摘要:

The paper generalizes a notion of the closed orbit for the case when the accelertor lattice is perturbed by a time‐dependent harmonic dipole field. The problem is motivated by effects of current ripple in a proton accelerator. Our result allows to estimate the amplitude of the beam excursions as a function of the amplitude and the frequency of the perturbation. It predicts that the deviation of the beam increases as the frequency of the ripple approaches the sideband betatron frequency.

ISSN:0094-243X    

DOI:10.1063/1.45113

出版商:AIP    

年代:1992

数据来源: AIP

摘要:

The dynamic aperture of the HERA proton ring is limited by persistent current field errors in the superconducting magnets. Its value as predicted by tracking studies is compared to preliminary aperture measurements in the machine. Since inclusion of tune modulation leads to a significant reduction of the aperture in the simulation, a theory is developed, which quantifies the impact of tune modulation on high‐order resonances. For a typical working point, parameters of resonances up to order 11 are calculated for a model of HERA using differential algebra and normal‐form algorithms. Based on these resonance parameters, estimate values are derived of amplitude‐dependent emittance growth rates caused by the interplay of tune modulation and nonlinear field errors.

ISSN:0094-243X    

DOI:10.1063/1.45114

出版商:AIP    

年代:1992

数据来源: AIP

摘要:

Looking at the simple model structure of a long FODO cell with one sextupole kick, we study the effect of tune modulation in the presence of sextupole nonlinearities.

ISSN:0094-243X    

DOI:10.1063/1.45115

出版商:AIP    

年代:1992

数据来源: AIP

摘要:

The theory of symplectic integrators for the orbital motion in accelerators is fairly well developed. However, the integration of the spin variables, for polarized particle beams, has received much less attention. Two simple examples of second‐order symplectic integrators for the spin are presented, together with simple geometrical interpretations of their effect on the spin motion.

ISSN:0094-243X    

DOI:10.1063/1.45116

出版商:AIP    

年代:1992

数据来源: AIP

摘要:

Normal form methods for solving nonlinear differential equations are reviewed and the comparative merits of three methods are evaluated. The concept of the minimal normal form is explained and is shown to be superior to other choices. The method is then extended to apply to the evaluation of discrete maps of an accelerator or storage ring. Such an extension, as suggested in this paper, is more suited for accelerator‐based applications than a formulation utilizing continuous differential equations. A computer code has been generated to systematically implement various normal form formulations for maps in two‐dimensional phase space. Specific examples of quadratic and cubic nonlinear fields were used and solved by the method developed. The minimal normal form method shown here gives good results using relatively low‐order expansions.

ISSN:0094-243X    

DOI:10.1063/1.45117

出版商:AIP    

年代:1992

数据来源: AIP

摘要:

Based on the perturbation theory with multiple scales, we have developed a new technique to study the evolution of particle distribution as a function of oscillation amplitudes in hadron storage rings. With a renormalization scheme for the zeroth‐order term, a uniformly valid perturbations such as the beam‐beam interaction at colliding points, this renormalization scheme results in a functional mapping for the particle distribution, and the diffusion processes of particles in the beam can be studied numerically without resorting to the tracking of individual particles. A case involving a single nonliner kick in the ring is presented to illustrate the method in detail.

ISSN:0094-243X    

DOI:10.1063/1.45118

出版商:AIP    

年代:1992

数据来源: AIP

摘要:

A simple model of betatronic dynamics is studied in which a modulation in tune is present, in order to describe the noise in a magnet power supply. Analytical and numerical results are presented.

ISSN:0094-243X    

DOI:10.1063/1.45119

出版商:AIP    

年代:1992

数据来源: AIP

摘要:

In this report we try to make estimates of both kinematic and field effects on the stability of a particle motion, by employing a truly Maxwellian representation of the magnetic field in exact equations of motion. For this purpose we adopt a simple FODO cell model, which repeats periodically to infinity. This model includes only quadrupoles and drifts, leaving out the bending magnets to avoid the problem of the trajectory curvature. We think this model is a physically consistent approximation of a storage ring. We derive several models with different levels of approximation and compare them by evaluating the importance of these effects. The relevance to long‐term stability is being investigated in the meantime by comparing the different models with extensive computer simulations. The results will be shown in a subsequent report. (AIP)

ISSN:0094-243X    

DOI:10.1063/1.45121

出版商:AIP    

年代:1992

数据来源: AIP

摘要:

A summary of the requirements for modulational (thick‐layer) diffusion to exist in a particle synchrotron is presented and applied to a simple tune‐modulated collider model of the Fermilab Tevatron where the only nonlinearities present are two beam‐beam kicks. For certain realistic tune modulation parameters and single‐particle base tunes, amplitude growth is observed over timescales appropriate to diffusive models. The character of this growth has qualitative features that are similar to those predicted by modulational diffusion models, but is significantly different in that the amplitude growth is exponential in time, not root‐time as in classical diffusion. Some possible explanations for this effect are briefly noted, and impact of the possible existence of such a mechanism on future Fermilab collider upgrades is mentioned.

ISSN:0094-243X    

DOI:10.1063/1.45122

出版商:AIP    

年代:1992

数据来源: AIP

摘要:

An analytic approach is developed for solving the inhomogeneous diffusion equation with the diffusion intensity being a fast‐growing function of the betatron energy. When applied to the survival data of particle tracking for LHC and SSC, the method shows that these data are inconsistent with (any) diffusion phenomenology. A similar inconsistency is observed in the data from CERN diffusion experiments.

ISSN:0094-243X    

DOI:10.1063/1.45124

出版商:AIP    

年代:1992

数据来源: AIP