摘要:

Intended as an introduction to the theory of transverse beam dynamics in circular accelerators, this contribution to the 1985 US Accelerator School deals mainly with linear theory. After establishing the physical concept of alternating gradient focusing for those new to the field, the classical matrix theory and betatron functions are derived from a Hamiltonian. Imperfections which cause closed orbit distortion are examined and the effect of momentum defect described in terms of dispersion and chromaticity. The theory of gradient errors is extended to point the way to more mathematical treatments of non‐linear effects in other contributions to the School.

ISSN:0094-243X    

DOI:10.1063/1.36370

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The formalism behind the motion of particles in circular accelerators storage rings is detailed in this review. Particular attention is given to the theoretical description of the dynamics of longitudinal motion of particle beams. (AIP)

ISSN:0094-243X    

DOI:10.1063/1.36355

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Two areas of accelerator physics are discussed in which computer programs have been used with much success: (i) single‐particle beam dynamics in circular machines, i.e. the design and matching of machine lattices, and tracking of particles through these lattices; much emphasis is put on the standardization of the machine description and the modular structure of the beam dynamics programs; (ii) computation of electromagnetic fields in RF cavities and similar objects, useful for the design of RF cavities and for the calculation of wakefields needed for stability calculations of intense beams.

ISSN:0094-243X    

DOI:10.1063/1.36373

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

This article is a compilation of some considerations encountered in the design of storage ring colliders. It consists of two chapters. The first chapter describes an approach to the collider design from a particular point of view at an elementary level. The second chapter discusses a few semi‐empirical scaling properties in the collider parameters.

ISSN:0094-243X    

DOI:10.1063/1.36363

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

This report is based on a series of two lectures on Charged Particle Optics presented by the first author at the SLAC Accelerator Physics Summer School in July 1985 and on presentations made by both authors at the Second International Conference on Charged Particle Optics in Albuquerque, New Mexico, May 19–23, 1986.

ISSN:0094-243X    

DOI:10.1063/1.36364

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The theory of single particle dynamics in circular accelerators is developed in this presentation. The Hamiltonian formulation of a relativistic particle in an electromagnetic field is used. (AIP)

ISSN:0094-243X    

DOI:10.1063/1.36365

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

We derive a Hamiltonian describing transverse particle motion in a storage ring. After a transformation to ‘‘action‐angle’’ variables we show how to apply Green’s function techniques to do Lie transform perturbation theory on this Hamiltonian. Two examples are worked out to second order; (1) normal and skew quadrupole field errors and (2) normal sextupoles. A brief discussion of the single resonance term Hamiltonian includes derivations of the two invariants and calculation of the resonance width for one degree of freedom systems. Finally, we generalize Courant’s treatment of modulational diffusion as an illustrative application of Chirikov’s criterion to a multi‐resonance problem.

ISSN:0094-243X    

DOI:10.1063/1.36366

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Nonlinear fields are so important in modern accelerators or storage rings that they have to be included in the basic lattice design for both chromaticity correction and aperture determination. The power of prediction of a nonlinear theory is not yet firm enough and numerical simulations are necessary. These lectures deal with the principles of particle tracking, the equations of the betatron motion and the envelope distortions and tune shifts induced by multipole fields. The theory is applied to the correction of beam envelope distortions produced by chromaticity sextupoles in a large acceptance machine, the Antiproton Collector.

ISSN:0094-243X    

DOI:10.1063/1.36367

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Space charge effects are due to the electromagnetic fields of the charged particles in a particle beam. The motion of a particle in the accelerator may be modified by the field of neighbor particles in the beam (if the fields are strong enough). Within this article space charge is formally defined and effects related to it, particularly, tune shifts and resonances, are discussed. (AIP)

ISSN:0094-243X    

DOI:10.1063/1.36368

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

It is the author’s hope that this document will help provide the novice with both an understanding of what dynamic aperture is and some insight as to why it is limited. In addition, we hope that this paper will provide information as to the analytical and numerical methods available for the study of dynamic aperture. Finally, we wish to present some interpretations and applications of these concepts and tools by means of examples. Those factors having an impact on the dynamic aperture of circular machines and storage rings will be discussed; applications to two types of machine of current popular interest (namely, large hadron colliders and synchrotron radiation electron storage rings) will be made in order to illustrate the ideas that are presented.

ISSN:0094-243X    

DOI:10.1063/1.36369

出版商:AIP    

年代:1987

数据来源: AIP