相关论文: Solving the Grad-Shafranov equation using spectral…

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…

One of the most well-established codes for modeling non-linear Magnetohydrodynamics (MHD) for tokamak reactors is JOREK, which solves these equations with a B\'ezier surface based finite element method. This code produces a highly sparse…

We study the dependence of some relevant tokamak equilibrium quantities on the toroidal plasma rotation. The Grad-Shafranov equation generalised to the rotating case is analytically solved employing two different representations for the…

The extended-MHD NIMROD code [C.R. Sovinec and J.R. King, J. Comput. Phys. 229, 5803 (2010)] is verified against the ideal-MHD ELITE code [H.R. Wilson et al. Phys. Plasmas 9, 1277 (2002)] on a diverted tokamak discharge. When the NIMROD…

We identify and study new nonlinear axisymmetric equilibria with incompressible flow of arbitrary direction satisfying a generalized Grad Shafranov equation by extending the symmetry analysis presented in [G. Cicogna and F. Pegoraro, Phys.…

This paper deals with the numerical reconstruction of the plasma current density in a Tokamak and of its equilibrium. The problem consists in the identification of a non-linear source in the 2D Grad-Shafranov equation, which governs the…

We extend previous work [Y. E. Litvinenko, Phys. Plasmas 17, 074502 (2010)] on a direct method for finding similarity reductions of partial differential equations such as the Grad-Shafranov equation, to the case of the generalized…

In toroidally confined plasmas, the Grad-Shafranov equation, in general a non-linear PDE, describes the hydromagnetic equilibrium of the system. This equation becomes linear when the kinetic pressure is proportional to the poloidal magnetic…

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…

In this work, we have revisited the Solov'ev analytical solution for a tokamak equilibrium. We point out that the vacuum solution in the Solov'ev formulation is inapplicable, since a distributed current density is assumed to fill the…

The features of the TRIMEG-GKX code are described with emphasis on the exploration using novel/different schemes compared to other gyrokinetic codes, particularly the use of object-oriented programming, filter/buffer-free treatment, and a…

A new force balance model for the EFIT magnetohydrodynamic equilibrium technique for tokamaks is presented which includes the full toroidal flow and anisotropy changes to the Grad-Shafranov equation. The free functions are poloidal flux…

A new approach to high pressure magnetically-confined plasmas is necessary to design efficient fusion devices. This paper presents an equilibrium combining two solutions of the Grad-Shafranov equation, which describes the…

One of the common tasks required for designing new plasma pulses or shaping scenarios is to design the desired equilibria using an equilibrium (Grad-Shafranov equation) solver. However, standard equilibrium solvers are time-independent and…

We study regularity and numerical methods for two-sided fractional diffusion equations with a lower-order term. We show that the regularity of the solution in weighted Sobolev spaces can be greatly improved compared to that in standard…

Recent development of real-time equilibrium code Equinox [1] using a fixed-point algorithm [2] allow major plasma magnetic parameters to be identified in real-time, using rigorous analytical method. The code relies on the boundary flux code…

The extended-MHD NIMROD code [C.R. Sovinec and J.R. King, J. Comput. Phys. 229, 5803 (2010)] models broadband-MHD activity from a reconstruction of a quiescent H-mode shot on the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)].…

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…

Fast and accurate solutions of the Grad--Shafranov (GS) equation are essential for equilibrium analysis, integrated modeling, and surrogate model construction in magnetic confinement fusion. In this work, we address a fundamental question:…

Calculations of tearing mode stability in tokamaks split conveniently into an external region, where marginally stable ideal MHD is applicable, and a resonant layer around the rational surface where sophisticated kinetic physics is needed.…