By Vladimir D Shiltsev
Springer
Also available at the CERN bookshop
With an energetic writing style, in this book Vladimir Shiltsev presents a novel device for accelerators and storage rings. These machines employ magnets to bend and focus particle trajectories, and magnets always create forces that increase monotonically with the particle displacement in the magnet. But a particle in a beam also experiences forces from the beam itself and from the other beam in a collider – forces that do not increase monotonically with amplitude. Therefore, magnets are not well suited to correct for beam-generated forces. However, another beam may do the job, and this is most easily realised with a low-energy electron beam stabilised in a solenoidal magnetic field – thus an electron lens is created. The lens offers options for generating amplitude-dependent forces that cannot be realised with magnets, and such forces can also be made time-dependent. The electron lens is in effect a nonlinear lens with a rather flexible profile that can either be static or change with every passing bunch.
D Gabor already proposed the use of electron-generated space-charge forces in 1947 (Nature 160 89–90), and E Tsyganov suggested the use of electron lenses for the SSC (SSCL-Preprint-519 1993). But it was Shiltsev who was the driving force behind the first implementation of electron lenses in a high-energy machine. Two such lenses were installed in the Tevatron in 2001 and 2004, where they routinely removed beam not captured by the radiofrequency (RF) system, and were used for numerous studies of long-range and head-on beam–beam compensation and collimation. In 2014, two electron lenses were also installed in the Relativistic Heavy Ion Collider (RHIC) for head-on beam–beam compensation, and their use for the LHC collimation system is under consideration.
Shiltsev’s experience and comprehensive knowledge of the topic make him perhaps the best possible author for an introductory text. The book is divided into five chapters: an introduction, the major pieces of technology, application for beam–beam compensation, halo collimation, and other applications. It draws heavily on published material, and therefore does not have the feel of a textbook. While a consistent notation for symbols is used throughout the book, the figures are taken from other publications, and the units are mostly but not entirely in the International System (SI).
At the heart of the book are descriptions of the major technical components of a working electron lens, and the two main applications to date: beam–beam compensation and halo collimation. Long-range and head-on beam–beam compensation as well as collimation applications are described exhaustively. It is somewhat regrettable that the latest results from RHIC were published too late to be included in the volume (e.g. W Fischer et al. 2015 Phys. Rev. Lett. 115 264801; P Thieberger et al. 2016 Phys. Rev. Accel. Beams 19 041002). The book names the hollow electron lens a collimator, but it is probably better to describe it as a diffusion enhancer (as suggested on p138) because its strength is at least an order of magnitude smaller than a solid-state collimator, and a hollow lens will not replace either a primary or a secondary collimator jaw.
The last chapter ventures into more speculative territory, with applications that are not all in colliders. Most prominently, space-charge compensation is discussed, largely in terms of tune spread but not resonance driving terms. The latter is only mentioned in the context of multiple electron lenses (up to 24 for a simulated Fermilab Booster example). For this and the other applications mentioned, it is clear that much work remains before these could become reality.
Overall, the book is an excellent entry point for anyone who would like to become familiar with the concepts, technology and possible application of electron lenses. It is also a useful reference for many formulas, allowing for fast estimates, and for the published work on this topic – up to the date of publication.
