MPhys Physics with Study in Europe

This unit provides a broad, physics-based introduction to particle accelerators and beam dynamics, covering how charged particle beams are generated, guided, focused, and accelerated in modern machines. It also introduces key applications, from high-energy colliders and light sources to plasma physics and advanced acceleration concepts. 

In this unit students will learn the working principles of particle accelerators, their applications and the future trend of the field. Students will be able to understand the main features of single particle motions in particle accelerators, accelerator design, plasma and wave phenomenon in plasmas. 

On the successful completion of the course, students will be able to:  

• Understand the concepts of particle accelerators and their applications. 
   
• Understand basic building blocks of particle accelerators and their functions.
   
• Demonstrate knowledge of beam dynamics in accelerators, including transverse and longitudinal single particle motion.
   
• Explain the principles of synchrotron radiation, free electron lasers and analyse the working principles of various colliders and their applications.
   
• Explain key features of plasmas, single particle motion and wave phenomena of plasmas.
   
• Examine novel acceleration methods including plasma and structure-based acceleration.

Week 1: Introduction

Basic mathematics and relativity, Various particle accelerators, high voltage accelerators, linac, cyclotron, synchrotron, basic working principles. Brief introduction on applications of particle accelerators in industry, medical and particle physics.

Weeks 2 and 3: Transverse Beam Dynamics  

Accelerator coordinators, various magnets and their configurations, bending, focusing,

Hill’s equation, solution to Hill’s equation, phase space, emittance and acceptance, matrix formalism, stable motion, betatron tune, dispersion, FODO cell, phase advance, TME lattice.

Week 4: Longitudinal Beam Dynamics  

Acceleration, bunches and buckets, pill-box cavity, RF cavities, synchronism, phase stability, phase slippage, transition energy, synchrotron tune, smooth approximation, separatrix.

Week 5: Accelerator Lattice Design

FODO cells, achromats, synchrotron lattices, insertions, practical lattice design, matching, MAD-X

Weeks 6 : Synchrotron Radiation and Free Electron Lasers  

Radiation sources, radiation power and spectrum, radiation from bending magnets, insertion devices, wiggler magnet radiation, undulator radiation, photon distribution, small gain regime, FEL gain, high gain free electron lasers, SASE and other novel FEL schemes, European XFEL and LCLS-II overview.

Week 7: High Energy Colliders  

Colliders, fix-target, head-on collision, luminosity, beam-beam effect, crab cavity

Past and future colliders such as SLC, KEKB, LEP, Tevatron, HERA, LHC (HL-LHC), ILC, CLIC, FCC, Muon colliders.

Weeks 8 and 9: Introduction to plasmas  

Definition of plasmas, plasma shielding, plasma oscillations, plasma parameter, single particle dynamics, drift motion, mirror trapping, collisions in plasmas, waves in plasmas, plasma applications (i.e. in fusion and astrophysical plasmas).

Week 10: Novel particle acceleration schemes  

Laser wakefield acceleration (LWFA), electron driven wakefield acceleration (PWFA), proton driven wakefield acceleration (AWAKE), THz driven accelerators, dielectric wakefield acceleration (DWA), colliders based on advanced acceleration schemes

Week 11: Revision, summary and project work

Weekly cycle

1. 7 or 8 10 mins videos prerecorded and released before the lecture each week;

2. 2 hours face-to-face lectures by highlighting the key contents of each week by one leading academic;

3. 1 hour delivered by the PG Teaching Assistants, with each week designed questions, computing problems. The solutions and feedback will be provided as well.

4. Notes will be released covering the weekly material.

5. Weekly Canvas-based multiple choice formative assessment.

weeks 1-6 : weekly problem-solving class weeks, 7-11 computational laboratory. 

1. R. Appleby et al., The Science and Technology of Particle Accelerators, CRC Press, 2021.

2. S. Y. Lee’s book, Accelerator Physics (4th edition), World Scientific, 2021.

3. H. Wiedemann, Particle Accelerator Physics (4th edition), Springer, 2019.

4. F. Chen, Introduction to Plasma Physics and Controlled Fusion, 3rd Edition, Springer 2019.