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By assuming well defined magnetic surfaces we examine the characteristics of special three dimensional equilibria with incompressible flows such that any two out of the vectors of velocity, vorticity, magnetic field and current density are parallel one another. In the majority of the equilibria considered, it turns out that the only isodynamic equilibrium configuration, defined so that the magnetic field modulus be uniform on magnetic surfaces, is the axisymmetric Palumbo one. Also, except for equilibria with the velocity parallel to the current density in the other five of the above mentioned special axisymmetric (non-isodynamic) equilibria the velocity should be parallel to the magnetic field. In addition, isodynamicity is removed by the non parallel component of the flow associated with the electric field in axisymmetric equilibria with either complex lamellar generalised velocity, ρ V where ρ is the density, or complex lamellar magnetic field. [ABSTRACT FROM AUTHOR]

Magnetosonic waves traveling in a MHD equilibrium may evolve into shocks. We develop a criterion for the creation of fast shocks in the equatorial plane of axisymmetric equilibria and analyze the influence of the most important parameters. The results are applied to Grad–Shafranov equilibria and accretion disks. [ABSTRACT FROM AUTHOR]

Nonlinear waves advancing into equilibrium states may become shocks. This possibility depends on the equilibrium quantities plus the velocity and shape of the wavefronts. The equation describing this phenomenon is described for the case of the fast magnetosonic waves, and the particular case of plane flow with vertical magnetic field is analyzed in detail. It is also shown that in two-species MHD, both collisions between species and their chemical reactivity tend to delay or prevent the formation of shocks. [ABSTRACT FROM AUTHOR]

The equations of ideal magnetohydrodynamic equilibria in the presence of gravitational forcing and in the absence of pressure gradient are relevant for large-scale, extremely cold plasmas. Its 2D formulation possesses a highly symmetrical form that allows a complete analysis of its solvability. It turns out that when the boundary condition is given by the vanishing of the normal component of the magnetic field, in the absence of vacuum, solutions exist precisely for doubly connected domains, and in that case there exists an infinity of solutions. [ABSTRACT FROM PUBLISHER]

Exact equal-field axisymmetric equipotentials are found for the Poisson equation in terms of elliptic integrals of the first and second kind. The method used has been introduced in 1967 by D. Palumbo in the context of magnetohydrodynamics. [ABSTRACT FROM AUTHOR]

This paper presents numerical analysis of finite element approximation to a nonlinear eigenvalue problem: −Δ u=λ u in Ω, u=−1 on Γ=∂Ω, where Ω is a bounded domain in R ( n=1, 2, 3). This problem arises in MHD (magnetohydrodynamics) equilibria and some other important physical phenomena. We consider a simple finite element scheme, and perform its error analysis. We also discuss a lumped finite element scheme, which is introduced to simplify the computations of the original scheme. Some numerical results are illustrated to show the validity of the analysis. [ABSTRACT FROM AUTHOR]

A previous investigation by one of us, concerning the self-consistent equilibria of a two-region (plasma+gas) cylindrical Tokamak, is extended to the similar equilibria of a Reversed-Field Pinch, where a significant current density is driven by a dynamo electric field due to turbulence. The previous model has been generalized under the following basic assumptions: a) to the lowest order, the turbulent dynamo electric field E is expressed as a homogeneous function of degree 1 of the magnetic field B, say E =α· B, with α being a 2nd-rank tensor, homogeneous of degree 0 in B, and generally depending on the plasma state; b) E does not appear in the plasma power balance, as if it were produced by a Maxwell demon able to extract the needed power from the plasma internal energy. In particular we show that, in the simplest case when both α and the plasma resistivity η are isotropic and constant, the magnetic field turns out force-free with constant abnormality αμ/η for vanishing axial electric field E . This case has also been solved analytically, for whatever E , under circular, besides cylindrical, symmetry. [ABSTRACT FROM AUTHOR]

We consider a dissipative model of a stationary, axisymmetric plasma configuration which allows to compute the pressure p and the toroidal magnetic field B as functions of the poloidal magnetic flux ι in Grad-Shafranov's equation. This will be obtained through the solution of four coupled equations in the four unknowns p, B , T (temperature) and ι. [ABSTRACT FROM AUTHOR]

Formula (60) of the original paper yielding the curvature of the wavefront transported by straight rays is wrong. The correct one yields much more information on shock formation for the example developed in Section 4. [ABSTRACT FROM AUTHOR]