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| Author | : Frank James Sacherer |
| Publisher | : |
| Total Pages | : 123 |
| Release | : 1968 |
| Genre | : Particle beams |
| ISBN | : |
| Author | : |
| Publisher | : |
| Total Pages | : |
| Release | : 1968 |
| Genre | : |
| ISBN | : |
The particles in an accelerator interact with one another by electromagnetic forces and are held together by external focusing forces. Such a many-body system has a large number of transverse modes of oscillation (plasma oscillations) that can be excited at characteristic frequencies by errors in the external guide field. In Part I we examine one mode of oscillation in detail, namely the quadrupole mode that is excited in uniformly charged beams by gradient errors. We derive self-consistent equations of motion for the beam envelope and solve these equations for the case in which the space-charge force is much less than the external focusing force, i.e., for strong-focusing synchrotrons. We find that the resonance intensity is shifted from the value predicted by the usual transverse incoherent space-charge limit; moreover, because the space-charge force depends on the shape and size of the beam, the beam growth in always limited. For gradient errors of the magnitude normally present in strong-focusing synchrotrons, the increase in beam size is small provided the beam parameters are properly chosen; otherwise the growth may be large. Thus gradient errors need not impose a limit on the number of particles that can be accelerated. In Part II we examine the other modes of collective oscillation that are excited by machine imperfections. For simplicity we consider only one-dimensional beams that are confined by harmonic potentials, and only small-amplitude oscillations. The linearized Vlasov and Poisson equations are used to find the twofold infinity of normal modes and eigenfrequencies for the stationary distribution that has uniform charge density in real space. In practice, only the low-order modes (the dipole, quadrupole, sextupole, and one or two additional modes) will be serious, and the resonant conditions for these modes are located on a tune diagram. These results, which are valid for all beam intensities, are compared with the known eigenfrequencies for the stationary distribution that has uniform particle density in phase space, and are extrapolated to the Gaussian distribution observed in the Brookhaven AGS.
| Author | : Ingo Hofmann |
| Publisher | : Springer |
| Total Pages | : 158 |
| Release | : 2017-09-20 |
| Genre | : Science |
| ISBN | : 3319621572 |
Understanding and controlling the physics of space charge effects in linear and circular proton and ion accelerators are essential to their operation, and to future high-intensity facilities. This book presents the status quo of this field from a theoretical perspective, compares analytical approaches with multi-particle computer simulations and – where available – with experiments. It discusses fundamental concepts of phase space motion, matched beams and modes of perturbation, along with mathematical models of analysis – from envelope to Vlasov-Poisson equations. The main emphasis is on providing a systematic description of incoherent and coherent resonance phenomena; parametric instabilities and sum modes; mismatch and halo; error driven resonances; and emittance exchange due to anisotropy, as well as the role of Landau damping. Their distinctive features are elaborated in the context of numerous sample simulations, and their potential impacts on beam quality degradation and beam loss are discussed. The book is intended for advanced beginners in accelerator research, and for experts interested in the mechanisms of direct space charge interaction and their modeling.
| Author | : Dornis C. Morin |
| Publisher | : |
| Total Pages | : 328 |
| Release | : 1962 |
| Genre | : Particles (Nuclear physics) |
| ISBN | : |
| Author | : |
| Publisher | : |
| Total Pages | : 23 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
The transverse instability of a bunch in a circular accelerator is elaborated in this paper. A new tree-modes model is proposed and developed to describe the most unstable modes of the bunch. This simple and flexible model includes chromaticity and space charge, and can be used with any bunch and wake forms. The dispersion equation for the bunch eigentunes is obtained in form of a third-order algebraic equation. The known head-tail and TMCI modes appear as the limiting cases which are distinctly bounded at zero chromaticity only. It is shown that the instability parameters depend only slightly on the bunch model but they are rather sensitive to the wake shape. In particular, space charge effects are investigated in the paper and it is shown that their influence depends on sign of wake field enhancing the bunch stability if the wake is negative. In addition, the resistive wall wake is considered in detail including a comparison of single and collective effects. A comparison of the results with earlier publications is carried out.
| Author | : |
| Publisher | : |
| Total Pages | : 48 |
| Release | : 1989 |
| Genre | : |
| ISBN | : |
The purpose of both linear and circular accelerator is, of course, to accelerate beams of charged particles. In order to do this it is necessary not only to accelerate particles but also to confine them transversely so that they remain in the vacuum environment. Originally, as accelerators were developed, the intensity of the beams was rather low and so the external fields could be applied without regard to the effects of the space-charge forces of the beams. However, as the demand for high intensity increased, collective effects that are due to the space-charge forces became increasingly important. In order to control a beam of particles we apply external fields. These focus the beam transversely and accelerate it and focus it longitudinally. In addition to these externally applied fields a particle within the beam feels a field due to the charge and current of all the other particles in the beam. By collective effects, we mean all those modifications to the beam behavior which are due to these beam-induced forces. The first two major topics discussed are linear and circular accelerators. In the linear accelerator case, we will consider as examples only electron linacs that have relatively high energy and so particles will have [nu] {approx equal} c. For circular accelerators we'll consider both protons and electrons or their anti-particles. The next two topics are single bunches and multi-bunches. In both linear accelerators and circular accelerators the particles have a bunched character because they are accelerated by an RF system, and the RF has a natural wavelength. The next two topics arise from the natural separation of longitudinal and transverse effects. 40 refs., 30 figs., 1 tab.
| Author | : H. Wiedemann |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 489 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642599087 |
Particle Accelerator Physics II continues the discussion of particle accelerator physics beyond the introductory Particle Accelerator Physics I. Aimed at students and scientists who plan to work or are working in the field of accelerator physics. Basic principles of beam dynamics already discussed in Vol.I are expanded into the nonlinear regime in order to tackle fundamental problems encountered in present-day accelerator design and development. Nonlinear dynamics is discussed both for the transverse phase space to determine chromatic and geometric aberrations which limit the dynamic aperture as well as for the longitude phase space in connection with phase focusing at very small values of the momentum compaction. Effects derived theoretically are compared with observations made at existing accelerators.
| Author | : R. A. Dory |
| Publisher | : |
| Total Pages | : 366 |
| Release | : 1962 |
| Genre | : Particle accelerators |
| ISBN | : |
| Author | : D. A. Edwards |
| Publisher | : John Wiley & Sons |
| Total Pages | : 304 |
| Release | : 2008-11-20 |
| Genre | : Science |
| ISBN | : 3527617280 |
The first half deals with the motion of a single particle under the influence of electronic and magnetic fields. The basic language of linear and circular accelerators is developed. The principle of phase stability is introduced along with phase oscillations in linear accelerators and synchrotrons. Presents a treatment of betatron oscillations followed by an excursion into nonlinear dynamics and its application to accelerators. The second half discusses intensity dependent effects, particularly space charge and coherent instabilities. Includes tables of parameters for a selection of accelerators which are used in the numerous problems provided at the end of each chapter.
| Author | : Martin Reiser |
| Publisher | : John Wiley & Sons |
| Total Pages | : 634 |
| Release | : 2008-09-26 |
| Genre | : Science |
| ISBN | : 3527617639 |
Although particle accelerators are the book's main thrust, it offers a broad synoptic description of beams which applies to a wide range of other devices such as low-energy focusing and transport systems and high-power microwave sources. Develops material from first principles, basic equations and theorems in a systematic way. Assumptions and approximations are clearly indicated. Discusses underlying physics and validity of theoretical relationships, design formulas and scaling laws. Features a significant amount of recent work including image effects and the Boltzmann line charge density profiles in bunched beams.
