Bound for the pressure integral in a toroidal-plasma equilibrium

Zensho Yoshida; Yoshikazu Giga

doi:10.1103/PhysRevE.48.2133

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Bound for the pressure integral in a toroidal-plasma equilibrium

Zensho Yoshida

Yoshikazu Giga

Department of Nuclear Engineering, University of Tokyo, Tokyo 113, Japan

Department of Mathematics, Hokkaido University, Sapporo 060, Japan

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Phys. Rev. E 48, 2133 – Published 1 September, 1993

DOI: https://doi.org/10.1103/PhysRevE.48.2133

Abstract

A bound for the pressure integral in a toroidal-plasma equilibrium has been studied, invoking an a priori estimate for a solution of the Grad-Shafranov equation. Earlier theories had to use approximate equilibrium solutions to calculate the pressure integral (poloidal beta ratio $β_{p}$ ), and, hence, fell short of being rigorous estimates. The present theory considers exact solutions and gives a rigorous bound for $β_{p}$ .

References (9)

S. A. Sabbagh et al., Phys. Fluids B 3, 2277 (1991); M. E. Mauel et al., Nucl. Fusion 32, 1468 (1992).
J. J. Ramos, Phys. Rev. A 42, 1021 (1990); Phys. Fluids B 3, 2247 (1991).
S. Yoshikawa, Phys. Fluids 17, 178 (1974); ibid. 20, 706 (1977).
G. Bateman, MHD Instabilities (MIT Press, Cambridge, 1978).
J. P. Friedberg, Ideal Magnetohydrodynamics (Plenum, New York, 1987).
J. F. Clarke and D. J. Sigmar, Phys. Rev. Lett. 38, 70 (1977).
R. A. Dory and Y.-K.M. Peng, Nucl. Fusion 17, 21 (1977).
L. E. Payne and M. E. Rayner, Z. Angew, Math. Phys. 23, 13 (1972); L. E. Payne, R. Sperb and I. Stakgold, Nonlinear Anal. Theory Methods Appl. 1, 547 (1977).
S. C. Cowley, P. K. Kaw, R. S. Kelly and R. M. Kulsrud, Phys. Fluids B 3, 2066 (1991).

[c1] S. A. Sabbagh et al., Phys. Fluids B 3, 2277 (1991); M. E. Mauel et al., Nucl. Fusion 32, 1468 (1992).

[c2] J. J. Ramos, Phys. Rev. A 42, 1021 (1990); Phys. Fluids B 3, 2247 (1991).

[c3] S. Yoshikawa, Phys. Fluids 17, 178 (1974); ibid. 20, 706 (1977).

[c4] G. Bateman, MHD Instabilities (MIT Press, Cambridge, 1978).

[c5] J. P. Friedberg, Ideal Magnetohydrodynamics (Plenum, New York, 1987).

[c6] J. F. Clarke and D. J. Sigmar, Phys. Rev. Lett. 38, 70 (1977).

[c7] R. A. Dory and Y.-K.M. Peng, Nucl. Fusion 17, 21 (1977).

[c8] L. E. Payne and M. E. Rayner, Z. Angew, Math. Phys. 23, 13 (1972); L. E. Payne, R. Sperb and I. Stakgold, Nonlinear Anal. Theory Methods Appl. 1, 547 (1977).

[c9] S. C. Cowley, P. K. Kaw, R. S. Kelly and R. M. Kulsrud, Phys. Fluids B 3, 2066 (1991).

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Bound for the pressure integral in a toroidal-plasma equilibrium

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