**Friday week 2, Lindermann lecture theatre, 4:00 – 6:00 pm**

*Elementary Group Theory – The Absolute Essentials by Ching Lok Chong*

Description:

Often times in physics we speak of symmetries and their importance in our conceptual understanding of the physical world, and this has prompted the extensive use of group theory. However, the idea of an abstract group extends far beyond physical applications, and can in fact be argued as one of the simplest structures in algebra. It is because of this generality that many mathematical objects familiar to us can be described as groups.

This class investigates the general structural properties that arise in anything we could call a group, namely subgroups, homomorphisms, and most importantly, the first isomorphism theorem, which (in some sense) is a powerful generalisation on the phenomena encountered in modular arithmetic.

**Friday week 4, Lindermann lecture theatre, 4:00 – 6:00 pm**

*Introduction to Green’s functions by Edmund Woolliams*

Description:

This lecture explores the basic applications of Green’s functions to solving general linear inhomogeneous ordinary differential equations, and the physical applications. Uses for solving linear inhomogeneous partial differential equations will be touched upon, with Poisson’s equation as an example. It is tailored towards those in second year physics and above, however an affluent first year student should not be discouraged, as the very basics will be brushed over (albeit fast).

Green’s functions are unfortunately an area of mathematics that are given little to no attention on the current undergraduate syllabus, yet they play an important role in many branches of physics. Hopefully this lecture will reduce future confusion with them, and give an interesting insight into how inhomogeneous differential equations can be solved.

**Friday week 5, Lindermann lecture theatre, 4:00 – 6:00 pm**

*A history of thermonuclear fusion – magnetic confinement and inertial confinement by Steven Rose*

Description:

Thermonuclear fusion powers the Sun, and the creation of controlled thermonuclear fusion on earth for energy generation has been a goal of many scientists and engineers since the 1940s. Two major schemes have been investigated to date. The first involves magnetic confinement, where the hot plasma of deuterium and tritium (the thermonuclear fuel) is held in place by strong magnetic fields. The second is inertial confinement, where the inertia of the plasma confines it for long enough for fusion to take place. Magnetic confinement fusion (MCF) was first discussed in public in 1956 at a famous meeting at Harwell at which the Russian programme was revealed to the West and since that time there has been an open international exchange of information and results. The world’s largest MCF device (called the Joint European Torus) is at the Culham Laboratory just south of Oxford and was the first device to generate (in 1997) about as much energy as it consumed, albeit for a time of the order of seconds. The next generation device called ITER (the International Thermonuclear Experimental Reactor) is currently being built at Cadarache in France. Inertial Confinement Fusion (ICF) was first discussed in public in 1972 in a famous paper published in Nature by John Nuckolls and colleagues at the Lawrence Livermore National Laboratory (LLNL) in the USA. The idea in the Nature paper is to compress and heat a small capsule containing a mixture of deuterium and tritium using high-power lasers. The compressed fuel is at this point in the plasma state and thermonuclear reactions take place until the fuel disassembles. Most recently experiments at the National Ignition Facility, a 2MJ laser at LLNL, have shown (in 2014) energy production that exceeds the thermal energy of the thermonuclear plasma. However ICF is still a long way from demonstrating energy gain – more energy from the thermonuclear reactions than is input from the laser. In this class we will look at the long histories of both MCF and ICF and discuss their future prospects.

**Friday week 7, Lindermann lecture theatre, 4:00 – 6:00 pm**

*Un-magnetised Plasmas – A journey into Hermite Space by Toby Adkins*

Description:

In this class, we shall first explore some of the basic concepts of kinetic plasma theory, before moving on to look at a 2D phase space model of non-linear plasma turbulence. We will arrive at quite an informative, and interesting result, while learning how to handle non-linear systems and scalings. It is recommended that students have at least done part of the Kinetic Theory Second Year Course.