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Rotating magnetic structures are common in astrophysics, from vortex tubes and tornados in the Sun all the way to jets in different astrophysical systems. The physics of these objects often combine inertial, magnetic, gas pressure and gravitational terms. Also, they often show approximate symmetries that help simplify the otherwise rather intractable equations governing their morphology and evolution. Here we propose a general formulation of the equations assuming axisymmetry and a self-similar form for all variables: in spherical coordinates $(r,theta,phi)$, the magnetic field and plasma velocity are taken to be of the form: ${bf B}={bf f}(theta)/r^n$ and ${bf v}={bf g}(theta)/r^m$, with corresponding expressions for the scalar variables like pressure and density. Solutions are obtained for potential, force-free, and non-force-free magnetic configurations. Potential-field solutions can be found for all values of~$n$. Non-potential force-free solutions possess an azimuthal component $B_phi$ and exist only for $nge2$; the resulting structures are twisted and have closed field lines but are not collimated around the system axis. In the non-force free case, including gas pressure, the magnetic field lines acquire an additional curvature to compensate for an outward pointing pressure gradient force. We have also considered a pure rotation situation with no gravity, in the zero-$beta$ limit: the solution has cylindrical geometry and twisted magnetic field lines. The latter solutions can be helpful in producing a collimated magnetic field structure; but they exist only when $n<0$ and $m<0$: for applications they must be matched to an external system at a finite distance from the origin.
Extragalactic jets are visualized as dynamic erruptive events modelled by time-dependent magnetohydrodynamic (MHD) equations. The jet structure comes through the temporally self-similar solutions in two-dimensional axisymmetric spherical geometry. Th
We examine the propagation of several CMEs with well-observed flux rope signatures in the field of view of the SECCHI coronagraphs aboard the STEREO satellites using the GCS fitting method of Thernisien, Vourlidas & Howard (2009). We find that the ma
In order to understand the flare trigger mechanism, we conducted three-dimensional magnetohydrodynamic simulations using a coronal magnetic field model derived from data observed by the Hinode satellite. Several types of magnetic bipoles were imposed
We derive a self-similar description for the 2D streamline topology and flow structure of an axi-symmetric, thermally driven wind originating from a disc in which the density is a power law function of radius. Our scale-free solution is strictly only
Characterized by cyclic axisymmetric perturbations to both the magnetic and fluid parameters, magnetohydrodynamic fast sausage modes (FSMs) have proven useful for solar coronal seismology given their strong dispersion. This review starts by summarizi