Related papers: Integrability, Normal Forms, and Magnetic Axis Coo…
We explore the existence of quasisymmetric magnetic fields in asymmetric toroidal domains. These vector fields can be identified with a class of magnetohydrodynamic equilibria in the presence of pressure anisotropy. First, using Clebsch…
Although the nuclear fusion process has received a great deal of attention in recent years, the amount of mathematical analysis that supports the stability of the system seems to be relatively insufficient. This paper deals with the…
Non-symmetric vacuum magnetic fields with closed magnetic field lines are of interest in the construction of stellarator equilibria. Beyond the result of D.Lortz (ZAMP \textbf{21}, 196 (1970)), few results are available. This work presents…
We study the free boundary problem for a plasma-vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, to better…
We consider the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region the flow is governed by the usual compressible MHD equations, while in the vacuum region we…
We investigate the role of magnetic fields in the fragmentation of self-gravitating discs using 3D global ideal magnetohydrodynamic simulations performed with the "phantom" smoothed particle hydrodynamics code. For initially toroidal…
We present a novel method for numerically finding quasi-isodynamic stellarator magnetic fields with excellent fast-particle confinement and extremely small neoclassical transport. The method works particularly well in configurations with…
It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux…
In this paper we study some aspects of integrable magnetic systems on the two-torus. On the one hand, we construct the first non-trivial examples with the property that all magnetic geodesics with unit speed are closed. On the other hand,…
Magnetic helicity is an invariant of ideal magnetohydrodynamics (MHD) that encodes information on the topology of magnetic field lines. It has long been appreciated that magnetic topology is an important constraint for the evolution of…
We prove the incompressible limit of compressible ideal magnetohydrodynamic(MHD) flows in a reference domain where the magnetic field is tangential to the boundary. Unlike the case of transversal magnetic fields, the linearized problem of…
The properties of two local reference frames based on the magnetic field and the current density are investigated for magnetized plasmas in toroidal geometry with symmetric angle. The magnetic field-based local frame of reference has been…
We make some remarks on reconnection in plasmas and want to present some calculations related to the problem of finding velocity fields which conserve magnetic flux or at least magnetic field lines. Hereby we start from views and…
Newly emerging magnetic flux can show a complicated linked or interwoven topology of the magnetic field. The complexity of this linkage or knottedness of magnetic flux is related to the free energy stored in the magnetic field. Magnetic…
The importance of accounting for the inhomogeneity of the magnetic field distribution and roundness of domain walls near the surface of type-I superconductors in the intermediate state for forming the equilibrium flux structure was…
Axisymmetric equilibria with incompressible flows of arbitrary direction are studied in the framework of magnetohydrodynamics under a variety of physically relevant side conditions. To this end a set of pertinent non-linear ODEs are…
We investigate the general plasma-vacuum interface problems for the ideal incompressible MHD equations with or without surface tension and prove their nonlinear local well-posedness in standard Sobolev spaces under either non-zero surface…
The Schrodinger equation for an electron on the surface of an elliptical torus in the presence of a constant azimuthally symmetric magnetic field is developed. The single particle spectrum and eigenfunctions as a function of magnetic flux…
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…