1. Particle Accelerators
Prof. Ted Wilson (CERN and Oxford University)
based on the book:
I am Ted Wilson and since I retired from designing a large number of CERN’s accelerators (from SPS through the Antiproton Accumulator. LEP and the initial design of LHC) I have been a visiting professor teaching postgraduate physics Students at this University – The John Adams Institute.
Let me ask you a question : are you in a second or thirdyear the physics course?
Whichever – my advice – based on my undergradute experience. Don’t be seduced by the social life- work hard to avoid looking back with the regret. Don’t end up saying “If only .. then I would have got a first or upper second and enjoyed thrill of doing research instead of the many mundane jobs the world offers.
The other advice I have is not to be too impressed by very academic subjects like theoretical physics . If you are not careful Oxford and its academic crucible will fool you
Choose a technical activity or applied science where you will be able to look back and say (when you are my age) “my work did something for living human beings”. Some of the accelrators I will tell you about today offer that alterntive and are just as challenging as LHC.
But not every accelerator has been built for particle physics, and accelerators for applications other than high-energy now outnumber the large atom-smashers by two orders of magnitude. The speaker will concentrate on some of the more practical uses of accelerators that directly benefit mankind, including medical diagnosis and therapy.
ISBN
This talk:

2. Theory of accelerators
by Ted Wilson
I. Electrostatic Machines
II. Cyclotrons
III. Linacs
IV. Synchrotrons
V. Colliders
VII. Synchrotron Radiation Sources
VIII. Other Applications
You have learned in lectures all about the many kinds of accelerators, electrostatic, cyclotrons, linacs, synchrotrons, colliders etc. – the different particles hadrons and leptons that are accelerated. You will find all this explained in words in our book but also we have tried to explain
how each idea grew from noise
what kind of people were those that made the discoveries.
The history of accelerators mirrors the development of the technologies of the 20th century from invention of radio to superconductivity.
If you wanted to chart the technology of the 19th century you might well look at how engineers made bridges and steam engines railways and early motor cars
A large number of sidebars about the people who invented things and dhow they operated. There are also sidebars on technical matters and on the way in which laboratories organized this Endeavour.

3. LHC: ρ = 2.8 km given by LEP tunnel!
Basic concepts
Charged particles are accelerated, guided and confined by electromagnetic fields.
- Bending: Dipole magnets - Focusing: Quadrupole magnets - Acceleration: RF cavities
In synchrotrons, they are ramped together synchronously to match beam energy.
- Chromatic aberration: Sextupole magnets
This slide is for those of you who have so far only done physics with cosmic rays
Magnetic rigidity
Centripetal Force ρ
Lorentz force
LHC: ρ = 2.8 km given by LEP tunnel! →
Fixes the relation between magnetic field and particle’s energy

4. Newton & Einstein

5. Some relativity

6. LHC injector complex
450 GeV
1.4 GeV
26 GeV

7. The Large Hadron Collider (LHC)
The project was first proposed in 1982 at a Snowmass Study, organised by the APS. At a cost of $2.9B to $3.2B, it was supposed to re-establish US supremacy in the field of high-energy particle physics following the discovery in Europe of the W and Z.
The next step was carried out. By 1986 a detailed design study, by a Central Design Group set up under Maury Tigner at Lawrence Berkeley Laboratory, was complete and in 1987 President Reagan set in motion the search for a site. In 1988 Waxahatchie, Texas was announced as the successful candidate and construction commenced. This decision was, perhaps, influenced by then Vice-President George Bush (senior) of Texas, Jim Wright of Fort Worth, then Speaker of the House of Representatives, and a powerful Senator, Lloyd Bentsen, also from Texas.
Meanwhile the cost, taking into account the more realistic estimates of the Central Design Group, and including the proposed experimental facilities, had risen from the initial estimate of 2.9 B$ to 3.2 B$ and then to 5.3 B$ in 1986.
The DOE took over the management of the project from the CDG and determined that the traditions of technical and cost control that had been built up in large laboratories, like Fermilab, were to be abandoned in favour of methods judged more appropriate for a project of this size. Contracts were placed and subsystems procured in a manner that had hitherto been used for large defense projects. This led to further escalation, first to 5.9 B$ and then, as review teams included into account “site-specific” costs, to 7.2 B$ and then 8.2 B$ (DOE, 1991). The final straw came when an Independent Cost Estimating Team of the DOE (1993) added 2.5 B$ for “peripheral expenses which would not have been incurred if the SSC had not been there”. The SSC was given a year’s reprieve but by 1994 when the US Congress saw fit to cut their losses and terminate the project the estimate was 11.8 B$.
The reasons for cancellation were not entirely budgetary. There was a rival project – the Space Station – that many in the House of Representatives preferred.

8. Superconducting magnets

9. Two-in-one magnet design
Bending
B field B p F
F force I B
Two-in-one magnet design
LHC: B = 8.33 T ⇒ E = 7 TeV

10. Focusing N S By Fx Fy
Circular machine – all accelerators need focussing – nowadays with quadrupole magnets, which act on the beam like an optical lens.
Linear increase of the magnetic field along the axes (no effect on particles on axis).
Focusing in one plane, de-focusing in the other!
On the left we see a room temperature quadrupole
On the right is a sc version
Coils define the field shape
Transverse focusing is achieved with quadrupole magnets, which act on the beam like an optical lens.
Linear increase of the magnetic field along the axes (no effect on particles on axis).
Focusing in one plane, de-focusing in the other! x y

11. Alternating gradient lattices x y
An illustrative scheme
(LHC: 2x3 dipoles per cell)
One can find an arrangement of quadrupole magnets that provides net focusing in both planes (“strong focusing”).
Dipole magnets keep the particles on the circular orbit.
Quadrupole magnets focus alternatively in both planes.
This is how it looks in practice
One can find an arrangement of quadrupole magnets that provides net focusing in both planes (“strong focusing”).
Dipole magnets keep the particles on the circular orbit.
Quadrupole magnets focus alternatively in both planes.
Coordinate system

12. Alternating gradients
This is how we get would the fact that they are focus in one plane and defocus in the other – optical ray diagram
Rays just have to be closer to the axis in D quads (either H or V)

13. Transverse equation of motion
Magnetic field [T] :
Field gradient [T m-1] :
Normalized grad. [m-2] :
Here we see a big K which is the same as the little on in the Hamiltonian and psub0/e which is brohThe Hamiltonian gives Hills equation
Don’t miss that K == 1/f
Alternating Gradient focusing → pseudo-harmonic oscillator with s- dependent spring constant K(s).
The general linear magnet lattice can be parameterized by a ‘varying spring constant’, K=K(s)
Note that dipoles give a “weak focusing” term in the horizontal plane, K(s) = K(s)+1/ρ2
Look closely - K varies around the ring
Like a sine wave but two amplitude beta and emittance (beam)
Phase advances more or less steadily aroung the ring (faster when beta is small)
Be careful of beta courant used alpha beta gamma
K(s) describes the distribution of focusing strength along the lattice.
Hill’s equation
G. Hill,
and its solution

14. LHC layout and accelerator systems
Eight arcs and eight straight sessions:
Point 1: Atlas, LHCf
Point 2: Alice, injection
Point 3: Momentum cleaning
Point 4: RF
Point 5: CMS, TOTEM
Point 6: Beam Dumps
Point 7: Betatron cleaning
Point 8: LHCb, injection

15. Nominal LHC parameters
LHC design parameters
Nominal LHC parameters
Beam injection energy (TeV)
0.45
Beam energy (TeV)
7.0
Number of particles per bunch
1.15 x 1011
Number of bunches per beam
2808
Max stored beam energy (MJ)
362
Norm transverse emittance (μm rad)
3.75
Colliding beam size (μm) 16
Bunch length at 7 TeV (cm)
7.55
- These are the key parameters of a collider – the LHC
Why are they important for physics?
What is the basic theory which limits each one of them to determine Luminosity?
- These are the key parameters of a collider – the LHC
- Why are they important for physics?
- What is the basic theory which limits each one of them?

16. Luminosity (single bunches)
Imagine a blue particle colliding with a beam of cross section area - A
Probability of collision for an interaction is
For N particles in both beams
Suppose they meet f times per second at the revolution frequency
Event rate
Of course the performance that experimenters are really interested in Luminosity – let use see how the parameters affect it
Make big
Make small
LUMINOSITY

17. Acceleration
Acceleration is performed with electric fields fed into Radio-Frequency (RF) cavities. RF cavities are basically resonators tuned to a selected frequency.
In circular accelerators, the acceleration is done with small steps at each turn.
LHC: 8 RF cavities per beam (400 MHz), located in point 4
At the LHC, the acceleration from 450 GeV to 7 TeV lasts ~ 20 minutes (nominal!), with an average energy gain of ~ 0.5 MeV on each turn. [Today, we ramp at a factor 4 less energy gain per turn than nominal!]
Acceleration is performed with electric fields fed into Radio- Frequency (RF) cavities. RF cavities are basically resonators tuned to a selected frequency.
In circular accelerators, the acceleration is done with small steps at each turn.
LHC: 8 RF cavities per beam (400 MHz), located in point 4
At the LHC, the acceleration from 450 GeV to 7 TeV lasts ~ 20 minutes (nominal!), with an average energy gain of ~ 0.5 MeV on each turn. [Today, we ramp at a factor 4 less energy gain per turn than nominal!] s

18. The particles oscillate back and forth in time/energy
Buckets and bunches
The particles oscillate back and forth in time/energy
The particles are trapped in the RF voltage:
this gives the bunch structure
RF Voltage
2.5 ns
time
First of all the rf frequency is not the revolution frequency – we want lots of small bunches h of them
Above it the time variation of voltage experienced by a particle passing through a cavity
Below we see longitudinal phase space E v t
We can think of it as E vs s ΔE
time
LHC bunch spacing = 25 ns = 10 buckets ⇔ 7.5 m
RMS bunch length cm cm
RMS energy spread % 0.011%
450 GeV TeV
RF bucket
2.5 ns

19. Synchroton Radiation
Electrons accelerating by running up and down in a radio antenna emit radio waves
Radio waves are nothing more than Long Wavelength Light-

20. Synchroton Light Sources
When the electron speed gets close to the speed of light,
e radiation comes out only in a narrow forward cone;
a laser-like concentrated stream

21. Very soon afterwards a real electron synchrotron was built – where to look for synchrotron radiation.
This 300 MeV electron synchroton at the General Electric Co. at Schenectady, built in the late 1940s. The photograph shows a beam of synchrotron radiation emerging.

22. Synchrotron Light Sources
Spring 8, a synchrotron light source located in Japan.
Synchtoron Light Sources – ESRF
First generation sources are electron synchrotrons built for other purposes: mainly for the study of high-energy physics
In second generation machines “wigglers” and “undulators.” Are used to enhance the intensity and frequency of the light.
User pressure developed to go to even shorter wavelengths; i.e., to even more energetic (“harder”) x-rays. meant that the facilities had to have even higher energy electrons and thus a larger “footprint.” These third generationfacilities employed the very latest in machine design and the latest insertion devices to produce very intense x-ray beams.:ESRF the Advanced Photon Source (APS) at Argonne, USA with 7 GeV SPring-8 (Japan) with 8 GeV electrons
Examples of Synchrotron Light Research – Protein Molecule
The x-rays from synchrotrons are being used by more than 20,000 researchers at 54 dedicated facilities in 19 different countries. There are eight more facilities under construction, and eleven more in the design and planning stage.
There have been 18 Nobel Prizes awarded for work related to x-rays: 8 in chemistry, 7 in physics and 3 in medicine.
x-rays from synchrotron radiation elucidates
structure of matter
magnetic properties of the material (for hard discs), high temperature superconductivity, Surface phenomena, structure of DNA and of protein, studies of osteoporosis, diseased human hearts,
Study of anthrax and cholera toxins ,drugs, enzymes for various industrial processes, Filters, art and archaeology
This intricate structure of a complex protein molecule structure
has been determined by reconstructing scattered synchrotron radiation

23. Linac Coherent Light Source and the European Union X-Ray Free Electron Laser (Fourth Generation)
FEL for a fourth generation source
What is an FEL
Invented by John Madey
Beam of tightly bunched electrons, accelerated in a linac, passes through a wiggler
The radiation emitted in the bends remains in phase with the bunches and, reacting back on the bunches, causes them to bunch even more sharply, enhancing the brilliance of the radiation.
Like a laser the light is coherent, adding up in amplitude so that double the amplitude produces four times the power.
“Self Amplified Spontaneous Emission” (SASE),
Pioneered by Claudio Pellegrini
It is effectively an amplifier for x-rays but one cannot feed x-ray radiation into the wiggler; there simply are no sources powerful enough.
This method is called “Self Amplified Spontaneous Emission” (SASE)
The first few wiggles produce some x-ray “noise,” enough for the rest of the wiggler to amplify.
FELs, invented in the late 1970’s at Stanford are now becoming the basis of major facilities in the USA (SLAC) and Europe (DESY) .They promise intense coherent radiation. The present projects expect to reach radiation of 1 Angstrom (0.1 nano-meters, 10kilo-volt radiation) ↓
Engines of Discovery

24. Basis of muon collider Neutrion Factory and Muon Colliders
Muons are leptons, like electrons have the advantage of an unambiguous point-like structure.
The muon will not radiate significant amounts of synchrotron light even at the energies at which the present generation of proton colliders operate.(an alternative to the linear collider)
The muon decays in about a microsecond But, the time and distance it travels before it decays increases in proportion to the energy. `At 100 GeV or more, the colliding beams will exist for about one millisecond in the laboratory reference frame: long enough to see some events.
The spread in angles of the muons is far larger than the acceptance of most accelerators (an exception is discussed below) and hence the muons must be “cooled.”
The only possible method is ionization cooling.
In the overall process of losing energy (momentum) by ionizing the atoms of an absorber — and then being reaccelerated in the forward direction — particles take up new trajectories closer to the axis of the beam.
A large international cooling experiment, the Muon Ionization Cooling Experiment (MICE), is under development at the Rutherford-Appleton Laboratory in England to prove it.
Basis of muon collider

25. Spallation Neutron Sources (SNS)
1GeV protons
mean current 1 mA
= 1.4 MW of power
In a
0.7 microsecuond burst
Cost is about 1.5 B$
Present Machines
Two spallation sources, a synchrotron called ISIS at the Rutherford-Appleton Laboratory in the UK and a cyclotron driven spallation source at PSI in Switzerland, share the honors for the most powerful sources in operation.
An even larger spallation source (the SNS) has just been completed in the US, at Oak Ridge and its design specification it will produce:
an average proton beam current of 1.4 mA
at 1 GeV will deposit 1.4 MW of power in the target and its surroundings.
each proton pulse on target is 0.7 microseconds long, short enough to provide excellent wavelength tagging of each neutron,
The cost of the SNS — about 1.5 B$ — is comparable with the big machines of particle physics.
Future Sources
While serious consideration of a similar spallation source has been going on for many years in Europe. The Japanese are constructing a large accelerator complex at the JAERI, Tokay site, the major part of which is a spallation source. In 2005 the Chinese initiated a design study for their own spallation source (the CSNS).
An overview of the Spallation Neutron Source (SNS) site at Oak Ridge National Laboratory.

26. An artist’s view of a heavy ion inertial fusion facility
An artist’s view of a heavy ion inertial fusion facility. Although the facility is large, it is made of components that all appear to be feasible to construct and operate.

27. Unstable Isotopes and their Ions
The next major project that nuclear physicists plan is an accelerator of radioactive species of very short half-life — the so called non-equilibrium nuclei.
Beams of these rare species have already been produced and studied at the ISOLDE facility at CERN, the Bevalac at LBL, and at the superconducting cyclotron at Michigan State University, but now new facilities of expanded capability are called for.
Different methods of producing radioactive beams
There are four projects of this type.
The first, already completed, is the Radioactive Isotope Beam Facility (RIBF) at RIKEN, Wako, in Japan;
the second, under construction, is the Facility for Antiproton and Ion Research (FAIR) at GSI, Darmstadt in Germany;
the third is SPIRAL2 at GANIL in Caen, France;
and the fourth is the Rare Isotope Accelerator under consideration in the US.
The heart of the facility is composed of a driver accelerator capable of accelerating every element of the periodic table up to at least 400 MeV/nucleon. Rare isotopes will be produced in a number of dedicated production targets and will be used at rest for experiments, or they can be accelerated to energies below or near the Coulomb barrier.
The Rare Isotope Accelerator (RIA) scheme. The heart of the facility is composed of a driver accelerator capable of accelerating every element of the periodic table up to at least 400 MeV/nucleon. Rare isotopes will be produced in a number of dedicated production targets and will be used at rest for experiments, or they can be accelerated to energies below or near the Coulomb barrier.

28. Energy amplifier

29. Proton Drivers for Power Reactors
Proton Drivers for Power Reactors (Energy Amplifier)
Reactor that could not remain critical without the accelerator beam.
No danger of a reactor meltdown due to a cooling failure or unplanned release as at Chernobyl
Detailed studies, including experimental work, have been made in Europe to design such a reactor burning thorium instead of uranium.
Thorium, cannot produce dangerous, long-lived transuranic isotopes such as plutonium.
Also achieves the “burning up” of longlived nuclear wastes.
The idea occurred to the Los Alamos group, and also a group in CERN under the direction of Carlo Rubbia
A Linac scheme from Los Alamos
A linac scheme for driving a reactor. These devices can turn thorium into a reactor fuel, power a reactor safely, and burn up long-lived fission products.

30. Sterilisation Chip manufacture Art and archaeology National Security
I have not mentioned
Sterilisation
Chip manufacture
Art and archaeology
National Security
Surface treatment
Etc. etc….

31. Links Author’s e-mail: ted.wilson@cern.ch “Engines of Discovery”:
“Particle Accelerators”
Just over 52 years ago I walked into my office here in RAL to start a career in accelerators the particle they drive.
There were no books no accelerator schools and I, like you, was hungry for information -.
People kept talking about quadrupoles and I almost daren’t ask what they were
Now I’m here to hope fill up a similar hole in your information in one hour.
I strongly advise you to read these books (particularly the black one).
You will have read my abstract and know why I think this is important.
If you are really interested send me an and I will help you follow the JAI course starting tomorrow.