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# Plasma Physics for Fusion - PHY00001M

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• Department: Physics
• Module co-ordinator: Dr. David Dickinson
• Credit value: 10 credits
• Credit level: M
• Academic year of delivery: 2022-23

• None

• None

## Module will run

Occurrence Teaching cycle
A Autumn Term 2022-23

## Module aims

Fusion, whether by inertial confinement or magnetic confinement, requires deuterium and tritium to be heated to such high temperatures that the electrons are stripped from the ions. The resulting conducting gas is called a plasma. Plasmas are common place around the universe so the topic of plasma physics is important in many branches of science including astrophysics and solar physics, as well as having industrial applications. This course aims to introduce the basic plasma physics principles through a combination of physical pictures and mathematical analyses, often using examples from fusion to provide specific applications.

## Module learning outcomes

Describe, both through physical pictures and mathematics, the orbits of individual particles in magnetic and electric fields: the cyclotron frequency, the guiding centre, the ExB drift, the gradB and curvature drifts and the polarisation drift

Write down expressions for the quantities that are conserved when a charged particle moves in a magnetic field: energy and magnetic moment. Use this principle to show how charged particles can be trapped in a magnetic mirror. Understand the limitations of a magnetic mirror for confining plasma for fusion

Demonstrate an understanding of the principles of magnetic confinement in a toroidal magnetic field configuration, including the roles of both the poloidal and toroidal magnetic fields. Describe the basic principles of tokamak operation.

Describe the process of inertial confinement fusion.

Describe the physics of Debye shielding and be able to derive the Debye length mathematically. Write down the definitions of a plasma.

Demonstrate an understanding of the distribution function and how to derive plasma density and flow by integrating over velocity space.

Without rigorous mathematical derivation, describe how plasma fluid equations can be obtained from the kinetic equations for plasma evolution. Given the fluid equations, describe the physics of the individual terms. Derive the ideal MHD equations from the 2-fluid equations. Describe, without proof, the concept of "frozen in" magnetic field.

Given the fluid equations, derive the diamagnetic drift. Provide a physical explanation for the origin of the diamagnetic drift, including why it is not experienced by a single particle.

Demonstrate an understanding of equilibria for cylindrical and toroidal plasma systems. Derive the equilibrium relations for cylindrical systems. Describe qualitatively the features of toroidal equilibria including the origin of the Grad-Shafranov equation (without rigorous proof); the concept of toroidal flux surfaces, and definitions of equilibrium quantities such as aspect ratio, safety factor, major and minor radius, etc.

Perturb and linearise the equilibrium equations. As examples, be able to derive expressions for the frequency of basic plasma waves: Langmuir wave, ion sound wave. Describe the physics responsible for the wave.

## Module content

PPfF Syllabus

• Charged particle orbits and drifts
• Magnetic mirror and toroidal magnetic confinement
• Debye shielding and formal definition of a plasma
• Inertial confinement
• Distribution functions and velocity space integration
• Kinetic equation and fluid equations, diamagnetic drift
• Ideal magneto-hydrodynamics (MHD), plasma equilibrium
• Plasma waves: Langmuir wave, sound wave

## Assessment

Task Length % of module mark
Online Exam - 24 hrs (Centrally scheduled)
Plasma Physics for Fusion
8 hours 100

None

### Reassessment

Task Length % of module mark
Online Exam - 24 hrs (Centrally scheduled)
Plasma Physics for Fusion
8 hours 100

## Module feedback

Our policy on how you receive feedback for formative and summative purposes is contained in our Department Handbook.

Chen F F: Introduction to plasma physics and controlled fusion (Plenum) ***

Wesson: Tokamaks, Oxford Science Publications ***

Atzeni and Meyer-ter-Vehn: The physics of inertial fusion (Oxford Science) **

Boyd T J M & Sanderson J J: The physics of plasma (CUP) **

Cairns R A: Plasma physics (Blackie) **

Dendy R O: Plasma dynamics (OUP) **

Goldston & Rutherford: Introduction to plasma physics (IoP) **

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.