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[en] The interrelationship between integrability and symmetries in classical mechanics is studied. Two-dimensional time- and velocity-independent potentials form the domain of the study. It is shown that, contrary to folklore, existence of a single finite symmetry does not ensure integrability. A method due to Darboux is used to construct potentials that admit a time-independent invariant. All potentials admitting invariants linear or quadratic in the momentum coordinates are constructed. These are the only integrable potentials which can be expressed as arbitrary functions of certain arguments. A complete construction of potentials admitting higher-order invariants does not seem possible. However, the necessary general forms for potentials that admit a particular invariant of arbitrary order are found. These invariants must be spherically symmetric in the leading terms. Two kinds of symmetries are studied: point Lie symmetries of the Newtonian equations of motion for conservative potentials, and point Noether symmetries of the action functionals obtained from the standard Lagrangians associated with these potentials. All conservative potentials which admit these symmetries are constructed. The class of potentials admitting Noether symmetries is shown to be a subclass of those admitting Lie symmetries
[en] Beam collisions with a crossing angle at the interaction point are often necessary in colliders to reduce the effects of parasitic collisions which induce emittance growth and decrease beam lifetime. The crossing angle reduces the geometrical overlap of the beams and hence the luminosity. Crab cavity offer a promising way to compensate the crossing angle and to realize effective head-on collisions. Moreover, the crab crossing mitigates the synchro-betatron resonances due to the crossing angle. A crab cavity experiment in SPS is proposed as a proof of principle before deciding on a full crab-cavity implementation in the LHC. In this paper, we investigate the effects of a single crab cavity on beam dynamics in the SPS and life time.
[en] This paper summarizes the presentations and discussions of the Beam-Beam'03 workshop, held in Montauk, Long Island, from May 19 to 23, 2003. Presentations and discussions focused on halo generation from beam-beam interactions; beam-beam limits, especially coherent limits and their effects on existing and future hadron colliders; beam-beam compensation techniques, particularly for long-range interactions; and beam-beam study tools in theory, simulation, and experiment
[en] Power supply ripple at frequencies of 720 Hz and its harmonies is expected to affect the motion of particles in the collider. These ripple frequencies are nearly resonant with the betatron frequencies. To estimate the tolerable ripple levels, we have tracked particles through the complete nonlinear lattice for 104 turns with ripple fed from 10 different power stations and including up to 7 different ripple frequencies. We presently estimate that relative ripple amplitudes must be below the 108 level for there to be no significant impact on the emittance over the short term
[en] The design process of modern high-energy synchrotrons involves the development of the accelerator lattice in pieces, typically an arc made up of repetitive cells interrupted by occasional matched insertions for injection, extraction, acceleration and various other systems required by the facility. The focusing elements of an insertion must be such that the periodic amplitude functions at the ends of the insertion match those of the cells on either side of the insertion. How well this match has to be and its sensitivity to the global betatron tunes of the accelerator as well as the particle momentum are the underlying themes of this report. Many of the relationships also are of use to the designers of beamlines which are used to transport and inject beams into a synchrotron. Most of the content of this paper is not new to the accelerator physics community, but we thought it would be useful to place this important, basic information all in one place. Besides the classic work of Courant and Snyder, our sources include other papers, internal reports, and numerous discussions with our colleagues
[en] Motivated by the desire to understand the longitudinal effects of beam-beam forces, we study the longitudinal dynamics of protons and anti-protons at injection and top energy in the Tevatron. Multi-turn data of the longitudinal profiles are captured to reveal information about frequencies of oscillation, and changes in the bunch distributions. Tomographic reconstruction is used to create phase space maps which are subsequently used to find the momentum distributions. Changes in these distributions for both proton and anti-proton beams are also followed through the operational cycle. We report on the details of interesting dynamics and some unexpected findings.
[en] As the development of extreme ultraviolet (EUV) lithography progresses, interest grows in the extension of traditional optical components to the EUV regime. The strong absorption of EUV by most materials and its extremely short wavelength, however, makes it very difficult to implement many components that are commonplace in the longer wavelength regimes. One such component is the diffractive optical element used, for example, in illumination systems to efficiently generate modified pupil fills. Here we demonstrate the fabrication and characterization of EUV binary phase-only computer-generated holograms allowing arbitrary far-field diffraction patterns to be generated
[en] An upgrade of the LHC interaction regions could potentially increase the luminosity by a factor of two or more. Several IR layouts are presented. The challenges and open questions related to the optics design, energy deposition and magnet design are discussed
[en] Preserving the beam size (or equivalently the emittance) is a primary aim of accelerator physics. Here we study the effect on the emittance of power supply ripple in the guiding magnetic fields. The collective behavior of forced Duffing oscillators is the natural model to understand this phenomenon. We consider the case when the external frequency is near the linearized natural frequency and nonlinearity and forcing are small. The method of averaging reduces the problem to an autonomous system. A coarse grained long time limit of the phase space density and the rate of approach to this limit are discussed in terms of the autonomous system. We find the frequencies which lead to the largest emittance growth in three different forcing regimes (weak, moderate and relatively large) and also characterize the dependence of emittance growth on forcing amplitude in these regimes
[en] We examine the stability of intense flat bunches in barrier buckets used in the Fermilab Recycler. We consider some common stationary distributions and show that they would be unstable against rigid dipole oscillations. We discuss the measurements which identify stable distributions. We also report on experimental studies on the impact of creating a local extremum of the incoherent frequency within the rf bucket. We considered two typical stationary distributions and found they were not adequate descriptions of the Recycler bunches. From the measured line density distribution we find (a) the tanh function is a good fit to the line density, and (b) the coherent frequency of the rigid dipole mode for this distribution is within the incoherent spread at nominal intensities. Stability diagrams when the beam couples to space charge and external impedances will be discussed elsewhere. Our initial experimental investigations indicate that longitudinal stability in the Recycler is, consistent with expectations, influenced by the ratio T2/(4T1) which determines the location of the extremum of the incoherent tune. The coherent tune depends strongly on the distribution in the bunch tails which is difficult to measure. Numerical studies using both a conventional tracking code and a Vlasov solver are in progress and should provide more insight into conditions that may lead to unstable behavior