Plasma Theory, 1st ed. 2023
An Advanced Guide for Graduate Students

This textbook, based on the author?s classroom-tested lecture course, helps graduate students master the advanced plasma theory needed to unlock results at the forefront of current research. It is structured around a two semester course, beginning with kinetic theory and transport processes, while the second semester is devoted to plasma dynamics, including MHD theory, equilibrium, and stability. More advanced problems such as neoclassical theory, stochastization of the magnetic field lines, and edge plasma physics are also considered, and each chapter ends with an illustrative example which demonstrates a concrete application of the theory. The distinctive feature of this book is that, unlike most other advanced plasma science texts, phenomena in both low and high temperature plasma are considered simultaneously so that theory of slightly ionized and fully ionized plasmas is presented holistically. This book will therefore be ideal as a classroom text or self-study guide for a wide cohort of graduate students working in different areas like nuclear fusion, gas discharge physics, low temperature plasma applications, astrophysics, and more. It is also a useful reference for more seasoned researchers.

1.1          Boltzmann equation

1.2          Collision operator

for Coulomb collisions

1.2.1 General expression for a flow in the velocity space caused by

collisions

1.2.2 Deceleration and diffusion of test particles cloud in the

velocity space

1.2.3 Momentum an energy loss of the test particles

1.2.4 Landau collision operator

1.3          Relativistic

collision operator

1.4          Fokker-Planck

equation

1.5          Runaway electrons

in fully ionized plasma

1.6          Distribution

function of electrons in slightly ionized plasma

1.6.1 Approximation 

1.6.2 Distribution function in the electric field

1.6.3 Impact of electron-electron collisions

1.6.4 General expression for 

1.7          Transport

coefficients for electrons in slightly ionized plasma

1.8          Drift kinetic

equation in a stationary electric and magnetic field

1.9          Gyrokinetic

equation

1.10        Pellet ablation in

a tokamak

2.1          Momentum equations

2.2          Transport

coefficients in fully ionized plasma. Method of Chapman and Enskog

2.3          Summary of the

results for the fully ionized plasma

2.4          Transport

coefficients in fully ionized plasma. Qualitative consideration

2.4.1 Friction caused by relative mean velocity, thermal force

2.4.2 Spitzer conductivity

2.4.3 Heat flux. Conductive and convective parts

2.4.4 Collisional heat production

2.4.5 Viscosity

2.5          Equation for

entropy

2.6          Viscosity in the

BGK approximation

2.7          Thermal force for

impurities

2.8          Finite ionization

potential effect and impurity retention in a tokamak edge

Chapter 3. Quasineutral Plasma and Sheath Structure

3.1          Quasineutrality

maintaining

3.2          Collisionless sheath

at the material surfaces

3.2.1 Electrons in a capacitor with reflecting electric field

3.2.2 Particle and energy fluxes to the material surfaces

3.2.3 Current-voltage characteristic of the sheath. Floating

potential

3.2.4 Sheath structure. Bohm criterion

3.3          Impact of electron

emission. Double sheath

3.4          Sheath in magnetic

field

3.5          Thermoelectric

current between two electrodes

Chapter 4. Diffusion in Partially Ionized Unmagnetized Plasma

4.1          Ambipolar

diffusion

4.2          Examples of

solutions of ambipolar diffusion equation

4.2.1 Decay of initial perturbation in infinite plasma

4.2.2 Positive column of glow discharge

4.2.3 Diffusive decay

4.2.4 Diffusive probe

4.3 Diffusion of slightly ionized multispecies plasma

4.4 Diffusion in the ionosphere

Chapter 5. Diffusion of Partially Ionized Magnetized Plasma

5.1          Diffusion and

mobility in magnetic field

5.2          One-dimensional

diffusion in magnetized plasma

5.2.1 Diffusion across magnetic field

5.2.2 One-dimensional diffusion at arbitrary angle with magnetic

field

5.3          Diffusion of

perturbation in unbounded plasma

5.4          Diffusion in

plasma restricted by dielectric walls

5.5          Diffusion in a

cylinder with conducting walls

5.6          Diffusive probe in

magnetic field

5.7          Experiments in

laboratory plasma

Chapter 6. Partially Ionized Plasma with Current

6.1          Plasma with net

current in the absence of magnetic field

6.1.1 Small perturbations

6.1.2 Nonlinear evolution

6.2          Magnetized plasma

with current

6.2.1 One - dimensional evolution

6.2.2 Multidimensional evolution of small perturbation in unbounded

plasma

6.2.3 Effect of conductivity recover in a weak magnetic field

6.3 Plasma clouds and layers in the ionosphere

6.3.1 Redistribution of metal ions in the polar ionosphere. Sporadic

layers

6.3.2 Active experiments with Barium clouds

Chapter 7. Transport in Strongly Ionized Plasma Across Magnetic

Field

7.1          Classical

diffusion of fully ionized plasma across magnetic field

7.2          Transport of

impurities in fully ionized plasma across magnetic field

7.3          Partially ionized

magnetized plasma with inhomogeneous neutral component

7.4          Penetration of

neutral particles into hot tokamak plasma

Chapter 8. Drift Waves and Turbulent Transport

8.1          Drift waves in

inhomogeneous plasma

8.2          Drift-dissipative

instability

8.3          Universal

instability

8.3.1      Fluid ions

8.3.2      Kinetic ions

8.4          Instabilities,

caused by the temperature gradient

8.5          Turbulent

transport caused by random electric fields

8.6          Effect of magnetic

shear on plasma instabilities

8.7          Turbulent

transport in dielectric tubes

Chapter 9. Dynamics of Fully Ionized Plasma in the Absence of

Magnetic Field

9.1          Ion acoustic waves

9.2          Nonlinear

dynamics. Self-similar solutions

9.3          Simple nonlinear

waves. Overturn

9.4          Nonlinear ion

acoustic waves with dispersion

9.5          Plasma expansion

during pellet injection

Chapter 10. Magnetohydrodynamics (MHD)

10.1        MHD equations

10.2        Magnetic field

frozen in and skin effect

10.3        MHD waves

10.4        Nonlinear MHD waves

10.5        Magnetosonic waves

with dispersion

10.6        Alfven masers

Chapter 11. Dynamics of Plasma Blobs and Jets in Magnetic Field

11.1        Plasma motion

across magnetic field in vacuum

11.2        Deceleration of

plasma jet by ambient plasma

11.3        Edge localized

modes and filaments

Chapter 12. Plasma Equilibrium

12.1.      On possibility of

equilibrium in the absence of vacuum magnetic field

12.2.      Equilibrium of a

pinch

12.3.      Magnetic flux

surface functions

12.4.      Grad-Shafranov

equation

12.5.      Integral equilibrium

in a tokamak

12.6.      Plasma equilibrium

in tokamak with circular cross sections

12.7.      Coordinates for

arbitrary flux surfaces

12.8.      Force-free

equilibrium and pinch with canonical profiles

12.9.      2D modeling of

tokamak edge

Chapter 13. Transport Phenomena in Tokamaks

13.1.      Fluid regime

(Pfirsch-Schlueter regime)

13.1.1 Qualitative estimates

13.1.2. Heat conductivity

13.1.3 Plasma flows on the flux surface, density, temperature and

potential perturbations

13.1.4 Particle fluxes

13.2.      Radial electric

field, poloidal and toroidal rotation

13.3.      Neoclassical

transport in collisionless regimes

13.3.1 Particle trajectories

13.3.2 Ware drift

13.3.3 Estimation of transport coefficients in the plateau regime

13.3.4 Estimation of transport coefficients in the banana regime

13.4.      Distribution

function in the collisionless regimes

13.4.1 Plateau regime

13.4.2 Banana regime

13.5.      Particle and heat

balance equations

13.6.      Transport codes

Chapter 14. Instabilities in Magnetized Plasma

14.1.      Rayleigh-Taylor

instability in fluids

14.2.      Flute instability

14.3.      Dissipative

modifications of flute instability

14.3.1 Rayleigh-Taylor instability in partially ionized plasma

14.3.2 Flute instability in plasma contacting with metal surfaces

14.3.3 Gravitational-dissipative flute instability

14.4.      Energy principle

14.5.      Kink instability

14.6.      Tearing instability

14.7.      Geodesic acoustic

mode and zonal flows

14.8.      Equatorial plasma

bubbles

Chapter 15. Magnetic Islands and Stochastic Magnetic Field

15.1.      Magnetic islands

15.2.      Stochastic

instability and magnetic field line diffusion

15.3.      Transport in

stochastic magnetic field

15.4.      Resonant magnetic

perturbations in tokamak

15.5.      Simulation of

resonant magnetic perturbations effects with codes and

     examples of experimental

results

Chapter 16. Improved Confinement Regime (H-mode)

16.1.        drift shear and transport barriers

16.2.      Transition from low

to high confinement regime (L-H transition)

16.3.      L-H transition power

threshold

Builds a solid foundation in the fundamentals, explores advanced research topics, and gives illustrative examples

Covers both low and high temperature plasmas simultaneously

Designed for a two-semester course, but is also ideal for self-study