S35 Particle Detectors and Accelerators

Accelerator Physics by Professor Adrian Oeftiger

Lecture 1: Introduction to Accelerators

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Today!

1. Intro to Accelerators
2. Accelerator Types
3. Facilities and Applications
4. Time Scales

A 2010 report titled Accelerators for Americas Future on the usefulness of particle accelerators:

"A beam of the right particles with the right energy at the right intensity can

• shrink a tumor,
• produce cleaner energy,
• spot suspicious cargo,
• make a better radial tire,
• clean up dirty drinking water,
• map a protein,
• study a nuclear explosion,
• design a new drug,

• make a heat-resistant automotive cable,
• diagnose a disease,
• reduce nuclear waste,
• detect an art forgery,
• implant ions in a semiconductor,
• prospect for oil,
• date an archaeological find,
• package a Thanksgiving turkey,

or... discover the secrets of the universe."

Accelerator Physics

Accelerators $\Longleftrightarrow$ Plasma

images: CERN and EPFL

• single-particle vs. multi-particle effects
• non-linear dynamics vs. collective instabilities

What fields make a "particle accelerator"?

$$\begin{matrix}\,\text{beam self fields} &>& \text{external applied fields} &\text{(plasma)} \\ \text{beam self fields} &\ll& \text{external applied fields}& \text{(accelerator)}\end{matrix}$$

$\implies$ perturbation technique applicable to higher-energy accelerators:

$$\begin{cases} \text{unperturbed motion} &= \text{external fields} \\ \text{perturbation} &= \text{self fields} \end{cases}$$

We will study: how to accelerate and focus a particle beam!

How many accelerators exist worldwide?

B.L. Doyle et al., "The Future of Industrial Accelerators and Applications" (2019)

What are accelerators used for?

Field	Application	Worldwide (%)
Research		7.6%
	Particle Physics	0.2%
	Nuclear Physics, solid state, materials	0.2–0.9%
	Neutron generators ...	6.5%
Medical Applications		33.1%
	Hadron therapy	0.2%
	Radioisotope production	3.2%
	Radiotherapy Linacs ...	29.7%
Industrial Applications		<60%
	Ion implantation	34.0%
	E-beam material processing	10.8%
	Non-destructive inspection	7.5%
	E-beam irradiation ...	6.9%

• S. Sheehy, "Applications of Particle Accelerators" (2024)

• A. Kambondo and Jie Wang, "Review on Digital Twin Applications in Medical Particle Accelerators" (2026)

Overview: beam control in accelerators

3 key beamline elements, exploiting Lorentz force:

$$F=q(\mathbf{E}+\mathbf{v}\times\mathbf{B})$$

1. radio-frequency (rf) cavities for bunching and acceleration
2. dipole magnets for steering
3. quadrupole magnets for (transverse) focusing

$\implies$ enforce oscillations to contain particles!

(Physicists like their harmonic oscillators...)

images: CERN

Circular accelerator: spot the 3 key beamline elements

One "Electron Volt"

1 eV $=$ gained kinetic energy of particle with elementary charge after traversing 1 V potential difference

Wave Lengths for Probing Structures

Energy Scales

$\implies$ Use photons just as well as electrons or protons/neutrons/ions (matter waves!) to probe

from scipy.constants import h, c, e, m_n

de Broglie wave length: $\lambda = \cfrac{h}{p}$ with relativistic momentum $p=\gamma m v$ and kinetic energy $E_{kin}=\sqrt{p^2c^2+m^2c^4}-mc^2$

lambda_ = 1e-10 # wave length in m
mass = m_n # mass (e.g. neutron, m_n)

p = (h / lambda_ / (e/c)) # momentum in eV/c
Ekin = ((p**2 * c**2 + mass**2 * c**4) - mass * c**2 ) * e
f"momentum p={p:.2e} eV/c, energy Ekin={Ekin:.2e} eV"

'momentum p=1.24e+04 eV/c, energy Ekin=2.21e+06 eV'

Major accelerator types

	Linac	Cyclotron	Synchrotron
How it accelerates	Single-pass RF cavities (linear)	Circular motion with fixed RF frequency	Circular motion with RF acceleration + ramped magnetic field
Particle type	Protons/ions & electrons	Protons/ions	Protons/ions & electrons
Energy limit	MeV .. GeV+ (length / gradient limited)	~10 .. 500 MeV (relativistic dephasing)	GeV .. TeV (magnetic field & radius)
Key feature	Single-pass acceleration (no recirculation)	Compact, quasi-continuous beam, high duty-cycle	Multi-turn acceleration with energy ramping (ms .. s timescale)
Typical uses	Injectors, Free Electron Lasers, medical linacs	Isotope/neutron/muon production, proton therapy	Colliders, light sources, hadron therapy
Example	UNILAC (GSI, Darmstadt/DE)	Ring Cyclotron (PSI, Villigen/CH)	LEIR (CERN, Geneva/CH)

Major accelerator types cont'd

	Plasma accelerator
How it accelerates	Plasma wakefields accelerate injected electrons (linear)
Particle type	electrons (primarily)
Energy limit	GeV-scale demonstrated (limited by staging & beam quality)
Key feature	Wakefields driven by lasers or particle beam; extremely high gradients (100 GV/m) → very compact; single-pass acceleration / no recirculation
Typical uses	R&D (goals: compact light sources, future colliders, ultrashort bunches)
Example	AWAKE (CERN, Geneva/CH)

UK Diamond Light Source

Accelerate electrons and store at 3 GeV. Bending = synchrotron radiation

$\leadsto$ highly focused, tunable and intense photon beams

$\implies$ probe atomic structure and material properties (proteins, drugs, batteries, archaeological artifacts, ...)

images: Diamond Light Source

UK ISIS Neutron and Muon Source

Accelerate protons to 800 MeV at 50 Hz. Impact on heavy-metal target = spallation

$\leadsto$ pulsed neutron and muon beams (time-of-flight measurements)

$\implies$ probe structure and dynamics of materials (quantum materials, superconductors, chemicals, engines, archaeological artifacts, ...)

(1) proton source and Linac,
(2) rapid cycling synchrotron,
(3) targets

images: ISIS

CERN: European Organization for Nuclear Research

Collide particles at highest possible energies!

$\implies$ probe fundamental structure of matter

image: CERN

CERN accelerator complex

Stepwise acceleration of protons to 7 TeV:

LINAC4 (160 MeV)

$\rightarrow$ Proton Synchrotron Booster (2 GeV)

$\rightarrow$ Proton Synchrotron (26 GeV)

$\rightarrow$ Super Proton Synchrotron (450 GeV)

$\rightarrow$ Large Hadron Collider (7 TeV)

$\implies$ store and collide for typically 10 .. 20h: high-energy physics experiments!

How many protons are in a beam, how many collide?

image: CERN

World-record LHC Fill Duration

image: CERN LHC OP logbook 2022

$\leadsto$ 57h of beam storage $=$ how many turns in 27 km long LHC?

"%e turns" % (57 * 60 * 60 * c / 27e3)

'2.278423e+09 turns'

Time Scales in a Synchrotron

A turn $\sim$ 1..100 μs:

• many per turn: transverse (betatron) oscillations
• once per turn: observation in a wall current monitor
• 100s of turns: longitudinal (synchrotron) oscillations
• 100s of turns: $e$-fold damping time of feedback systems
• 100'000s to $>$ millions of turns: storage times

(compare: stability of the Earth's orbit around the Sun (age: 4.6 bya))

Precise control required!

Study accelerators experimentally, computationally and analytically $=$ accelerator physics!

$\implies$ control and predict stability across these time scales!

$\implies$ learn about required basic concepts in the following lectures! :-)

Summary

1. Intro to Accelerators
   • similarities to plasma physics, importance of external fields
   • rf cavities, dipole and quadrupole magnets
2. Accelerator Types
   • linear accelerators (linacs)
   • cyclotrons
   • synchrotrons
3. Facilities & Applications
   • light sources
   • neutron spallation sources
   • high-energy physics
4. Time Scales

Literature:

• A. Wolski, Beam Dynamics in High Energy Particle Accelerators
• S.Y. Lee, Accelerator Physics