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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…
Controlling instability in plasma is one of the central challenges in fusion energy research. Among the various sources of instability, kinetic effects play a significant role. In this work, we aim to suppress the instability induced by…
The Vlasov-Poisson system describes the time evolution of a plasma in the so-called collisionless regime. The investigation of a high-temperature plasma that is influenced by an exterior magnetic field is one of the most significant aspects…
Magnetic fusion aims to confine high-temperature plasma within a device, enabling the fusion of deuterium and tritium nuclei to release energy. Due to the very large temperatures involved, it is essential to isolate the plasma from the…
We consider the stabilization of Vlasov--Poisson plasma dynamics, a central control problem in nuclear fusion. Our focus is the gap between what an ideal controller would use and what experiments can actually observe: while optimal policy…
The aim of various technical applications (for example fusion research) is to control a plasma by magnetic fields in a desired fashion. In our model the plasma is described by the Vlasov-Poisson system that is equipped with an external…
Plasma instabilities are a major concern in plasma science, for applications ranging from particle accelerators to nuclear fusion reactors. In this work, we consider the possibility of controlling such instabilities by adding an external…
We consider the Vlasov-Poisson system that is equipped with an external magnetic field to describe the time evolution of the distribution function of a plasma. An optimal control problem where the external magnetic field is the control…
We address the existence of stationary solutions of the Vlasov-Poisson system on a domain $\Omega\subset\mathbb{R}^3$ describing a high-temperature plasma which due to the influence of an external magnetic field is spatially confined to a…
Stabilizing plasma dynamics through externally applied electric and magnetic fields is a fundamental control problem. We study this question for a plasma evolving under a uniform external magnetic field. Although the governing dynamics are…
The paper presents a review of dynamic stabilization mechanisms for plasma instabilities. One of the dynamic stabilization mechanisms for plasma instability was proposed in the papers [Phys. Plasmas 19, 024503(2012) and references therein],…
This work explores a novel approach to mitigating turbulence in fusion plasmas through spatially modulated plasma profiles. By imposing a harmonic modulation on plasma parameters, we introduce conditions that alter the propagation…
We study the possibility of controlling kinetic plasma instabilities by using lasers to apply external electromagnetic fields. We derive the dispersion relation for the corresponding mathematical description, a reduced Vlasov--Maxwell…
The time evolution of a collisionless plasma is modeled by the relativistic Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We consider the case that the plasma…
The principle behind magnetic fusion is to confine high temperature plasma inside a device in such a way that the nuclei of deuterium and tritium joining together can release energy. The high temperatures generated needs the plasma to be…
We consider the three dimensional Vlasov-Poisson system that is equipped with an external magnetic field to describe a plasma. The aim of various concrete applications is to control a plasma in a desired fashion. This can be modeled by an…
To meet the demands of instantaneous control of instabilities over long time horizons in plasma fusion, we design a dynamic feedback control strategy for the Vlasov-Poisson system by constructing an operator that maps state perturbations to…
A new optimization framework to design steady equilibrium solutions of the Vlasov-Poisson system by means of external electric fields is presented. This optimization framework requires the minimization of an ensemble functional with…
The time evolution of a two-component collisionless plasma is modeled by the Vlasov-Poisson system. In this work, the setting is two and one-half dimensional, that is, the distribution functions of the particles species are independent of…
Full self-consistent stationary Vlasov-Maxwell solutions of magnetically confined plasmas are built for systems with cylindrical symmetries. The stationary solutions are thermodynamic equilibrium solutions. These are obtained by computing…