# MMath&Phys Mathematics and Physics

Year of entry: 2023

## Course unit details:Nuclear Fusion and Astrophysical Plasmas

Unit code PHYS30511 10 Level 3 Semester 1 Department of Physics & Astronomy No

### Overview

Nuclear Fusion and Astrophysical Plasmas

### Pre/co-requisites

Unit title Unit code Requirement type Description
Electromagnetism PHYS20141 Pre-Requisite Compulsory
Mathematics of Waves and Fields PHYS20171 Pre-Requisite Compulsory
Statistical Mechanics PHYS20352 Pre-Requisite Compulsory

### Aims

To introduce the concept of plasma as the fourth state of matter, and to show why the study of plasma is important in contemporary physics; to give a grounding in the theory explaining the basic properties of the plasma state; to develop an understanding of the principles of fusion research as well as some plasma phenomena observed in space and astrophysics.

### Learning outcomes

On completion of the course, students should be able to demonstrate an understanding of:

1. the basic concepts, parameters and modelling approaches of plasma physics;
2. single particle motion in plasmas;
3. the macroscopic (fluid) plasma model, including simple magnetohydrodynamic descriptions of equilibrium, Alfven waves and magnetic reconnection;
4. the  reactions and power balance relevant to controlled nuclear fusion and the principles of various approaches to controlled fusion;
5. the  physics behind such phenomena as the Earth's radiation belts, solar and stellar coronae, solar and stellar flares, the solar wind and its interaction with planetary magnetospheres.

### Syllabus

1. Introduction to fusion and astrophysical plasmas
What is a plasma? Overview of natural and man-made plasmas. Fusion reactions and energetics; the Lawson criterion. Magnetic confinement fusion devices; the tokamak. Inertial confinement and lasers. Magnetic fields and activity in the heliosphere.

2. Basic concepts and parameters of plasma physics

Quasi-neutrality and Debye length. Plasma frequency. Collisions. Magnetic fields.

3.  Single particle motion in non-uniform magnetic and electric fields

Drift approximation and guiding-centre theory. Magnetic moment and mirroring. The Earth's magnetic field and radiation belts. Particle orbits and confinement in tokamaks.

4.  The magnetohydrodynamic description

Fluid model of plasmas,  equations of MHD. Magnetic Reynolds number, ideal MHD. Magnetostatic equilibrium and force-free magnetic fields; solar prominences and loops, pinches, tokamaks. Alfven waves. Instabilities. The  solar wind. Magnetic reconnection; solar and stellar  flares, planetary magnetospheres, reconnection in fusion plasmas. The structure of the Earth’s magnetosphere.

### Assessment methods

Method Weight
Written exam 100%

### Feedback methods

Feedback will be available on students’ individual written solutions to examples sheets, and model answers will be issued.

Recommended texts:
Chen, F.F. Plasma Physics and Controlled Fusion (Plenum Publishers)

Gurnett, D.A. and Bhattarcharjee A. Introduction to Plasma Physics with Space and Fusion applications (Cambridge U.P.)

Inan, U.S.  and Golkowski. M.  Principles of Plasma Physics for Engineers and Scientists   (Cambridge U.P.)

Baumjohann, W. & Treumann, R.A. Basic Space Plasma Physics (Imperial College Press

J. Friedberg, J. Plasma Physics and Fusion Energy (Cambridge U.P.)

Goedbloed, H. & Poedts, S. Principles of Magnetohydrodynamics with Applications to Laboratory and Space Plasmas (Cambridge U.P.)

Golub, L. and Pasachoff, J.M. The solar corona (Cambridge U.P.)

McCracken,G. and Stott,P.  Fusion: the energy of the universe (Elsevier)

Stacey, W.M. Fusion (Wiley)

### Study hours

Scheduled activity hours
Assessment written exam 1.5
Lectures 22
Independent study hours
Independent study 76.5

### Teaching staff

Staff member Role
William Bertsche Unit coordinator