Interaction For Solitary Waves In Coasting Charged Particle Beams

In recent years, the research on the transport properties and applications of charged particle beam has become a hot topic in modern physics. High energy accelerators, trans-port systems, and storage rings have a wide range of applications ranging from basic research in high energy and nuclear physics, to applications such as spallation neutron sources, heavy ion fusion, and nuclear waste transmutation, to mention a few examples. Charged particle beams are subject to various collective processes that can affect the beam quality. Of particular importance at the high beam currents and charge densities of prac-tical interest are the effects of the intense self-fields produced by the beam space charge and current on determining detailed equilibrium, stability, and transport properties. The work is mainly studying on the theory of the coasting charged particle beams system which base on the Vlasov model of the beam with momentum discretization. The model is extended to establish a one-dimensional Vlasov model for the beam current of charged particles in a fully conducting long straight conducting tube. The one-dimensional Vlasov model is used to describe the dynamics evolution the longitudinal density distribution and the electric field distribution in the charged particle beam, and then we derive the theoret-ical description of the solitary wave which is described by the classical Korteweg-deVries equation in the system. Finally, by using the extended Poincare-Lighthill-Kuo perturba-tion method, the collision of solitary waves in a coasting charged particle beams is studied. The results show that the system admits a solution with two solitary waves, which move in opposite directions and can be described by two Korteweg-deVries equation in small-amplitude limit. The collision of two solitary waves is elastic, and after the interaction they preserve their original properties. Then the weak phase shift in travelling direction of collision between two solitary waves is derived explicitly. The main work of this paper is:In the first chapter, the physical background and the related physical knowledge are briefly introduced, including the coasting charged particle beams system and the historical research of the solitary wave.In the second chapter, we introduce the first observation of solitary wave in the beam on the laboratory. Then, we apply the Vlasov Maxwell model to describes the self-consistent nonlinear evolution of the longitudinal distribution function Fb(z,pz,t), the average self-generated axial electric field Ezs (r, z, t), and the line density ?b. We use a one-dimensional kinetic model based on the Vlasov-Maxwell equations to describe nonlinear wave and soliton excitations in coasting charged particle beams. By using the extended Poincare-Lighthill-Kuo perturbation method, the collision of solitarv waves in a coasting charged particle beams is studied. The results show that the system admits a solution with two solitary waves which move in opposite directions and can be described by two Korteweg-deVries equations in small amplitude limit, respectively. The collision of two solitary waves is elastic, and after the interaction they preserved their original properties. Then the weak phase shift in travelling direction of collision between two solitary waves is derived explicitly. Finally, we summarize the main results and give an outlook of the future in this field.