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.
Cite this paper
nullM. Asif, "Plasma Internal Energy for Toroidal Elliptic Plasmas with Triangularity," Journal of Modern Physics, Vol. 2 No. 1, 2011, pp. 5-7. doi: 10.4236/jmp.2011.21002.
 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.
V. D. Shafranov, “Plasma Equilibrium in a Magnetic Field,” Reviews of Plasma Physics, Vol. 2, 1966, p. 103.
J. W. Bates and D. C. Montgomery, “Toroidal Visco-Resistive Magnetohydrodynamic Steady States Contain Vortices,” Physics of Plasmas, Vol. 5, 1998, 2649-2653.
D. C. Montgomery, Abstracts and Proceedings Current Trends in International Fusion Research: A Review, Washington D. C., March 2001, p. 67.
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.
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.
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.
P. Mart?n, “Magnetohydrodynamic treatment of collisional transport in toroidal configurations: Application to elliptic cross sections,” Physics of Plasmas, Vol. 7, 2000, 2915-2922.
P. Mart?n and M. G. Haines, “Poloidal magnetic field around a tokamak magnetic surface,” Physics of Plasmas, Vol. 5, 1998, 410-416.
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.
E. Hameiri, “The equilibrium and stability of rotating plasmas,” Physics of Fluids, Vol. 26, 1982, 230-237.
M. Tendler, “Important Issues of Physics of Improved Confinement in Tokamaks,” Astrophysics and Space Science, Vol. 256, 1998, 205-218.
F. L. Hinton and G. M. Staebler, “Particle and energy confinement bifurcation in tokamaks,” Physics of Fluids B, Vol. 5, 1993, 1281-1288.
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