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- D. Fanelli, A. Antoniazzi, S. Ruffo
Università di Firenze, Florence
- J. Barre'
Université de Nice Sophia-Antipolis, Nice
- T. Dauxois
ENS LYON, Lyon
- G. De Ninno
ELETTRA, Basovizza, Trieste
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Long range interactions are such that the two-body interaction potential decreases at large distance with a power which is smaller or equal to the space dimension. Examples include gravitational forces, unshielded Coulombic interaction. In presence of long-range interactions, physics is very peculiar and a wide range of striking phenomena appears. In particular energy is non additive, hence the system under scrutiny cannot be divided into independent macroscopic parts, as it is usually the case for short-range interactions. These unexpected features are systematically detected, independently of the specific nature of the long-range interactions involved. FEL are one of the most interesting examples of systems with long-range interactions, where the interplay between collective (wave) and individual (particles) degrees of freedom is well known to be central and, in this respect, provides a unique experimental ground to investigate such universal pecularities. In this presentation I will review the main characteristics of such systems and dicuss the statistical theory of the Vlasov equation, a wide general approach that enables to analytically investigate the laser saturated regime.
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