Related papers: Control strategies for magnetized plasma: a polar …
Modern Tokamaks have evolved from the initial axisymmetric circular plasma shape to an elongated axisymmetric plasma shape that improves the energy confinement time and the triple product, which is a generally used figure of merit for the…
Stellarators confine fusion plasmas using three-dimensional magnetic fields composed of nested toroidal magnetic surfaces. In generic stellarators, trapped particles can drift across these surfaces and degrade plasma confinement. Certain…
We analyze an axisymmetric equilibrium of a plasma endowed with toroidal and poloidal velocity fields, with the aim to characterize the influence of the global motion on the morphology of the magnetic confinement. We construct our…
In this work, a Model Predictive Controller (MPC) is proposed to control the plasma shape in the Tokamak \`a Configuration Variable (TCV). The proposed controller relies on models obtained by coupling linearized plasma response models,…
Nowadays, divertors are used in the main tokamaks to control the magnetic field and to improve the plasma confinement. In this article, we present analytical symplectic maps describing Poincar\'e maps of the magnetic field lines in confined…
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…
The subject matter of this paper concerns the magnetic confinement of plasma. We investigate the long time behavior of the Vlasov-Maxwell-Fokker-Planck system under the effect of a strong external magnetic field. We first formally derive an…
Goal of this paper is to investigate several numerical schemes for the resolution of two anisotropic Vlasov equations. These two toy-models arise from a kinetic description of a tokamak plasma confined by strong magnetic fields. The…
The magnetic field that supports tokamak and stellarator plasmas must be produced by coils well separated from the plasma. However the larger the separation, the more difficult it is to produce a given magnetic field in the plasma region,…
The use of an external transverse magnetic field to trigger and to control electron self-injection in laser- and particle-beam driven wakefield accelerators is examined analytically and through full-scale particle-in-cell simulations. A…
A common optimization problem in the areas of magnetized plasmas and fusion energy is the design of magnets to produce a given three-dimensional magnetic field distribution to high precision. When designing arrays of permanent magnets for…
Starting from a simple marginally stable model considered for Lyapunov based boundary control of flexible mechanical systems, we add a term driving an instability and prove that for an appropriate control condition the system can become…
In this work, we are interested in the controllability of Vlasov-Poisson systems in the presence of an external force field (namely a bounded force field or a magnetic field), by means of a local interior control. We are able to extend the…
We construct fully three-dimensional (3D) equilibria with pressure anisotropy and closed, nested toroidal magnetic surfaces that are strongly asymmetric in the toroidal direction by applying a sinusoidal perturbation to the axisymmetric…
We develop protocols to confine charged particles using time-varying magnetic fields and demonstrate the possible non-torus configuration resulting from the distribution of single-particle motion orbits. A two-step strategy is proposed to…
The time evolution of a collisionless plasma is modeled by the Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We only consider a 'two-dimensional' version of…
We conjecture that for a plasma in a spatial domain with a boundary, the specular reflection effect of the boundary can be approximated by a large magnetic confinement field in the near-boundary region. In this paper, we verify this…
We propose and analyze a class of particle methods for the Vlasov equation with a strong external magnetic field in a torus configuration. In this regime, the time step can be subject to stability constraints related to the smallness of…
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 $w=\lambda e^{i\alpha}$…
Achieving controlled burning plasma in tokamaks requires precise regulation of external particle and energy sources to reach and maintain target core densities and temperatures. This work presents an inverse modeling approach using a…