Formation of Patterns in Intense Hadron Beams. The Amplitude Equation Approach

We study the longitudinal motion of beam particles under the action of a single resonator wave induced by the beam itself. Based on the method of multiple scales we derive a system of coupled amplitude equations for the slowly varying part of the longitudinal distribution function and for the resonator wave envelope, corresponding to an arbitrary wave number. The equation governing the slow evolution of the voltage envelope is show to be of Ginzburg-Landau type.Comment: LaTeX, 12 page

Nonlinear Longitudinal Waves in High Energy Stored Beams

We solve the Vlasov equation for the longitudinal distribution function and find stationary wave patterns when the distribution in the energy error is Maxwellian. In the long wavelength limit a stability criterion for linear waves has been obtained, and a Korteweg-de Vries-Burgers equation for the relevant hydrodynamic quantities has been derived.Comment: LaTeX, 10 page

Nonlinear Waves and Coherent Structures in Quasi-neutral Plasmas Excited by External Electromagnetic Radiation

Starting from the Vlasov-Maxwell equations describing the dynamics of various species in a quasi-neutral plasma, an exact relativistic hydrodynamic closure for a special type of water-bag distributions satisfying the Vlasov equation has been derived. It has been shown that the set of equations for the macroscopic hydrodynamic variables coupled to the wave equations for the self-consistent electromagnetic field is fully equivalent to the Vlasov-Maxwell system. Based on the method of multiple scales, a system comprising a vector nonlinear Schrodinger equation for the transverse envelopes of the self-consistent plasma wakefield, coupled to a scalar nonlinear Schrodinger equation for the electron current velocity envelope, has been derived. Using the method of formal series of Dubois-Violette, a traveling wave solution of the derived set of coupled nonlinear Schrodinger equations in the case of circular wave polarization has been obtained. This solution is represented as a ratio of two formal Volterra series. The terms of these series can be calculated explicitly to every desired order.Comment: 10 pages, 3 figure

Description of GADEL

This article describes the first implementation of the GADEL system : a Genetic Algorithm for Default Logic. The goal of GADEL is to compute extensions in Reiter's default logic. It accepts every kind of finite propositional default theories and is based on evolutionary principles of Genetic Algorithms. Its first experimental results on certain instances of the problem show that this new approach of the problem can be successful.Comment: System Descriptions and Demonstrations at Nonmonotonic Reasoning Workshop, 2000 6 pages, 2 figures, 5 table