numerical transport codes,” Fusion Science and Technology, 49, 337-345 (2006).

 

  1. 21.              F.L. Hinton and R.D. Hazeltine, “Theory of plasma transport in toroidal confinement systems,” Reviews of Modern Physics, 48, 239-308 (1976).

 

A.H. Boozer, “Physics of magnetically confined plasmas,” Reviews of Modern Physics, 76, 1071-1141 (2004).

Keywords

Tokamak Devices
Neoclassic Transport Theory
Plasma Radial Profile
Magnetic Field Configurations
Plasma
Trapped Particles Instability
  1. 1.    J. Wesson, ed, “Tokamaks,” 3rd edition, Clarendon Press, Oxford, (2004).

 

  1. 2.    T.J. Dolan, “Fusion Research,” rev. ed, Pergamon Press, (2001).

 

  1. 3.    S. Dean, “Fifty years of U.S. fusion research, an overview of programs,” Nuclear News, 34-40 (2002).

 

  1. 4.    N.B. Morley, M.A. Abdou, M. Anderson, P. Calderoni, R.J. Kurtz, R. Nygren, R. Raffray, M. Sawan, P. Sharpe, S. Smolentsev, S. Willms, A.Y. Ying, “Overview of fusion nuclear technology in the US,” Fusion Engineering and Design, 81, 33-43 (2006).

 

  1. 5.    S. Tanaka, “Overview of research and development activities on fusion nuclear technologies in Japan,” Fusion Engineering and Design, 81, 13-24 (2006).

 

  1. 6.    Y. Strebkov and V. Belyakov, “Review of the activity in Russia in the area of fusion nuclear technology,” Fusion Engineering and Design, 81, 45-58 (2006).

 

  1. 7.    R. Andreani, E. Diegele, W. Gulden, R. Lässer, D. Maisonnier, D. Murdoch, M. Pick, Y. Poitevin and The ITER-EFDA team at Garching, “Overview of the European Union fusion nuclear technologies development and essential elements on the way to DEMO,” Fusion Engineering and Design, 81, 25-32 (2006).

 

  1. 8.    Y. Shimomura and for the ITER International Team and Participant Teams, “Preparation of ITER construction and operation,” Fusion Engineering and Design, 81, 3-11 (2006).

 

  1. 9.    L.S. Soloveev, Soviet Physics JETP, Vol. 26, 400 (1968).

 

  1. 10.              H. Maaberg and C.D. Beidler, “Self-consistent neoclassical transport coefficients for elongated Tokamaks,” Proceedings of 31st EPS Conference on Plasma Physics, London, 28G, 1.100 (28 June-2 July 2004).

 

  1. 11.              ف. دینی، «شبیه‌سازی ترابرد در حوزه زمان در توکامک دماوند،» پایان‌نامه دکتری، دانشکده مهندسی هسته‌ای، دانشگاه صنعتی امیرکبیر، تهران (دی 1382).                                                       
  2. 12.              ر. امراللهی، ف. دینی، س. خراسانی، «شبیه‌سازی تعادل پلاسمای کشیده در توکامک دماوند،» مجموعه مقالات اولین کنفرانس کاربردهای فیزیک و علوم هسته‎ای، دانشگاه صنعتی امیرکبیر، تهران، 259- 261 (بهمن 1378).                                                  

 

 

  1. 13.              S.P. Hirshman and D.J. Sigmar, “Neoclassical transport of impurities in Tokamak plasmas,” Nuclear Fusion, 21, 1079-1180 (1981)

 

  1. 14.              S.P. Hirshman, “Finite-aspect-ratio effects on the bootstrap current in Tokamaks,” Physics of Fluids, 31, 3150-3152 (1988).

 

  1. 15.              M.C.R. Andrade and G.O. Ludwig, “Comparison of bootstrap current and plasma conductivity models applied in a self-consistent equilibrium calculation for Tokamak plasmas,” Nuclear Fusion, 45, 48-64 (2005).

 

  1. 16.              Y.R. Lin-Liu and R.L. Miller, “Upper and lower bounds of the effective trapped particle fraction in general Tokamak equilibria,” Physics of Plasmas, 2, 1666-1668 (1995).

 

  1. 17.              A.A. Galeev and R.Z. Sagdeev, “Transport phenomena in a collisionless plasma in a toroidal magnetic system,” Soviet Physics JETP, 26, 233-240 (1968).

 

  1. 18.              S.P. Hirshman, R.J. Hawryluk, B. Birge, “Neoclassical conductivity of a Tokamak plasma,” Nuclear Fusion, 17, 611-614 (1977).

 

  1. 19.              O. Sauter, C. Angioni, Y.R. Lin-Liu, “Neoclassical conductivity and bootstrap current formulas for general axisymmetric equilibria and arbitrary collisionality regime,” Physics of Plasmas, 6, 2834-2839 (1999); Erratum: 9, 5140 (2002).

 

  1. 20.              J.P.H.E. Ongena, M. Evard, D. McCune, “Numerical transport codes,” Fusion Science and Technology, 49, 337-345 (2006).

 

  1. 21.              F.L. Hinton and R.D. Hazeltine, “Theory of plasma transport in toroidal confinement systems,” Reviews of Modern Physics, 48, 239-308 (1976).

 

A.H. Boozer, “Physics of magnetically confined plasmas,” Reviews of Modern Physics, 76, 1071-1141 (2004).

Journal of Nuclear Science, Engineering and Technology (JONSAT)
Volume 28, Issue 2 - Serial Number 40
September 2007
Pages 25-33

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