The relationship between symmetry fields and first integrals of divergence-free vector is explored in three dimensions light its relevance to plasma physics magnetic confinement fusion. A Noether-type theorem known: for each such symmetry, there corresponds a integral. extent which the converse true investigated. In doing so, reformulation this found holds on what called toroidal region. Some c...

the vertex arboricity $rho(g)$ of a graph $g$ is the minimum number of subsets into which the vertex set $v(g)$ can be partitioned so that each subset induces an acyclic graph‎. ‎a graph $g$ is called list vertex $k$-arborable if for any set $l(v)$ of cardinality at least $k$ at each vertex $v$ of $g$‎, ‎one can choose a color for each $v$ from its list $l(v)$ so that the subgraph induced by ev...

The usual method of separation of variables to find a basis of solutions of Laplace’s equation in toroidal coordinates is particularly appropriate for axially symmetric applications; for example, to find the potential outside a charged conducting torus. An alternative procedure is presented here that is more appropriate where the boundary conditions are independent of the spherical coordinate y...

The effect of ergodisation (either by additional coils like in TEXTOR-DED or by intrinsic plasma effects like in W7-X) defines the need for transport models being able to describe this properly. A prerequisite for this is the concept of local magnetic coordinates allowing a correct discretization with minimized numerical errors [1]. For these coordinates the full respective metric tensor has to...

We present a finite element analogue to the second-order, finite difference scheme for the solution of the heat diffusion equation in strongly magnetised plasmas given in Günter et al. [S. Günter et al., J. Comp. Phys. 209 (2005) 354]. Compared to standard finite element or finite difference formulations it strongly reduces the pollution of perpendicular heat fluxes by parallel ones even withou...

The use of radio frequency (RF) waves to generate plasma current and to modify the current profile in magnetically confined fusion devices is well documented. The current is generated by the interaction of electrons with an appropriately tailored spectrum of externally launched RF waves. In theoretical and computational studies, the interaction of RF waves with electrons is represented by a qua...

Particle transport in thermonuclear plasmas depends basically on the number of directions of symmetry in the plasma configuration. The search for toroidal confinement devices alternative to the tokamak has led to systems like the stellarator, heliac, etc., all with less symmetry and consequently enhanced diffusion, especially at low collisionality regimes. Even for the tokamak, asymmetry effect...

In this work we investigate the finite-size effects on phase structure of a two-flavor four-fermion interaction model with flavor-mixing four-body and in presence magnetic background, taking into account different boundary conditions. We employ mean-field approximation Schwinger's proper-time method toroidal topology antiperiodic periodic The chiral susceptibility constituent quark masses are s...

Abstract Hopfions are three-dimensional (3D) topological states discovered in field theory, magnetics, and hydrodynamics that resemble particle-like objects physical space. inherit the features of Hopf fibration, a homotopic mapping from unit sphere 4D space to 3D Here we design demonstrate dynamic scalar optical hopfions shape toroidal vortex expressed as an approximate solution Maxwell’s equa...