Related papers: Toroidal equilibria in spherical coordinates
We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibrium whose distribution function decreases monotonically…
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 kinetic motion of the stars of a galaxy is considered within the framework of a relativistic scalar theory of gravitation. This model, even though unphysical, may represent a good laboratory where to study in a rigorous, mathematical…
A fully geometrical treatment of general relativistic magnetohydrodynamics (GRMHD) is developed under the hypotheses of perfect conductivity, stationarity and axisymmetry. The spacetime is not assumed to be circular, which allows for…
We explore gravitating relativistic spheres composed of an anisotropic, barotropic uid. We assume a bi-polytropic equation of state which has a linear and a power-law terms. The generalized Tolman-Oppenheimer-Volkoff (TOV) equation which…
It is shown that the magnetohydrodynamic equilibrium states of an axisymmetric toroidal plasma with finite resistivity and flows parallel to the magnetic field are governed by a second-order partial differential equation for the poloidal…
We construct spherically symmetric solutions to the Einstein-Euler equations, which give models of gaseous stars in the framework of the general theory of relativity. We assume a realistic barotropic equation of state. Equilibria of the…
We provide all basic equations and concepts required to carry out a general study on axially symmetric static sources. The Einstein equations and the conservation equations are written down for a general anisotropic static fluid endowed…
A method is presented for the evaluation of integrals on tetrahedra where the integrand has an integrable singularity at one vertex. The approach uses a transformation to spherical polar coordinates which explicitly eliminates the…
In the above entitled recent publication by Giovanni Lapenta [Phys. Rev. Lett. Vol 90, 135005 (2003) ] it is claimed construction of a new class of solitonlike solutions for the Grad-Shafranov equation in plane geometry. It is proved here…
A microscopic theory of linear response based on the Vlasov equation is extended to systems having spheroidal equilibrium shape. The solution of the linearized Vlasov equation, which gives a semiclassical version of the random phase…
Relativistic, spherically symmetric configurations consisting of a gravitating magnetized anisotropic fluid are studied. For such configurations, we obtain static equilibrium solutions with an axisymmetric, poloidal magnetic field produced…
A general analytic spherically symmetric solution of the Bogomol'nyi equations is found. It depends on two constants and one arbitrary function on radius and contains the Bogomol'nyi-Prasad-Sommerfield and Singleton solutions as particular…
The series solution to Laplace's equation in a helical coordinate system is derived and refined using symmetry and chirality arguments. These functions and their more commonplace counterparts are used to model solenoidal magnetic fields via…
Gravitational theories generated from Lagrangians of the form f(R) are considered. The spherically symmetric solutions to these equations are discussed, paying particular attention to features that differ from the standard Schwarzschild…
CheasePy is code written in Python to run the CHEASE (Cubic Hermite Element Axisymmetric Static Equilibrium) code, which solves the Grad-Shafranov equation for toroidal MHD equilibria using pressure and current profiles and fixed plasma…
The problem posed by the possible existence/non-existence of spatially non-symmetric kinetic equilibria has remained unsolved in plasma theory. For collisionless magnetized plasmas this involves the construction of stationary solutions of…
Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal MHD equilibrium and stability of…
This article reports the spherical coordinate form of three-dimensional generalized dynamics of soft-matter quasicrystals with 12-fold symmetry which provides a basis for solving initial-boundary value problems of the equations under some…
Starting from a general transformation for spherically symmetric metrics where g\_11=-1/g\_00, we analyze coordinates with the common property of conformal flatness at constant solid angle element. Three general possibilities arise: one…