Lecture

MHD Stability and Equilibrium

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In course

PHYS-325: Introduction to plasma physics

Introduction à la physique des plasmas destinée à donner une vue globale des propriétés essentielles et uniques d'un plasma et à présenter les approches couramment utilisées pour modéliser son comportement. Application à la fusion thermonucléaire ainsi qu' ...

Description

This lecture introduces the physics of plasmas, focusing on MHD equilibrium and stability. Topics include MHD stability conditions, magnetic surfaces, and the screw-pinch configuration. The lecture explores the analogy between mechanical and MHD stability, emphasizing the importance of energy considerations in determining stability.

Instructors (2)

Stefano Alberti

Teaching & PhD Past EPFL PhD Students Gilles Arnoux, Falk Braunmüller, Jérémy Genoud

Joaquim Loizu Cisquella

Joaquim Loizu graduated in Physics at the École Polytechnique Fédérale de Lausanne, carrying out his Master thesis project at the Center for Bio-Inspired Technology, Imperial College London, on the theoretical and numerical study of the biophysics of light-sensitive neurons. In 2009, he started his PhD studies with Prof. Paolo Ricci at the Swiss Plasma Center, the major plasma and fusion laboratory in Switzerland. His thesis focused on the theory of plasma-wall interactions and their effect on the mean flows and turbulence in magnetized plasmas. He obtained his PhD in December 2013. In 2014, he joined the Max-Planck-Princeton Center for plasma research as a Postdoctoral Research Fellow, spending one year at the Princeton Plasma Physics Laboratory and one year at the Max-Planck-Institute for Plasma Physics in Greifswald, Germany. During this time, he worked on three-dimensional magnetohydrodynamics, studying the formation of singular currents and magnetic islands at rational surfaces. In 2016, he obtained a two-years Eurofusion Postdoctoral Fellowship to carry out research at the Max-Planck-Institute for Plasma Physics in Greifswald, Germany. During this time, he focused on the computation of 3D MHD equilibria in stellarators, including the possibility of magnetic islands and magnetic field-line chaos. In 2018, he joined the Swiss Plasma Center as a Scientist and Lecturer. He is also one of the leaders of the Simons Collaboration on Hidden Symmetries and Fusion Energy. His current research interests include MHD equilibrium and stability, magnetic reconnection, self-organization, non-neutral plasmas, plasma sheaths, and plasma transport in chaotic magnetic fields.

Official source

Related concepts (32)

Magnetohydrodynamics

Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is a model of electrically conducting fluids that treats all interpenetrating particle species together as a single continuous medium. It is primarily concerned with the low-frequency, large-scale, magnetic behavior in plasmas and liquid metals and has applications in numerous fields including geophysics, astrophysics, and engineering. The word magnetohydrodynamics is derived from magneto- meaning magnetic field, hydro- meaning water, and dynamics meaning movement.

Linear map

In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .

Diamagnetism

Diamagnetism is the property of materials that are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted by a magnetic field. Diamagnetism is a quantum mechanical effect that occurs in all materials; when it is the only contribution to the magnetism, the material is called diamagnetic.

Plasma stability

The stability of a plasma is an important consideration in the study of plasma physics. When a system containing a plasma is at equilibrium, it is possible for certain parts of the plasma to be disturbed by small perturbative forces acting on it. The stability of the system determines if the perturbations will grow, oscillate, or be damped out. In many cases, a plasma can be treated as a fluid and its stability analyzed with magnetohydrodynamics (MHD).

Linear independence

In the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be . These concepts are central to the definition of dimension. A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space.

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