The Principles of Circular Accelerators and Storage Rings

Abstract

This book is a basic introduction to the principles of circular particle accelerators and storage rings, for scientists, engineers and mathematicians. Particle accelerators used to be the exclusive province of physicists exploring the structure of the most fundamental constituents of matter. Nowadays, particle accelerators have also found uses as tools in many other areas, including materials science, chemistry, and medical science. Many people from these fields of study, as well as from particle physics, have learned about accelerators at various courses organised by CERN, the European Organisation for Nuclear Research which has established a reputation as the world's top accelerator facility. Kjell Johnsen and Phil Bryant, the authors of this book, are distinguished accelerator physicists who have also run the CERN Accelerator School. The text they present here starts with a historical introduction to the field and an outline of the basic concepts of particle acceleration and phase focusing. It goes on to give more details of how the transverse and longitudinal motions of the particle beams can be analysed, including treatments of lattice design, compensation schemes, transition crossing, and other radio frequency effects. The book will be an essential reference to anyone working with particle accelerators as a designer, operator or user, as well as being a good preparation for those intending to go to the frontiers of accelerator physics.

Crystalline ion beams in the RF quadrupole storage ring PALLAS

“…Numerical simulations yield that to maintain a beam crystal (and, more fundamental, to prevent envelope instabilities of space charge dominated beams [26,27]), the number of repeating focusing sections P (the periodicity of the ring) has to be larger than 2V2-. Q, the storage ring tune Q being the number of radial oscillations per revolution [28]. This criterion coincides with the validity criterion for treating (time dependent) strong focusing in the (timeaveraging) smooth approximation [29].…”

“…625 kHz. This transverse oscillation in the confining pseudopotential is equivalent to the betatron oscillation [28] of particles in a synchrotron with its alternating focusing and de-focusing magnets. In the quadrupole ring, these discrete but periodic structures are represented by the alternating phase of the rf voltage.…”

Rotators for matching non-symmetric ion-therapy beams to rotating gantries

“…10,11 A rotator is a bending-free, dispersion-free, and coupling-free section of the transfer line featuring a special transfer matrix, MROT, in the form (it is sufficient to consider a 4 × 4 matrix for the two transverse planes): …”

Measurement of the modulus and phase of the linear coupling coefficient by analysis of the transverse beam profile

“…Linear coupling (i.e., coupling by linear fields) may be caused by tilted quadrupoles, vertical closed orbit deviations in sextupoles, and solenoidal fields in detectors, whereas nonlinear coupling may be produced by interaction with the electric fields of ions trapped in the electron beam [3] as well as by space charge or beam-beam forces [4]. Close to a resonant condition, the dynamics of linear coupling can be described by a single complex parameter: the coupling coefficient k. The measurement of jkj is routinely done by measuring the separation between the oscillating frequencies of the normal modes of the coupled system [5]. Other techniques to measure coupling usually involve transversely exciting the beam and observing the resulting coherent oscillations.…”