Analytical Estimation of the Dynamic Apertures of Circular Accelerators
نویسنده
چکیده
By considering delta function sextupole, octupole, and decapole perturbations and using difference action-angle variable equations, we find some useful analytical formulae for the estimation of the dynamic apertures of circular accelerators due to single sextupole, single octupole, single decapole (single 2m pole in general). Their combined effects are derived based on the Chirikov criterion of the onset of stochastic motions. Comparisons with numerical simulations are made, and the agreement is quite satisfactory. These formulae have been applied to determine the beam-beam limited dynamic aperture in a circular collider.
منابع مشابه
Analytical Estimation of the Beam-Beam Interaction Limited Dynamic Apertures and Lifetimes in e+e− Circular Colliders
Physically speaking, the delta function like beam-beam nonlinear forces at interaction points (IPs) act as a sum of delta function nonlinear multipoles. By applying the general theory established in ref. [1], in this paper we investigate analytically the beam-beam interaction limited dynamic apertures and the corresponding beam lifetimes for both the round and the flat beams. Relations between ...
متن کاملDynamic Analysis of Circular Plates in Contact with Fluid and Resting on Two-Parameter Foundations
The dynamic behaviour of a circular plate in contact with fluid and resting on two-parameter elastic foundations is of interest in the field of geotechnics, structure, highway, railway, oil and gas and mechanical engineering. In this work, the dynamic behaviour of circular plate in contact with fluid and resting on Winkler and Pasternak foundations is investigated. The coupled differential equa...
متن کاملAnalytical Solution for a Two-Layer Transversely Isotropic Half-Space Affected by an Arbitrary Shape Dynamic Surface Load
The dynamic response of a transversely isotropic, linearly elastic layer bonded to the surface of a half-space of a different transversely isotropic material under arbitrary shape surface loads is considered. With the help of displacements and stresses Green’s functions, an analytical formulation is presented for the determination of the displacements and stresses at any point in both surface l...
متن کاملAnalytical and Numerical Investigation of Effective Parameters on Energy Absorption Circular Composite Tube under Internal Pressure and Axial
In this paper the energy absorption capacity of stiffened circular composite tube is considered. The governing equations and dynamic equilibrium are first derived and then solved. Additionally, a finite element model of reinforced circular composite tube structure is modeled. At the following, the effects of various parameters such as structural geometry, number of rings and stingers on mechani...
متن کاملFree Vibration Analysis of Nonlinear Circular Plates Resting on Winkler and Pasternak Foundations
Dynamic behaviour of nonlinear free vibration of circular plate resting on two-parameters foundation is studied. The governing ordinary differential equation is solved analytically using hybrid Laplace Adomian decomposition method. The analytical solutions obtained are verified with existing results in literature. The analytical solutions are used to determine the influence of elastic fou...
متن کامل