# Symmetries, weak symmetries, and related solutions of the Grad-Shafranov equation

## Related Articles

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A three-dimensional equilibrium theory [J. Geophys. Res. 92, 11 101 (1987)] for stretched plasma configurations, such as the Earthâ€™s magnetotail, is extended to include the effects of field-aligned flow. The magnetohydrodynamic (MHD) equations for this case can be solved in a general way...

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The tangential layers are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. They have been extensively described in the frame of the magnetohydrodynamic (MHD) theory. But the MHD theory does not look inside the transition region if the...

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Determines the effects of plasma equilibria on dipolar magnetic configurations. Derivation of equations governing the plasma equilibria; Evaluation on magnetohydrodynamic stability of plasma equilibria; Consideration of the equilibria of rotating plasmas and flows in a gravitational field.

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Excitation of continuously phase-locked (autoresonant) plasma waves in a nonuniform plasma via stimulated Raman backscattering is analyzed with a focus on the kinetic regime (kÎ»Dâˆ¼1). The dominant nonlinear effect in this regime is that of resonant particles, and the plasma wave...

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We discuss some interesting aspects of the wave breaking in localized solutions of the dispersionless Kadomtsev-Petviashvili equation, an integrable partial differential equation describing the propagation of weakly nonlinear, quasi-one-dimensional waves in 2+1 dimensions, which arise in several...

- Schwarzschild-NUT solution in modified teleparallel gravity theory. Nashed, Gamal // Astrophysics & Space Science;Apr2014, Vol. 350 Issue 2, p791
Spherically symmetric tetrad field is applied to the field equation of modified teleparallel gravity theory. Some constraints are assumed on the resulting non-linear partial differential equations. Exact vacuum solution is derived with two constants of integration. The derived solution has a...

- Quasi-helical symmetry at finite aspect ratio. Nührenberg, C.; Mikhailov, M.; Nührenberg, J.; Shafranov, V. // Plasma Physics Reports;Jul2010, Vol. 36 Issue 7, p558
Computational stellarator optimization is used to create a configuration which is quasi-helically symmetric at finite aspect ratio. For the aspect ratio per period chosen (âˆ¼2), this procedure results in benign properties throughout the plasma volume.

- Role of bumpy fields on single particle orbit in near quasihelically symmetric stellarators. Seol, JaeChun; Hegna, C.C. // Physics of Plasmas;Jul2004, Vol. 11 Issue 7, p3672
The role of symmetry breaking on single particle orbits in near helically symmetric stellarators is investigated. In particular, the effect of a symmetry-breaking bumpy term is included in the analysis of trapped particle orbits. It is found that all trapped particle drift orbits are determined...

- Pressure insensitivity of a high-ï¿½ quasi-isodynamic stellarator. Mikhailov, M.; Shafranov, V.; N�hrenberg, J. // Plasma Physics Reports;Jul2009, Vol. 35 Issue 7, p529
The sensitivity of a high-ï¿½ quasi-isodynamic stellarator equilibrium with respect to changes of the plasma pressure is investigated. It is shown that a plasma boundary near to the high-ï¿½ boundary exists with the property that the magnetohydrodynamic and drift-kinetic properties of the...