Department: PhysicsModule co-ordinator: Dr. David DickinsonCredit value: 20 creditsCredit level: MAcademic year of delivery: 2022-23

- See module specification for other years: 2021-22

## Pre-requisite modules

- None

## Co-requisite modules

- None

## Prohibited combinations

Occurrence | Teaching period |
---|---|

A | Autumn Term 2022-23 to Spring Term 2022-23 |

This module has two components. The first provides a basis for understanding the physics of plasmas in general and includes a discussion of laboratory plasmas and in particular the application of plasma physics to fusion. The second applies this knowledge to describe space and astrophysical plasmas. This module will convey how our understanding of plasma physics extends to a description of a huge diversity of systems over hugely varying scales of space, time, density, and temperature.

**Plasma Physics for Fusion (PPfP):** 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. This course draws on the considerable research expertise in York

**Astrophysical Plasmas (APP):** Plasma fills much of space from the interior of the Sun to the upper layers of the Earth's atmosphere, the Solar System, Galaxy and beyond. We start from an energy budget of the interstellar mediumand a description of astrophysical plasmas and then quickly move from basic plasma physics parameters of astrophysical plasmas to hydro- and magnetohydro- dynamics. The focus is on the dynamics of the interstellar medium, the processes that heat and cool interstellar medium, and the effects of stellar winds, shocks associated with supernova remnants, and jets. This includes a discussion of the role of magnetic fields and the acceleration of cosmic rays. Finally, we identify and use dimensionless scaling of plasma models to link laboratory plasmas to the study of fundamental plasma processes that occur in astrophysical plasmas.

**PPfF Subject content**

- 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 fieldconfiguration, 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.

**APP Subject content**

- State typical characteristics of various astronomical plasmas.
- Outline the sources and losses of radiation in astronomical systems and effects this has on the systems.
- Understand the effect of stellar radiation emitted on the surrounding interstellar medium.
- Explain the role of collisions in gases and plasmas and the Coulomb logarithm.
- Explain the phenomenon of collisionless plasmas and ‘effective’ collisions.
- Determine when a fluid approximation can be applied to plasma.
- Explain the meaning of ideal magneto-hydrodynamics or MHDs, and know when such models are applicable.
- Explain the need for an equation of state (in polytropic form) and Ohm’s law and be able to use them.

•Describe viscosity, thermal conductivity and magnetic field diffusion and identify

situation when these are not important. Outline the approximations used to derive

hydrodynamic magnetohydrodynamics (MHDs) models.

- Explain the concept of flux freezing and the impact this has on astrophysics.
- Derive Rankine-Hugoniot relations and be able to apply them to astrophysical phenomena in the shock and stellar frame. Explain the effects radiation and magnetic fields can have on shocks.
- Describe the evolution of supernova remnants and the impact these systems have on the interstellar medium.
- Explain evidence that suggests supernova remnants are the source of Galactic cosmic rays, diffusive shock acceleration and the importance of cosmic rays in the interstellar medium.
- State the origin of stellar winds, and explain why the solar wind is supersonic and describe the interaction with a magnetosphere.
- Through scaling of the ideal hydrodynamic and magneto-hydrodynamic equations show how laboratory experiments can simulate dynamical aspects of astronomical plasmas.

**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

**APP Syllabus**

- The diversity of space and astrophysical plasmas and the interstellar medium
- Introduction to hydrodynamics and MHD dynamics, shocks and the concept of dimensionless scaling
- Kinetically driven systems: stellar winds, Supernova explosions, remnants, and blast waves
- Radiation driven systems: nebulae and Strömgren spheres
- Relativistic particles: cosmic rays
- Laboratory facilities and type of experiments undertaken

**Lecture notes**

Students are expected to take their own notes during lectures. A set of skeleton notes will be made available online at the end of the course.

Task | Length | % of module mark |
---|---|---|

Online Exam - 24 hrs (Centrally scheduled)Advanced Plasma Physics: Astrophysical Plasmas |
8 hours | 50 |

Online Exam - 24 hrs (Centrally scheduled)Advanced Plasma Physics: Plasma Physics for Fusion |
8 hours | 50 |

None

Task | Length | % of module mark |
---|---|---|

Online Exam - 24 hrs (Centrally scheduled)Advanced Plasma Physics: Astrophysical Plasmas |
8 hours | 50 |

Online Exam - 24 hrs (Centrally scheduled)Advanced Plasma Physics: Plasma Physics for Fusion |
8 hours | 50 |

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

**PPfP**

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 and Sanderson J J: *The physics of plasma *(CUP) **

Cairns R A:* Plasma physics* (Blackie) **

Dendy R O:* Plasma dynamics *(OUP) **

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

**APP**

Choudhuri A R:* Physics of Fluids and Plasmas *(CUP 1998)

Drake R P: *High-Energy- Density Physics: Fundamentals, Inertial Fusion, and Experimental Astrophysics* (Springer 2006)

Dyson J E, Williams D A: *The Physics of the Interstellar Medium* (PUP 1997) ***

Frank J, King A, Raine D:* Accretion Power in Astrophysics* (CUP 2002)

Kulsrud R M, Spergel D: *Plasma Physics for Astrophysics* (PUP 2005)

Longair M S:* High Energy Astrophysics* (CUP 2011) ***

Parks G: *An Introduction Physics of Space Plasmas *(Perseus 2003)

Shu F H: *The Physics of Astrophysics: Gas Dynamics* (University Science Books 1992)