The aim is to carefully introduce the basic ideas and concepts and transverse and longitudinal beam dynamics, for students working in all areas of accelerator physics.

Pre-requisites

Electromagnetism, mechanics, relativity at undergraduate level.

Syllabus

Introduction
Let’s look at a synchrotron
Periodicity and stability
Hierarchy of beam descriptions
SHM and the pendulum
Newton and Hamilton

Hill’s equations
Beams and magnets
Derivation of Hill’s equations
The transfer matrix approach
Matrix properness

Lattice functions
Lattice functions
The Courant-Synder formalism
How to transform the lattice functions
Stability
Tune

Optics and lattice design
The FODO cell
Lattice design
Mini beta insertions
Principles of lattice design
Optical structures

Errors in our lattice
Field errors
Closed orbit distortion
Tune shifts

Real particles
Dispersion
Momentum compaction Chromaticity
Emittance

Longitudinal dynamics
The principle of phase stability
The pill-box cavity and real cavities
Longitudinal dynamics
Buckets and bunches

## Aim

The aim is to carefully introduce the basic ideas and concepts and transverse and longitudinal beam dynamics, for students working in all areas of accelerator physics.## Pre-requisites

Electromagnetism, mechanics, relativity at undergraduate level.## Syllabus

IntroductionLet’s look at a synchrotron

Periodicity and stability

Hierarchy of beam descriptions

SHM and the pendulum

Newton and Hamilton

Hill’s equationsBeams and magnets

Derivation of Hill’s equations

The transfer matrix approach

Matrix properness

Lattice functionsLattice functions

The Courant-Synder formalism

How to transform the lattice functions

Stability

Tune

Optics and lattice designThe FODO cell

Lattice design

Mini beta insertions

Principles of lattice design

Optical structures

Errors in our latticeField errors

Closed orbit distortion

Tune shifts

Real particlesDispersion

Momentum compaction Chromaticity

Emittance

Longitudinal dynamicsThe principle of phase stability

The pill-box cavity and real cavities

Longitudinal dynamics

Buckets and bunches

Radiation effectsSynchrotron radiation

Damping effects (directed reading)

## Lecture Notes

Part 1, Part 2