The Science and Technology of Particle Accelerators

Rob Appleby, Graeme Burt, James Clarke, Hywel Owen

• Publisher: CRC Press
• Year: 2020
• eBook ISBN: 9781351007948
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

The Science and Technology of Particle Accelerators provides an accessible introduction to the field, and is suitable for advanced undergraduates, graduate students, and academics, as well as professionals in national laboratories and facilities, industry, and medicine who are designing or using particle accelerators.

Providing integrated coverage of accelerator science and technology, this book presents the fundamental concepts alongside detailed engineering discussions and extensive practical guidance, including many numerical examples.

For each topic, the authors provide a description of the physical principles, a guide to the practical application of those principles, and a discussion of how to design the components that allow the application to be realised.

Features:

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• Written by an interdisciplinary and highly respected team of physicists and engineers from the Cockcroft Institute of Accelerator Science and Technology in the UK

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• Accessible style, with many numerical examples

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• Contains an extensive set of problems, with fully worked solutions available

Rob Appleby is an academic member of staff at the University of Manchester, and Chief Examiner in the Department of Physics and Astronomy.

Graeme Burt is an academic member of staff at the University of Lancaster, and previous Director of Education at the Cockcroft Institute.

James Clarke is head of Science Division in the Accelerator Science and Technology Centre at STFC Daresbury Laboratory.

Hywel Owen is an academic member of staff at the University of Manchester, and Director of Education at the Cockcroft Institute.

All authors are researchers within the Cockcroft Institute of Accelerator Science and Technology and have extensive experience in the design and construction of particle accelerators, including particle colliders, synchrotron radiation sources, free electron lasers, and medical and industrial accelerator systems.

1

An Invitation: Acceleration!

This book is about particle accelerators, what they accelerate, how they work, and how (and why) we build them. In this opening chapter we shall take a short tour of a typical accelerator, moving along the beamline and making sense of the different kinds of accelerator elements. This will give a kind of map for the rest of the book and a map of the subject. We hope the reader finds it useful for an overview and orientation. We are scientists and engineers, and as such are concerned with the observation and understanding of the physical world. The first step to any kind of deeper – and if we are lucky, quantitative – understanding of that world is to group and classify those aspects attracting our attention. How do we classify particle accelerators? Before we start, we should first define what a particle accelerator is.

We may define a particle accelerator as a device – often called a ‘machine’ – that endows subatomic particles with large and variable amounts of kinetic energy. ‘Large’ here is in comparison with the sorts of energies one obtains from a particle source such as a simpler electron gun or ion source that might produce particles of tens of thousands of electron-volts (eV).^∗ Particle accelerators differ from other sources of energetic particles – such as radioactive decay – in that an accelerator allows us (more or less) to freely choose the particle energy; for example, alpha particles from a given radionuclide – say, americium-241^∗ – are emitted with only a single energy (of several MeV). We will see in the next chapter that electric fields are the predominant method of providing a particle with kinetic energy, and this demands that the particles we accelerate are charged so as to experience an acceleration from that field; the beams of particles that travel through an accelerator are therefore often described in terms of the equivalent current they carry. However, there are also so-called secondary sources of particles, some of which may be electrically neutral; three important examples are the photon, the neutron and the neutrino, all commonly produced by accelerators and used extensively in science and engineering for quite different things.

^∗The electron-volt is generally the most appropriate unit to quantify that kinetic energy.

^∗Americium-241 is chosen as an example here because it is the most commonly-encountered radioisotope; around 1 μCurie activity (about 0.3 mg of AmO₂) is present in virtually every domestic smoke detector.

In the following chapters we will deal with the manner in which particles are produced, accelerated and used – each of which of course depends on the particular particle. But first let us take an overview, and attempt to classify them by type. A first observation is that some accelerators are straight (i.e. linear), in which the accelerated species pass through each element of the accelerator only once; often the predominant element is the one that performs the acceleration. These are usually called linear accelerators, or linacs for short. The alternative is the circular accelerator, in which particles circulate many times, very often repeatedly through the same elements; this can allow the re-use of accelerating elements (such as accelerating gaps or cavities), or allow repeated production of some secondary species – such as photons, for instance – from the same primary particle.

So we can classify accelerators into two broad categories – those that accelerate particles in a straight line and those that accelerate particles approximately in a circle (usually called a ring). In the straight (or linear) type, the particles start at one end and pass through every element only once (including the accelerating elements), finishing up at the end of the accelerator. This type of linear accelerator (usually abbreviated as ‘linac’) is very common and is used all over the world, mostly commonly as the device that supplies electrons at ∼10 MeV in an X-ray radiotherapy machine. To construct the second type, we imagine bending our linear accelerator into a ring using dipole magnets (also therefore called bending magnets), so that the particle makes many laps (or turns) of the ring, also passing through the elements making up that ring many times. A widely-encountered example of this type of accelerator is the synchrotron; many synchrotrons are used today to produce high-energy photons (with energies typically of a few keV or more) by bending the circulating beam of electrons; these photons are then used in a variety of techniques by researchers. Other synchrotrons are used to accelerate – for example – protons to high energies to hundreds of GeV or more to undergo collisions to study particle physics.

If we visit a particle accelerator (‘accelerator’ for short) we find that many are composed of several distinct systems, each of which is commonly regarded as an accelerator in its own right. A famous example is CERN’s Large Hadron Collider (LHC), a proton accelerator that lies many metres under the ground near Geneva, and which is large enough, with a 27 km circumference, to cross the Swiss-French border twice! The LHC facility is really a number of connected accelerators, and the protons begin their lives within a bottle of hydrogen gas. An ion source is used to strip the electrons from the hydrogen atoms and deliver the protons at some (modest) energy of 70 keV to a pre-injector; a chain of further accelerators, first linacs and then circular synchrotrons, progressively increases each proton’s energy to a final value of 6.5 TeV (tera-electron-volts).^∗ Two independent beams of protons of the same energy travel around the ring, one clockwise and the other counter-clockwise, and these are made to collide head on into each other at specific locations within the storage ring to produce reaction products useful for experiments in fundamental particle physics.^∗ Another example is the free-electron laser (or FEL). Here, electrons are generated from an electron gun (a cathode from which electrons are emitted in the presence of a strong voltage, sometimes with some assistance from a short pulse of laser photons) and then progressively accelerated by a linac; these electrons then pass through a special magnetic device that prompts the electrons to emit light with laser-like properties (the FEL proper) and so generate tailored pulses of photons. An example of an electron gun is shown in Fig 1.1.

^∗7 TeV is the anticipated energy in the future.

^∗A storage ring is a type of synchrotron, but one in which the energy of the circulating particles is constant.

Figure 1.1 Here we see one of the electron guns at CLARA, situated at Daresbury Laboratory. This is a typical photo-injector source, in which a pulsed laser is directed (from the left) onto a cathode (on the right of the photograph) and produces an intense, short-duration bunch of electrons that contains tens of picocoulombs of charge. The electrons are then accelerated to the left by a strong oscillating electric field produced in several coupled cavities, up to a kinetic energy of several MeV. ©STFC

The basic building blocks of any accelerator are: the devices that generate the particles (the sources); the devices that accelerate the particles, which is almost always done with electric fields; and the devices that confine and control the particles, which are commonly built using magnets. For example, electromagnets are used to deflect (bend) particles into a curved path – so-called dipole electromagnets are used to construct a circular accelerator. Other electromagnets such as quadrupoles, sextupoles and so on are used to confine particles into some desired size (envelope). All these devices generate a predetermined magnetic field that is experienced by the passing charged particles, using some sort of beam-optical arrangement; an example is shown in Fig 1.2.

Figure 1.2 Part of the ALICE energy-recovery linac electron beam transport system, previously installed at Daresbury Laboratory. Individual beamline magnets are typically mounted onto a girder (usually steel), adjusted so that their magnet centres are aligned and then fixed (with position accuracy of some tens of μm); the girder may then be lifted into its operating position without significant relative movement of the magnets, and they may be adjusted together for efficiency. A typical alignment accuracy from girder to girder of a few tens of μm is also commonly achieved. ©STFC

The effect of the electric and magnetic fields can be summarised by a single basic law that is the most important equation encountered in this book, and in the field of particle accelerators – the Lorentz equation (also known as the Lorentz force law). This describes the force 퐅 on a particle with charge q from an electric field E and magnetic field B and is given by

F=qE+v×B, (1.1)

where v is the particle velocity. The consequences of this seemingly-simple equation – combined with the other laws of electromagnetism – will occupy us in the following chapters, but straight away we seem two very important differences between the way electric and magnetic fields act upon charged particles; electric fields can perform work upon the charges, and therefore can impart (kinetic) energy to them, whereas magnetic fields produce a force at right angles to a charge’s motion and so do no work. A static magnetic field cannot change the energy of a charged particle, and particularly can do nothing at all if the charge is stationary; we will discuss this more in the next chapter. We also note now the very important consequence of special relativity, which is that our accelerated particles often significantly increase in mass rather than velocity as they gain energy. This is always considered when calculating the effect of the Lorentz force, and obviously relativity ultimately determines that our particles cannot travel faster than the speed of light, c. Surprisingly, the ideas of quantum physics do not normally have to be considered, although on occasion we will; this is most often encountered in the context of photon emission from charges. An important but sometimes overlooked aspect of particle accelerators is that that the beam pipe through which the particles pass (and which the electromagnets surround) must be evacuated to allow the particles to pass by with little scattering or absorption; residual gas within the vacuum system can give rise to such undesirable phenomena as particle loss, emittance degradation (blow-up), ion trapping by electron beams and the analogous electron cloud instability experienced by proton beams.

The most important magnetic devices are the dipole and the quadrupole. Let’s look at a dipole first, which can be seen in Fig 1.3, which induces charged particles to follow a curved path (the arc of a circle to be exact); it bends a beam of particles and is composed of two poles (north and south). Linacs often need to utilise dipoles to produce some defined bend angle, for example to steer a produced beam to a precise final location; of course, a circular accelerator requires 360 ° -worth of total bend, and this is typically achieved using a number of dipoles each contributing a part of the overall deflection. The cyclotron is an example of a circular accelerator that utilises only one dipole, in the form of a single circular magnet. In a dipole a combination of current-carrying copper coils and steel poles produces an almost uniform magnet field, bending the passing charges through some angle determined by the magnetic field and each particle’s momentum. This deflection angle θ is proportional to the field strength B; for very large values of B the coil currents must be large, and this may require them to be superconducting. As a general guide, ordinary electromagnetic dipoles generate fields up to 1 or 2 T, and superconducting dipole magnets typically generate fields up to ∼8 T (with the prospect for significantly higher fields than this in the future). In Chapter 4 we will see how magnet designers construct dipole magnets to some specified strength and field accuracy and we’ll see in Chapter 5 how we can compute the motion of particles in a (perhaps non-ideal) dipole field.

Figure 1.3 A dipole magnet used to deflect (bend) a beam of charged particles. A current-carrying coil – here made of copper channels wound a number of times around each of the two pole pieces – drives the magnetic field. The outer yoke closes the magnetic field lines to maximise efficiency and to limit the stray field away from the magnet so the magnetic field is essentially only present in air between the north and south poles. A vacuum vessel between the poles follows the 60 ° deflection angle, but also includes extra pieces (here with temporary flanges on) that allow for other uses such as vacuum pumping or for emitted light to be extracted and utilised. ©STFC

The quadrupole – the ‘four-pole’ magnet – is often the most numerous type of magnet found in an accelerator, and can be seen in Fig 1.2. The magnetic field inside the aperture of a quadrupole has a strength By∝x (the vertical field rises as one moves horizontally from the magnet centre) and also Bx∝y; a quadrupole provides a gradient g=∂B/∂x in the field with zero field at the magnet centre, so on average provides no deflection at all. As a rule of thumb we typically use gradients of 10 to 100 T/m; smaller magnet apertures make larger gradients easier to achieve. The purpose of quadrupoles is to focus and so basically to confine the beam to within some stable envelope, and in Chapter 5 we will discuss Hill’s equation and how it determines if an arrangement of quadrupoles – called a magnetic lattice – gives a stable focusing channel. Often we use a matrix formalism, based on Hill’s equation, which allows us to follow – or track – the paths of individual particles. We will see in Chapter 5 how the Courant-Snyder formalism can be used to describe the envelope around those particles using the so-called β-function and the other Twiss functions. We will also discuss higher-order magnets with more poles, such as the sextupole (in Chapters 4 and 5); these are commonly used to correct beam-optical aberrations and thereby enable magnet lattices to give better stability to the transported particles. Most particle accelerators require magnets that generate these higher-order fields.

At the heart of any accelerator are the devices that generate the accelerating fields, which we will see in Chapter 2 can only be electric fields. A common device is the accelerating cavity, within which a time-va...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Contents
• Preface
• 1 An Invitation: Acceleration!
• 2 ABC: Accelerators, Beams, and Charges
• 3 Acceleration
• 4 Magnets for Beam Control and Manipulation
• 5 Single Particle Motion
• 6 Particles and Radiation
• 7 Multi-Particle Motion
• Index