No abstract

No abstract

The Vlasov-Maxwell equations are used to investigate the nonlinear evolution of an intense sheet beam with distribution function f b ͑x, x 0 , s͒ propagating through a periodic focusing lattice k x ͑s 1 S͒ k x ͑s͒, where S const is the lattice period. The analysis considers the special class of distribution functions with uniform phase-space density f b ͑x, x 0 , s͒ A const inside of the simply connected boundary curves, x 0 1 ͑x, s͒ and x 0 2 ͑x, s͒, in the two-dimensional phase space ͑x, x 0 ͒. Coupled nonlinear equations are derived describing the self-consistent evolution of the boundary curves, x 2 . The resulting model is shown to be exactly equivalent to a (truncated) warm-fluid description with zero heat flow and triple-adiabatic equation of state with scalar pressure P b ͑x, s͒ const͓n b ͑x, s͔͒ 3 . Such a fluid model is amenable to direct analysis by transforming to Lagrangian variables following the motion of a fluid element. Specific examples of periodically focused beam equilibria are presented, ranging from a finite-emittance beam in which the boundary curves in phase space ͑x, x 0 ͒ correspond to a pulsating parallelogram, to a cold beam in which the number density of beam particles, n b ͑x, s͒, exhibits large-amplitude periodic oscillations. For the case of a sheet beam with uniform phase-space density, the present analysis clearly demonstrates the existence of periodically focused beam equilibria without the undesirable feature of an inverted population in phase space that is characteristic of the Kapchinskij-Vladimirskij beam distribution.

A highly accurate self-consistent particle code to simulate the beam-beam collision in e 1 e 2 storage rings has been developed. It adopts a method of solving the Poisson equation with an open boundary. The method consists of two steps: assigning the potential on a finite boundary using Green's function and then solving the potential inside the boundary with a fast Poisson solver. Since the solution of Poisson's equation is unique, our solution is exactly the same as the one obtained by simply using Green's function. The method allows us to select a much smaller region of mesh and therefore increase the resolution of the solver. The better resolution makes more accurate the calculation of the dynamics in the core of the beams. The luminosity simulated with this method agrees quantitatively with the measurement for the PEP-II B Factory ring in the linear and nonlinear beam current regimes, demonstrating its predictive capability in detail.

A Hamiltonian approach to the solution of the Vlasov-Poisson equations has been developed. Based on a nonlinear canonical transformation, the rapidly oscillating terms in the original Hamiltonian are transformed away, yielding a new Hamiltonian that contains slowly varying terms only. The formalism has been applied to the dynamics of an intense beam propagating through a periodic focusing lattice, and to the coherent beam-beam interaction. A stationary solution to the transformed Vlasov equation has been obtained.

EMMA -the Electron Model of Many Applicationsis to be built at the STFC Daresbury Laboratory in the UK and will be the first non-scaling FFAG ever constructed. EMMA will be used to demonstrate the principle of this type of accelerator and study its features in detail. The design of the machine and its hardware components are now far advanced and construction is due for completion in Autumn 2009.

We study the evolution of a two component fluid consisting of "blue" and "red" particles which interact via strong short range (hard core) and weak long range pair potentials. At low temperatures the equilibrium state of the system is one in which there are two coexisting phases. Under suitable choices of space-time scal-ings and system parameters we first obtain (formally) a mesoscopic kinetic Vlasov-Boltzmann equation for the one particle position and velocity distribution functions, appropriate for a description of the phase segregation kinetics in this system. Further scalings then yield Vlasov-Euler and incompressible Vlasov-Navier-Stokes equations. We also obtain, via the usual truncation of the Chapman-Enskog expansion, com-pressible Vlasov-Navier-Stokes equations.

Abstract. The renormalization group (RG) method is applied to the study of discrete dynamical systems. As a particular example, the Hénon map is considered as being applied to describe the transverse betatron oscillations in a cyclic accelerator or storage ring possessing a FODO-cell structure with a single thin sextupole. A powerful RG method is developed that is valid correct to fourth order in the perturbation amplitude, and a technique for resolving the resonance structure of the Hénon map is also presented. This calculation represents an application of the RG method to the study of discrete dynamical systems in a unified manner capable of reducing the dynamics of the system both far from and close to resonances, thus preserving the symplectic symmetry of the original map. Contents