Related papers: Tokamak plasma boundary reconstruction using toroi…
The paper suggests certain regimes of fusion plasma with magnetic confinement, when the Larmor radius $\lambda$ and the angle $\alpha$ (determining the orientation of the local coordinates) form an analytic function $w=\lambda e^{i\alpha}$…
In this paper, we present the analytical and numerical study of the optimization approach for determining the space-dependent source function in the parabolic inverse source problem using partial boundary measurements. The Lagrangian…
Effects of reversed magnetic shear on the plasma rotation stabilization of resistive wall modes in tokamaks are investigated using the AEGIS code. MHD equilibria in toroidal configuration from circular cross-sections to realistic CFETR-like…
The edge density and temperature of tokamak plasmas are strongly correlated with energy and particle confinement and their quantification is fundamental to understanding edge dynamics. These quantities exhibit behaviours ranging from sharp…
Nuclear fusion represents one of the best alternatives for a sustainable source of clean energy. Tokamaks allow to confine fusion plasma with magnetic fields and one of the main challenges in the control of the magnetic configuration is the…
The simulation of turbulence in the boundary region of a tokamak is crucial for understanding and optimizing the performance of fusion reactors. In this work, the use of low-rank linear algebra techniques is shown to enhance the efficiency…
This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…
This paper tackles the data completion problem related to the Helmholtz equation. The goal is to identify unknown boundary conditions on parts of the boundary that cannot be accessed directly, by making use of measurements collected from…
Although the nuclear fusion process has received a great deal of attention in recent years, the amount of mathematical analysis that supports the stability of the system seems to be relatively insufficient. This paper deals with the…
A lumped parameter model for tokamak plasma current and inductance time evolution as function of plasma resistance, non-inductive current drive sources and boundary voltage or poloidal field (PF) coil current drive is presented. The model…
Standard reduced models often fail to adequately describe the complex geometric response of tokamak plasmas to strong toroidal rotation. In this work, we present VEQ-R, a computationally efficient spectral solver designed to calculate…
We consider the problem to reconstruct a wave speed $c \in C^\infty(M)$ in a domain $M \subset \R^n$ from acoustic boundary measurements modelled by the hyperbolic Dirichlet-to-Neumann map $\Lambda$. We introduce a reconstruction formula…
A free-boundary, axisymmetric magnetohydrodynamic (MHD) equilibrium code, pyIPREQ, has been developed for Tokamak plasmas using finite difference and Green's function approach. The code builds upon the foundational frameworks of the PEST…
This overview presents a tutorial introduction to the theory of magnetic plasma confinement in toroidal confinement systems with particular emphasis on axisymmetric equilibrium geometries, and tokamaks. The discussion covers three important…
We propose a new numerical method for the solution of the problem of the reconstruction of the initial condition of a quasilinear parabolic equation from the measurements of both Dirichlet and Neumann data on the boundary of a bounded…
The Grad-Shafranov (GS) equation is a nonlinear elliptic partial differential equation that governs the ideal magnetohydrodynamic equilibrium of a tokamak plasma. Previous studies have demonstrated the existence of multiple solutions to the…
Plasma shape control in tokamaks requires a real-time controller that tracks dynamically changing shape targets while tolerating diagnostic failures. Classical approaches decompose the problem into equilibrium reconstruction followed by a…
Designing superconducting coils for a tokamak fusion device is a highly coupled, non-linear design problem. The coils have many disparate engineering requirements from structural to power electronics, as well strict limits placed on the…
Plasma toroidal metric singularities in helical devices and tokamaks, giving rise to magnetic surfaces inside the plasma devices are investigated in two cases. In the first we consider the case of a rotational plasma on an helical device…
The goal of this paper is to understand from a mathematical point of view the magnetic confinement of plasmas for fusion. Following Fr\'enod and Sonnendr\"ucker \cite{FS2}, we first use two-scale convergence tools to derive a gyrokinetic…