The Vlasov Equation 1

History and General Properties

The Vlasov Equation 1

Pierre Bertrand, University of Lorraine, France
Daniele Del Sarto, University of Lorraine, France
Alain Ghizzo, University of Lorraine, France

ISBN : 9781786302618

Publication Date : September 2019

Hardcover 316 pp

155.00 USD



The Vlasov equation is the master equation which provides a statistical description for the collective behavior of large numbers of charged particles in mutual, long-range interaction. In other words, a low collision (or “Vlasov”) plasma. Plasma physics is itself a relatively young discipline, whose “birth” can be ascribed to the 1920s. The origin of the Vlasov model, however, is even more recent, dating back to the late 1940s. This “young age” is due to the rare occurrence of Vlasov plasma on Earth, despite the fact it characterizes most of the visible matter in the universe.

This book – addressed to students, young researchers and to whoever wants a good understanding of Vlasov plasmas – discusses this model with a pedagogical presentation, focusing on the general properties and historical development of the applications of the Vlasov equation. The milestone developments discussed in the first two chapters serve as an introduction to more recent works (characterization of wave propagation and nonlinear properties of the electrostatic limit).


1. Introduction to a Universal Model: the Vlasov Equation.
2. A Paradigm for a Collective Description of a Plasma: the 1D Vlasov–Poisson Equations.
3. Electromagnetic Fields in Vlasov Plasmas: General Approach to Small Amplitude Perturbations.
4. Electromagnetic Fields in Vlasov Plasmas: Characterization of Linear Modes.
5. Nonlinear Properties of Electrostatic Vlasov Plasmas.

About the authors

Pierre Bertrand is Emeritus Professor at the University of Lorraine, France. He has been working for more than 50 years in various fields of theoretical physics, and numerical simulation involving plasma physics, quantum mechanics, signal theory and fluid mechanics.

Daniele Del Sarto is Associate Professor at the Jean Lamour Institute, University of Lorraine, France. Her main research field is fundamental physics of warm plasmas, with applications to astrophysics, magnetic confinement fusion and laser-plasma interactions.

Alain Ghizzo is Professor at the Jean Lamour Institute, University of Lorraine, France. He is active in plasma Vlasov modeling, high performance computing, laser-plasma interactions and gyrokinetic modeling.

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