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

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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...

- Exact nonlinear analytic Vlasovâ€“Maxwell tangential equilibria with arbitrary density and temperature profiles. Mottez, F. // Physics of Plasmas;Jun2003, Vol. 10 Issue 6, p2501
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.

- 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...

- Magnetohydrodynamic equilibrium of plasma ball lightning. Wu, Hanming; Chen, Yunming // Physics of Fluids B: Plasma Physics;Aug89, Vol. 1 Issue 8, p1753
A study is done of magnetohydrodynamic (MHD) equilibrium of a self-confined plasma ball imbedded in an atmosphere with constant pressure p0. It is found that there is more than one equilibrium state for the plasma ball and the average pressure inside the ball is less than p0. It is also shown...

- The role of edge current density on kink mode stability and its implication for magnetohydrodynamic activity associated with edge localized modes. Manickam, Janardhan // Physics of Fluids B: Plasma Physics;Jul92, Vol. 4 Issue 7, p1901
The stability of a plasma equilibrium to the external kink mode is shown to be dependent on the details of the current density near the plasma edge and the value of the safety factor, q, at the edge. The buildup of the current density near the plasma edge is shown to decrease the shear in the...

- Equilibrium and resistive steady state of an axisymmetric co-axial helicity injection plasma. Tang, X. Z.; Boozer, A. H. // Physics of Plasmas;Sep2003, Vol. 10 Issue 9, p3661
Steady state (âˆ‚B/âˆ‚t=âˆ‚v/âˆ‚t=0) coaxial helicity injection (CHI) has a purely electrostatic E =-âˆ‡[uppercase_phi_synonym](Ïˆ,Î¸) field. The electrostatic potential implies an EÃ—B flow that scales with the externally imposed voltage and is negligibly affected by...