Turbulence and instabilities in magnetised plasmas. Volume 2, Gyrokinetic theory and gyrofluid turbulence. / Bruce Scott.

Format:

Book

Author/Creator:

Scott, Bruce, author.

Series:

IOP Series in Plasma Physics Series

Language:

English

Subjects (All):

Plasma instabilities.

Physical Description:

1 online resource (526 pages)

Edition:

First edition.

Place of Publication:

Bristol, England : IOP Publishing, [2021]

Summary:

This book is the second of a two-volume set, providing a comprehensive fundamental introduction to gyrokinetic theory and gyrofluid turbulence.

Contents:

Intro

Preface

Outline placeholder

Preface to both volumes

Author biography

Bruce Scott

Chapter 1 Prelude to volume two

1.1 Plasma, magnetised, parameters

1.2 Low frequency, flute mode ordering

1.3 Drifts, ExB flow, currents

1.4 Polarisation and quasineutrality

1.5 Turbulence

1.5.1 Energy and enstrophy

1.5.2 Magnetic field responses

1.6 Turbulence in magnetised plasmas

1.6.1 Adiabatic response

1.6.2 Two-fluid dynamics

1.6.3 Energetics

1.6.4 Total-f versus delta-f models

1.6.5 Mode structure

1.7 Kinetic theory, turbulence, and MHD instabilities

Further Reading

Chapter 2 Effects of the electron temperature

2.1 Introduction-electron temperature

2.2 Conservative effects

2.2.1 Parallel dynamics and energetics

2.2.2 Diamagnetic fluxes and energetics

2.2.3 Gradient forcing

2.3 Dissipative effects

2.3.1 Conventional treatment

2.3.2 Time dependent heat flux

2.4 Equations for magnetised plasma turbulence

2.5 Parameters, normalised equations, geometry

2.5.1 Parameters

2.5.2 Normalisation

2.5.3 Equations

2.5.4 Magnetic geometry

2.5.5 Numerics

2.6 Energetics

2.7 Heat flux and kinetic shear Alfvén waves

2.8 Drift Alfvén turbulence

2.8.1 Computational examples

2.9 Mode structure

2.9.1 Details of the energetics

2.10 Dependence on parameters

2.10.1 Electromagnetic induction

2.10.2 The heat flux versus its collisional form

2.10.3 Thermal effect on electromagnetic responses

2.11 Summary

Chapter 3 Effects of the ion temperature

3.1 Introduction-ion temperature as independent

3.2 The Larmor radius and gyro averaging

3.3 Gyroaveraging versus gyroviscosity

3.4 Effects on cold ion dynamics

3.5 Ion temperature gradient (ITG) modes

3.6 Warm-ion toroidal drift Alfvén model

3.6.1 Equations.

3.6.2 Energetics

3.7 Electromagnetic ITG turbulence in a hot plasma

3.7.1 Mode structure

3.7.2 Microtearing and the electron energetics

3.7.3 Gradient threshold

3.8 Warm ion drift Alfvén turbulence

3.8.1 Inductivity

3.8.2 Collisionality

3.8.3 Gradient synergy

3.8.4 The heat flux versus its collisional form

3.9 On gyroviscosity

3.9.1 Gyroviscous cancellation in the brackets

3.9.2 Effect on energetics

3.9.3 Effect on the turbulence

3.10 Summary

Chapter 4 Lagrangian field theory and drifts

4.1 Low frequency drifts

4.1.1 Meaning/significance of ExB drift motion

4.1.2 Outline of the rest of this lecture

4.2 Lagrangian field theory

4.3 Canonical representation

4.3.1 Canonical form

4.3.2 Canonical representation of electrodynamics

4.4 Lagrangian field theory in canonical form

4.4.1 Functional derivatives for the fields

4.4.2 For electrodynamics

4.5 Towards drifts

4.6 Quasineutrality

4.7 Interlude-Noether's theorem

4.7.1 Symmetry and total variations

4.7.2 Example of a single particle in a field

4.7.3 Self-consistent field

4.7.4 Maxwell's equations

4.7.5 Spatial dependence in the background

Chapter 5 Introduction to gyrokinetic theory

5.1 Ideas behind the gyrokinetic representation

5.2 Lagrangian basis of kinetic theory

5.2.1 Euler-Lagrange equations

5.3 The strategy of gyrokinetics

5.4 The drift-kinetic Lagrangian

5.5 The field variables as perturbations

5.6 The Lie transform

5.6.1 The Lie derivative

5.6.2 Initial arrangement

5.6.3 First order

5.6.4 Second order-polarisation

5.6.5 Collected result

5.7 The gyroaverage

5.7.1 Continuous basis

5.7.2 Integration space

5.8 The gyrocentre phase space density and flow

5.9 The gyrokinetic field Lagrangian.

5.9.1 Field equations

5.10 Simplified limits

5.10.1 Electrostatic polarisation

5.10.2 Linearised polarisation

5.10.3 No gyroaveraging in induction

5.10.4 Long wavelengths

5.10.5 Importance of energetic consistency

Chapter 6 Phase space and energetic consistency

6.1 Summary of ideas

6.2 Basic structure of the model

6.3 The Euler-Lagrange equations for gyrocentres

6.4 Symmetry in gyrocentre dynamics

6.4.1 Poisson bracket form

6.4.2 Phase space incompressibility

6.4.3 Phase space conservation

6.5 Application of Noether's theorem

6.6 Energy conservation

6.7 Momentum conservation

6.7.1 Plasma versus canonical momentum

6.7.2 The polarisation cancellation

6.7.3 Wave fluxes

6.7.4 Local momentum conservation

6.7.5 MHD correspondence

6.7.6 Computational consistency

6.8 Gyrokinetic drifts

6.9 Gyrokinetic energetics

6.9.1 Long-wave electrostatic systems

6.9.2 Electromagnetic energetics

6.10 Simplified geometry and the form of the Jacobian

Chapter 7 Gyrokinetic theory for local dynamics

7.1 Ideas behind delta-f gyrokinetics

7.2 Total-f Lagrangian and energetics

7.3 Linearised polarisation

7.3.1 Conserved energy

7.3.2 Field equations

7.4 The free energy

7.5 Sketch of the delta-f approach

7.6 Systematics of the delta-f equations

7.6.1 Field equations

7.7 Delta-f energetics and correspondence

7.7.1 Field equations

7.8 On consistency

7.8.1 Parallel phase space consistency

7.8.2 Difficulty of a global model

7.9 The gyroaveraged magnetic field

7.10 What happened to momentum

Chapter 8 Gyrokinetic treatment of waves

8.1 Introduction

8.2 Kinetic responses

8.2.1 Landau damping

8.3 Adiabatic drift acoustic wave

8.3.1 Drift waves with electron Landau damping.

8.4 Kinetic shear Alfvén wave

8.5 Drift-Alfvén wave

8.6 Landau damping as thermal conduction

8.6.1 Symmetrisation into even and odd components

8.6.2 Evolution of the field variables

8.6.3 The wave equation and thermal conduction

8.7 Kinetic resonance-Landau damping

8.8 Summary

Chapter 9 Introduction to gyrofluid theory

9.1 Introduction

9.2 Heuristic gyrofluid 2D turbulence

9.3 Heuristic gyrofluid 3D turbulence

9.4 Gyrofluid systematics

9.4.1 Representation

9.4.2 Free energy

9.4.3 On not gyroaveraging the magnetic potential

9.4.4 Field variable equations

9.4.5 Moment variable equations

9.4.6 Auxiliary gyrofluid variables

9.4.7 ExB advection

9.4.8 Curvature terms

9.4.9 Parallel dynamics

9.4.10 The Landau closure

9.4.11 Expression of the moment equations

9.4.12 System normalisation

9.5 Gyrofluid energetics

9.6 Summary

Chapter 10 Gyrofluid equations for thermal dynamics

10.1 Introduction

10.2 The gyrofluid model with thermal responses

10.2.1 List of moment variables

10.2.2 Moment variable equations

10.2.3 Field equations

10.3 Collisions in general

10.4 Thermal gyrofluid energetics

10.5 Correspondence to the fluid model

10.5.1 Polarisation and vorticity

10.5.2 Thermal conduction

10.5.3 Thermal anisotropy and parallel viscosity

10.6 On usefulness

Chapter 11 Gyrofluid Drift-Alfvén turbulence

11.1 Introduction-gyrofluid turbulence

11.2 Electromagnetic gyrofluid equations

11.2.1 Six-moment electromagnetic equations

11.2.2 Collisional dissipation

11.2.3 Field equations

11.3 Energetics

11.4 ITG turbulence in a hot plasma

11.4.1 Dependence on inductivity

11.4.2 Temperature gradient threshold

11.4.3 Stabilisation by flows.

11.4.4 Comparison to the fluid drift model

11.5 Drift Alfvén turbulence in a warm plasma

11.6 Thermal anisotropy

11.6.1 in temperature responses

11.6.2 in flows

11.7 Summary

Chapter 12 Electron gyroscale turbulence

12.1 Introduction-the gyroscale

12.2 Responses below the ion gyroradius

12.3 Heuristic 2D electron gyroscale model

12.4 ITG and ETG isomorphism

12.4.1 Flows and the adiabatic response

12.4.2 Polarisation in the ETG and ITG or EZF models

12.5 Three-dimensional adiabatic ETG turbulence

12.5.1 Normalised gyrofluid moment equations

12.5.2 ETG and EZF polarisation and induction

12.5.3 Comparison within the standard case

12.5.4 Dependence on the temperature gradient

12.5.5 Dependence on inductivity

12.5.6 Dependence on radial domain size

12.5.7 Dependence on field line length

12.5.8 The warm plasma case, steeper gradients

12.6 The two-scale problem

12.6.1 Computational requirements for the two-scale problem

12.6.2 The hot plasma case

12.6.3 The warm plasma case

12.6.4 The two-scale problem is work in progress

12.7 Summary

Chapter 13 Trapped-electron turbulence

13.1 Introduction-magnetic trapping

13.2 Gyrokinetic Hamiltonian in a system with symmetry

13.2.1 Simplest case: 1D mirror field

13.2.2 The dipole magnetic field

13.2.3 The tokamak magnetic field

13.3 The toroidal precession drift

13.3.1 Equilibrium and Orthogonal Coordinates

13.3.2 Drift combinations

13.3.3 The tokamak magnetic field

13.3.4 The dipole magnetic field

13.3.5 Contrast to the tokamak case

13.4 Single-centre drifts versus gyrokinetics

13.5 Trapped electrons as separate species in turbulence

13.5.1 Bounce averaged objects

13.5.2 Simple exposition of the energetics.

13.5.3 Integration into the six moment gyrofluid model.

Notes:

Description based on publisher supplied metadata and other sources.

Description based on print version record.

ISBN:

9780750344746

0750344741

OCLC:

1429732518