Plasma Internal Energy for Toroidal Elliptic Plasmas with Triangularity

Muhammad Asif

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DOI: 10.4236/jmp.2011.21002                

Abstract

The Plasma internal energy is not conserved on a magnetic surface if nonlinear flows are considered. The analysis here presented leads to a complicated equation for the plasma internal energy considering nonlinear flows in the collisional regime, including viscosity and in the low-vorticity approximation. Tokamak equilibrium has been analyzed with the magnetohydrodynamics nonlinear momentum equation in the low vorticity case. A generalized Grad–Shafranov-type equation has been also derived for this case.

Keywords

Plasma Internal Energy, Toroidal Elliptic Plasmas

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	H. Grad and H. Rubin, “Hydromagnetic Equilibria and Force-Free Fields,” Proceedings of the 2nd UN Conference on the Peaceful Uses of Atomic Energy, Geneva, Vol. 31, 1958, p. 190.
[2]	V. D. Shafranov, “Plasma Equilibrium in a Magnetic Field,” Reviews of Plasma Physics, Vol. 2, 1966, p. 103.
[3]	J. W. Bates and D. C. Montgomery, “Toroidal Visco-Resistive Magnetohydrodynamic Steady States Contain Vortices,” Physics of Plasmas, Vol. 5, 1998, 2649-2653. doi:10.1063/1.872952
[4]	D. C. Montgomery, Abstracts and Proceedings Current Trends in International Fusion Research: A Review, Washington D. C., March 2001, p. 67.
[5]	R. Iacono, A. Bondeson, F. Troyon and R. Gruber, “Axisymmetric Toroidal Equilibrium with Flow and Anisotropic Pressure,” Physics of Fluids B, Vol. 2, 1990, 1794-1803. doi:10.1063/1.859451
[6]	P. Martin et al., “Conserved functions and extended Grad-Shafranov equation for low vorticity viscous plasmas with nonlinear flows,” Physics of Plasmas, vol. 12, 2005, p. 102505. doi:10.1063/1.2080587
[7]	L. Guazzotto, R. Betti, J. Manickam and S. Kaye, “Numerical study of tokamak equilibria with arbitrary flow,” Physics of Plasmas, Vol. 11, 2004, 604-614. doi:10.1063/1.1637918
[8]	P. Mart?n, “Magnetohydrodynamic treatment of collisional transport in toroidal configurations: Application to elliptic cross sections,” Physics of Plasmas, Vol. 7, 2000, 2915-2922. doi:10.1063/1.874142
[9]	P. Mart?n and M. G. Haines, “Poloidal magnetic field around a tokamak magnetic surface,” Physics of Plasmas, Vol. 5, 1998, 410-416. doi:10.1063/1.872740
[10]	E. K. Maschke and H. Perrin, “Exact solutions of the stationary MHD equations for a rotating toroidal plasma,” Plasma Physics, Vol. 22, 1980, 579-594. doi:10.1088/0032-1028/22/6/007
[11]	E. Hameiri, “The equilibrium and stability of rotating plasmas,” Physics of Fluids, Vol. 26, 1982, 230-237. doi:10.1063/1.864012
[12]	M. Tendler, “Important Issues of Physics of Improved Confinement in Tokamaks,” Astrophysics and Space Science, Vol. 256, 1998, 205-218. doi:10.1023/A:1001183424542
[13]	F. L. Hinton and G. M. Staebler, “Particle and energy confinement bifurcation in tokamaks,” Physics of Fluids B, Vol. 5, 1993, 1281-1288. doi:10.1063/1.860919
[14]	M. Tendler, “Different Scenarios of Transition into Regimes with Improved Confinement,” Plasma Physics and Controlled Fusion, Vol. 39, 1997, B371-382. doi:10.1088/0741-3335/39/12B/028