The course comprises four lectures covering the main ideas of Special Relativity and Electromagnetism that will be needed for work in accelerator physics. The lectures review material that should already have been studied in most undergraduate physics degrees, so some familiarity with the subject will be assumed. Historically, Maxwell's electromagnetic theory revealed light to be an electromagnetic phenomenon whose speed of propagation proved to be observer-independent. This discovery led to the overthrow of classical Newtonian mechanics, in which space and time were absolute, and its replacement by Special Relativity and space-time. The theories together with quantum theory are essential for an understanding of modern physics; in particular, without these discoveries, accelerators would not work!

Synopsis:

Relativity (2 lectures) Historical overview. Constancy of the speed of light; Lorentz transformations; time dilation, length contraction and the relativistic Doppler effect. Four-vectors; four-velocity and four-momentum; equivalence of mass and energy; particle collisions and four-momentum conservation; four-acceleration and four-force. Examples illustrating the use of four-vectors. Inter-relation between relativistic quantities used in accelerator physics. An accelerator problem in relativity. As time permits: Relativistic particle dynamics; Lagrangian and Hamiltonian Formulation; radiation from an accelerating charge. Photons and the wave four-vector. Motion faster than the speed of light

Electromagnetism (2 lectures) Review of Maxwell’s equations; interconnection between E and B fields with worked examples. The Lorentz force law; motion of a charged particle under constant electric and magnetic fields. Relativistic transformations of E and B fields. (If time permits: Potentials, E/M four-vectors; worked example.) Electromagnetic energy conservation. Review of waves; phase velocity, group velocity; electromagnetic waves in (i) vacuo, (ii) conducting media. Waves in a uniform conducting guide: a simple example, idea of propagation constant, cut-off frequency, illustrations.

Level and Pre-requisites:

Previous exposure to simple ideas of relativity and a knowledge of Maxwell’s equations of Electromagnetism. Familiarity with basic vector calculus including the use of div, grad and curl and standard theorems such as Gauss, Stokes and Green.

## Synopsis:

Relativity (2 lectures)Historical overview. Constancy of the speed of light; Lorentz transformations; time dilation, length contraction and the relativistic Doppler effect. Four-vectors; four-velocity and four-momentum; equivalence of mass and energy; particle collisions and four-momentum conservation; four-acceleration and four-force. Examples illustrating the use of four-vectors. Inter-relation between relativistic quantities used in accelerator physics. An accelerator problem in relativity. As time permits: Relativistic particle dynamics; Lagrangian and Hamiltonian Formulation; radiation from an accelerating charge. Photons and the wave four-vector. Motion faster than the speed of light

Electromagnetism (2 lectures)Review of Maxwell’s equations; interconnection between E and B fields with worked examples. The Lorentz force law; motion of a charged particle under constant electric and magnetic fields. Relativistic transformations of E and B fields. (If time permits: Potentials, E/M four-vectors; worked example.) Electromagnetic energy conservation. Review of waves; phase velocity, group velocity; electromagnetic waves in (i) vacuo, (ii) conducting media. Waves in a uniform conducting guide: a simple example, idea of propagation constant, cut-off frequency, illustrations.

Previous exposure to simple ideas of relativity and a knowledge of Maxwell’s equations of Electromagnetism. Familiarity with basic vector calculus including the use of div, grad and curl and standard theorems such as Gauss, Stokes and Green.Level and Pre-requisites: