Related papers: Integrability, Normal Forms, and Magnetic Axis Coo…
In magnetized plasma, the magnetic field confines particles around field lines. The ratio between the intensity of the parallel and perpendicular viscosity or heat conduction may reach the order of $10^{12}$. When the magnetic fields have…
We focus on a dilute uniform suspension of magnetic nanoparticles in a nematic-filled micron-sized shallow well with tangent boundary conditions, as a paradigm system with two coupled order parameters. This system exhibits spontaneous…
Exact solutions to the static equilibrium magnetohydrodynamic equations are presented and discussed for both axially and helically reduced systems. For both symmetries, physical restrictions on the solutions are discussed and it is seen…
The fusion created by magnetically confined plasma is a promising clean and essentially unlimited future energy source. However, net energy generation has not been yet demonstrated in fusion experiments. Some of the main problems hindering…
In magnetically confined plasma, it is possible to qualitatively describe the magnetic field configuration via phase spaces of suitable symplectic maps. These phase spaces are of mixed type, where chaos coexists with regular motion, and the…
While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer 1991a,b; Plunk & Helander 2018), we have obtained the first such solutions using a vacuum surface expansion formalism. We…
Ideal MHD relaxation is the topology-conserving reconfiguration of a magnetic field into a lower energy state where the net force is zero. This is achieved by modeling the plasma as perfectly conducting viscous fluid. It is an important…
Quasi-poloidal (QP) magnetic fields have desirable properties for confining plasma: no radial drift of guiding centres (with positive implications for neoclassical transport), zero Pfirsch-Schl\"uter current, a lower level of damping for…
Magnetic field topology frozen in ideal magnetohydrodynamics (MHD) and its breakage in near ideal MHD are reviewed in two parts. The first part gives a physically complete description of the frozen in field topology, taking magnetic flux…
New high-resolution observations reveal that small-scale magnetic flux concentrations have a delicate substructure on a spatial scale of 0.1''. Its basic structure can be interpreted in terms of a magnetic flux sheet or tube that vertically…
We examine the dynamics of magnetic flux tubes containing non-trivial field line braiding (or linkage), using mathematical and computational modelling, in the context of testable predictions for the laboratory and their significance for…
We construct fully three-dimensional (3D) equilibria with pressure anisotropy and closed, nested toroidal magnetic surfaces that are strongly asymmetric in the toroidal direction by applying a sinusoidal perturbation to the axisymmetric…
The energy production through thermo-nuclear fusion requires the confinement of the plasma into a bounded domain. In most of the cases, such configurations are obtained by using strong magnetic fields. Several models exist for describing…
Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the…
We consider the plasma-vacuum interface problem in a horizontally periodic slab impressed by a uniform non-horizontal magnetic field. The lower plasma region is governed by the incompressible inviscid and resistive MHD, the upper vacuum…
A direct construction of equilibrium magnetic fields with toroidal topology at arbitrary order in the distance from the magnetic axis is carried out, yielding an analytical framework able to explore the landscape of possible magnetic flux…
We construct two classes of magnetohydrostatic (MHS) equilibria for an axisymmetric vertical flux tube spanning from the photosphere to the lower part of the transition region within a realistic stratified solar atmosphere subject to solar…
We construct smooth, non-symmetric plasma equilibria which possess closed, nested flux surfaces and solve the magnetohydrostatic (steady three-dimensional incompressible Euler) equations with a small force. The solutions are also `nearly'…
In three-dimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotational-transform and pressure gradients, as these features together produce unphysical, infinite currents. A proposed set of equilibria…
We prove the existence of a straight-field-line coordinate system we call generalized Boozer coordinates. This coordinate system exists for magnetic fields with nested toroidal flux surfaces} provided $…