Related papers: A Grad-Shafranov model for compact quasisymmetric …
Accurate and rapid simulation of the free boundary tokamak plasma equilibrium evolution is essential for modern plasma control, stability analysis, and scenario development. This paper presents the Free-Boundary Grad-Shafranov Evolutive…
A necessary and sufficient set of conditions for a quasisymmetric magnetic field in the form of constraint equations is derived from first principles. Without any assumption regarding the magnetohydrodynamic (MHD) equilibrium of the plasma,…
In this work we present a robust and accurate arbitrary order solver for the fixed-boundary plasma equilibria in toroidally axisymmetric geometries. To achieve this we apply the mimetic spectral element formulation presented in [56] to the…
A method is proposed to solve the Grad-Shafranov partial differential equation for the poloidal flux function associated with the equilibrium of a plasma magnetically confined in an axisymmetric torus under the assumption that the sources…
A method is given to rapidly compute quasisymmetric stellarator magnetic fields for plasma confinement, without the need to call a three-dimensional magnetohydrodynamic equilibrium code inside an optimization iteration. The method is based…
The standard Grad-Shafranov equation for axisymmetric toroidal plasma equilibrium is customary expressed in cylindrical coordinates with toroidal contours, and through which benchmark equilibria are solved. An alternative approach to cast…
In this paper, we present a semi-implicit numerical solver for a first order hyperbolic formulation of two-phase flow with surface tension and viscosity. The numerical method addresses several complexities presented by the PDE system in…
We propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modelling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved…
We present several numerical solutions to a generalized Grad-Shafranov equation (GGSE), which governs axisymmetric plasma equilibria with incompressible flows of arbitrary direction, using fully connected, feed-forward, deep neural…
We consider the problem of performing the preliminary "symmetry classification'' of a class of quasi-linear PDE's containing one or more arbitrary functions: we provide an easy condition involving these functions in order that nontrivial…
We present a new fast solver to calculate fixed-boundary plasma equilibria in toroidally axisymmetric geometries. By combining conformal mapping with Fourier and integral equation methods on the unit disk, we show that high-order accuracy…
The goal of this presentation is in paying attention to the 1D cylindrical version of the Grad-Shafranov (GS) equation. In our opinion, this approach is more rich than classical self-similar ones, and more suitable for astrophysical jets we…
A method is demonstrated to rapidly calculate the shapes and properties of quasi-axisymmetric and quasi-helically symmetric stellarators. In this approach, optimization is applied to the equations of magnetohydrodynamic equilibrium and…
Recent results will be presented on steady states of magnetically confined plasmas obtained by conventional and Hamiltonian methods. The presentation consists of three parts. The first one concerns the derivation of a generalized…
A new class of soliton-like solutions is derived for the Grad-Shafranov (GS) equations. A mathematical analogy between the GS equation for MHD equilibria and the cubic Schr\"odinger (CS) equation for non-linear wave propagation forms the…
This work considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…
Recent developments in the design of magnetic confinement fusion devices have allowed the construction of exceptionally optimized stellarator configurations. The near-axis expansion in particular has proven to enable the construction of…
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…
We consider surface quasi-geostrophic equation with dispersive forcing and critical dissipation. We prove global existence of smooth solutions given sufficiently smooth initial data. This is done using a maximum principle for the solutions…
Context: Calculating stellar pulsations requires a sufficient accuracy to match the quality of the observations. Many current pulsation codes apply a second order finite-difference scheme, combined with Richardson extrapolation to reach…