Related papers: New axisymmetric equilibria with flow from an expa…
Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for…
We discuss a new family of solutions of the Grad--Shafranov (GS) equation that describe D-shaped toroidal plasma equilibria with sharp gradients at the plasma edge. These solutions have been derived by exploiting the continuous Lie symmetry…
To effectively describe the plasma with strong magnetic field, the force-free electrodynamics was introduced, within which the Grad-Shafranov equation plays the key role. The Grad-Shafranov equation governs the global structure of a…
In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation known as the Grad-Shafranov equation, the solution of which determines the poloidal…
The plasma edge of a tokamak configuration is characterized by turbulent dynamics leading to enhanced transport. We construct a simplified 3D Hasegawa--Wakatani model reducing to a single partial differential equation for the turbulent…
The structure of poloidal and toroidal flows of trace impurities in the edge pedestal of tokamak plasmas is studied analytically and numerically. Parallel momentum balance is analysed upon retaining the following terms: poloidal and…
Exact solutions of the equation governing the equilibrium magetohydrodynamic states of an axisymmetric plasma with incompressible flows of arbitrary direction [H. Tasso and G.N.Throumoulopoulos, Phys. Pasmas {\bf 5}, 2378 (1998)] are…
Exact Solov'ev equilibria for arbitrary plasma cross-sections are calculated using a constrained least-squares method. The boundary, with or without $X$-points, can be specified with an arbitrarily large number of constraints to ensure an…
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…
A free-boundary Tokamak Equilibrium Solver (TES), developed for advanced study of tokamak equilibra, is described with two distinctive features. One is a generalized method to resolve the intrinsic axisymmetric instability, which is…
We derive exact solutions of a linear form of the Grad-Shafranov (GS) equation, including incompressible equilibrium flow, using ansatz-based similarity reduction methods. The linearity of the equilibrium equation allows linear combinations…
Equilibrium equations for magnetically confined, axisymmetric plasmas are derived by means of the energy-Casimir variational principle in the context of Hall magnetohydrodynamics (MHD). This approach stems from the noncanonical Hamiltonian…
A new important relation between fluid mechanics and differential geometry is established. We study smooth steady solutions to the Euler equations with the additional property: the velocity vector is orthogonal to the gradient of the…
The coupled system of the spherically symmetric Einstein--Maxwell differential equations is solved under two different source conditions: non-zero electric charge and pressure anisotropy. Expressions for the metric functions, and pressures…
(Abridged) We develop a theoretical framework to construct axisymmetric magnetic equilibria in stars, consisting of both poloidal and toroidal magnetic field components. In a stationary axisymmetric configuration, the poloidal current is a…
An analysis of axisymmetric equilibria with arbitrary incompressible flow and finite resistivity is presented. It is shown that with large aspect ratio approximation or vanishing poloidal current, a uniform conductivity profile is…
In this brief review, the historical aspects of the generalization of the Grad--Shafranov equation to the case of anisotropic plasma are discussed.
A largely unsolved theoretical issue in controlled fusion research is the consistent \textit{kinetic} treatment of slowly-time varying plasma states occurring in collisionless and magnetized axisymmetric plasmas. The phenomenology may…
Dynamic plasma equilibrium systems, both in isotropic and anisotropic framework, possess infinite-dimensional Lie groups of point symmetries, which depend on solution topology and lead to construction of infinite families of new physical…
We present a series of analytically solvable axisymmetric flows on the torus geometry. For the single-component flows, we describe the propagation of sound waves for perfect fluids, as well as the viscous damping of shear and longitudinal…