Some lecturers may provide additional recommended reading and resources on the Indico pages.
Special Relativity, Electro-magnetism and Formalisms for Classical Mechanics
What to remember for particle accelerators.
Pre-recorded videos from the ARIES MOOC to be viewed prior to the live revision session on Day 1
Transverse Beam Dynamics
The Ideal Storage Ring: Lorentz force & particle momentum - defining the magnetic guide field / Focusing elements & the equation of motion / Single particle trajectories / Matrix description of lattice elements
Particle Trajectographies in a Circular Accelerator: Beam orbit / Transverse particle oscillation and tune / Defining the beam size / General solution of the equation of motion: the amplitude betatron function / Phase space area of a particle ensemble: Beam emittance / Stability criterion in periodic structures.
Lattice Design in Particle Accelerators: Calculation of the optical parameters / FoDo cells: design and optimisation / Interaction regions: the low beta insertion.
Changing the Particle Momentum: beam acceleration and adiabatic shrinking of the emittance / Dispersion trajectories / Orbit lengthening and the momentum compaction factor.
Errors in Field and Gradient: Quadrupole errors and tune shift / Chromaticity and its correction / Sextupole magnets and the dynamic aperture
Introduction to the principles of beam optics / Analytical treatment of the motion of charged particles in electric and magnetic fields / Guiding and focusing electrostatic and magnetostatic devices / Equations of motion of charged particles in optical assemblies / Transport matrix / Phase space, emittance, beam matrix / Examples of optical systems and their treatment: spectrometer, mass separator ...
Longitudinal Beam Dynamics
Fields and forces / Acceleration by time varying fields / Relativistic equations
Overview of acceleration / Transit time factor / Main RF parameters / Momentum compaction factor / Transition energy
Equations related to synchrotrons / Synchronous particle / Synchrotron oscillations / Principle of phase stability
RF acceleration for synchronous and non-synchronous particles / Small and large amplitude oscillations
Prerequisites: classical mechanics and electromagnetism
A description of the potential and limitation of the MAD-X code will be given together with daily-life tricks and fully-fledged examples.
The MAD-X tutorials will be complementary to the transverse dynamics ones for putting in practice the transverse beam dynamics theory
Transverse Linear Imperfections
Closed orbit distortion (steering error): Beam orbit stability importance / Imperfections leading to closed orbit distortion / Dispersion and chromatic orbit / Effect of single and multiple dipole kicks / Closed orbit correction methods
Optics function distortion and gradient error: Imperfections leading to optics distortion / Tune-shift and beta distortion due to gradient errors / Gradient error correction
Coupling error: Coupling errors and their effect / Coupling correction
Basic methods of linear acceleration / Fundamental parameters of accelerating structures / Energy gain in linear accelerating structures / Single particle dynamics in linear accelerators / Multi-particle dynamics in linear accelerators.
Prerequisites: general mechanics, Maxwell equations, relativistic dynamics in magnetic and electric fields, maths for physicists and engineers (Fourier transform, Bessel functions...)
Introduction to synchrotron light sources / Radiation of accelerated charged particles / Radiation from bending magnets / Radiation from undulators and wigglers / Electron dynamics with radiation / Brightness and Low emittance lattices / Introduction to FELs / Workshop: “Design your light source”
Transverse Non-linear Effects
Accelerator performance parameters and non-linear effects
Linear and non-linear oscillators: Integral and frequency of motion / Pendulum / Damped harmonic oscillator
Phase space dynamics: Fixed point analysis
Non-autonomous systems: Driven (damped) harmonic oscillator / Resonance conditions
Linear equations with periodic coefficients - Hill’s equations: Floquet solutions and normalized coordinate
Perturbation theory: Non-linear oscillator / Perturbation by periodic function – single dipole perturbation / Application to single multipole – resonance conditions / Examples: single quadrupole, sextupole, octupole perturbation / General multi-pole perturbation / Examples: linear coupling / Resonance conditions and working point choice
Resonances and the path to chaos: Topology of 3rd and 4th order resonance / Path to chaos and resonance overlap / Dynamic aperture
Frequency map analysis: NAFF algorithm / Aspects of frequency maps / Frequency and diffusion maps for the LHC / Frequency map for lepton rings / Working point choice / Beam-beam effect
Experiments: Experimental frequency maps / Beam loss frequency maps / Space-charge frequency scan
Twiss formalism / Special insertions / Accelerator design / Design workshop in groups
Collective Effects - Space Charge and Instabilities
Space charge force / Effects of space charge in circular accelerators / Wake fields and coupling impedances / Effects of wake fields in linear accelerator: the Beam Break Up example / Brief remarks on effects of wake fields in circular accelerators.
Prerequisites - maths: differential equations and Fourier transform / mechanics: free and driven oscillators / basic electromagnetism and boundary conditions
Cyclotrons and FFAs
Introduction and principle / Basic equations / Cyclotron components and subsystems / Beam dynamics, stability and focusing / Beam quality and phase space / Extraction / History and applications
Single-turn injection / Off-axis injection / Injection into the longitudinal phase space / Phase space matching / Topping-up / Fast extraction / Resonant extraction / Septum and kicker magnets