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Les Publications    Toutes les publications    V-Langevin Equations, Continuous Time Random walks and Fractional Diffusion
Radu Balescu

V-Langevin Equations, Continuous Time Random walks and Fractional Diffusion

Textes du quatrième de couverture du mémoire

Until a decade ago, stochastic differential equations describing test particle transport in magnetically confined plasmas, or mapping techniques for magnetic field line transport studies, were not serious competitors to kinetic or fluid solvers especially in the turbulence or chaotic regime.

This is not true anymore. One of the best examples is the mapping technique now at the heart of the description of the stochastic magnetic field structure produced by the dynamic ergodic divertor of the tokamak TEXTOR at Jülich (Germany). The success of the method comprises the understanding of filamentary particle and heat transport from the plasma core to the tokamak edge tiles. In almost the same way stochastic differential equations, in conjunction with new resolution methods, allows to consider a wide variety of transport regimes, collisional, magnetically dominated, and even bursty behaviour as observed in a turbulent tokamak edge.

The recent works of Prof. R. Balescu, which often rely on simple physically acceptable model equations, like the V-Langevin system of equations, have permitted the use of these methods for applications involving very complex phenomena.

The analysis of strange transport through the V-Langevin equations and its connection to continuous random walks was introduced to us by Prof. R. Balescu during a meeting in Craiova (Romania) in September 2005. The text published here is a revised version dated February 2, 2006 which in Prof. Balescu’s own words “is essentially a working tool for himself and his co-workers, not intended to be published in a (scientific) journal”. We wish, by making this document available to present and “future” co-workers to widespread the exceptional pedagogical talent of a master, as well as to provide the state of the art knowledge in a quickly developing scientific field.

Radu Balescu (1932-2006) was emeritus professor at the Université libre de Bruxelles, he was a member of the Académie royale des Sciences, des Lettres et des Beaux-Arts de Belgique and an honorary member of the Romanian Academy.

Winner of the Théophile De Donder Prize in 1961, of the Francqui Prize in 1970 and of theVan Engel Prize in 1999, he was awarded the Hannes Alfven Prize of the European Society of Physics in 2000.

Honorary doctor of the Universities of Craiova and of Iasi in Romania, he was the Director of the Service statistique, Plasmas et Optique non linéaire of the Université libre de Bruxelles (1988-1997). Head of a group of the Association Euratom-État belge pour la Fusion thermonucléaire contrôlée (1969-1997), he was Guest Professor at the Universities of Austin (Texas), Moscou, Essen, Düsseldorf, Marseille, Craiova and Kyushu (Japan).

His research domains were non equilibrium Statistical Physics and Statistical Physics of plasmas and fusion.

Radu Balescu is the author of the following monographs : Statistical Mechanics of Charged Particles (1963), Equilibrium and non equilibrium Statistical Mechanics (1975), Transport Processes in Plasmas (1988), Statistical Dynamics (1997), Aspects of Anomalous Transport in Plasmas (2005), Ilya Prigogine. Sa vie, son oeuvre (2006). He also wrote 200 articles in scientific reviews.
ÉditeurAcadémie royale de Belgique
Numéro d'édition2051
CollectionMémoires de la Classe des Sciences
Formatin 8°
Nombre de pages85
N° Fiche2457
Radu Balescu, V-Langevin Equations, Continuous Time Random Walks and Fractional Diffusion - format pdf