Related papers: Multiple solutions to the static forward free-boun…
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…
We consider the free boundary problem for the two-dimensional plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region, the flow is governed by the usual compressible MHD equations, while in the vacuum…
Tokamak fusion reactors are actively studied as a means of realizing energy production from plasma fusion. However, due to the substantial cost and time required to construct fusion reactors and run physical experiments, numerical…
In this paper, we consider an open-loop, finite-time, optimal control problem of attaining a specific desired current profile during the ramp-up phase by finding the best open-loop actuator input trajectories. Average density, total power,…
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…
Given a bounded domain $G \subset \R^d$, $d\geq 3$, we study smooth solutions of a linear parabolic equation with non-constant coefficients in $G$, which at the boundary have to $C^1$-match with some harmonic function in $\R^d \setminus…
We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are…
The simulation of the elastodynamics equations at high-frequency suffers from the well known pollution effect. We present a Petrov--Galerkin multiscale sub-grid correction method that remains pollution free in natural resolution and…
We consider the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region the flow is governed by the usual compressible MHD equations, while in the vacuum region we…
We study the possibility of constructing steady magnetic fields satisfying the force balance equation of ideal magnetohydrodynamics with tangential boundary conditions in asymmetric confinement vessels, i.e. bounded regions that are not…
A unified energy principle approach is presented for analysing the magnetohydrodynamic (MHD) stability of plasmas consisting of multiple ideal and relaxed regions. By choosing an appropriate gauge, we show that the plasma displacement…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
We consider the initial-boundary value problem of a thermodynamically consistent diffuse interface model for incompressible two-phase flows with unmatched densities in a bounded domain $\Omega\subset\mathbb{R}^3$. Our first aim is to study…
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 hybrid Vlasov-Maxwell system of equations is suitable to describe a magnetized plasma at scales of the order of or larger than proton kinetic scales. An exact stationary solution is presented by revisiting previous results with a…
Accurate modeling of core instabilities in tokamak plasmas is essential to understand the underlying physical mechanisms and their impact on plasma confinement. The ideal stability of the internal kink mode and the m = 1 collisionless…
Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equation with diffuse reflection boundaries, where one plate is…
This paper aims to establish the global well-posedness of the free boundary problem for the incompressible viscous resistive magnetohydrodynamic (MHD) equations. Under the framework of Lagrangian coordinates, a unique global solution exists…
Combined plasma-coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria is proposed. Four distinct categories of stellarator optimization, two of which are novel…
Fusion energy offers the potential for the generation of clean, safe, and nearly inexhaustible energy. While notable progress has been made in recent years, significant challenges persist in achieving net energy gain. Improving plasma…