PLASMA
1 Introduction
1.1.1 What is Plasma?
1.1.1 An ionized
gas
1.1.2 Plasmas are
QuasiNeutral
1.2 Plasma Shielding
1.2.1 Elementary
Derivation of the Boltzmann Distribution
1.2.2 Plasma
Density in Electrostatic Potential
1.2.3 Debye
Shielding
1.2.4 PlasmaSolid
Boundaries (Elementary)
1.2.5 Thickness of
the sheath
1.3 The `Plasma Parameter'
1.4 Summary
1.5 Occurrence of Plasmas
1.6 Different Descriptions of Plasma
1.6.1 Equations of
Plasma Physics
1.6.2 Self
Consistency
2
Motion of Charged Particles in Fields
2.1 Uniform B field, E = 0.
2.1.1 Qualitatively
2.1.2 By Vector
Algebra
2.2 Uniform B and
nonzero E
2.2.1 Drift due to
Gravity or other Forces
2.3 NonUniform B Field
2.4 Curvature Drift
2.4.1 Vacuum Fields
2.5 Interlude: Toroidal Confinement of Single Particles
2.5.1 How to solve
this problem?
2.5.2 The
Solution: Rotational Transform
2.6 The Mirror Effect of Parallel Field Gradients: E = 0, ∇B B
2.6.1 Force on an
Elementary Magnetic Moment Circuit
2.6.2 μ is a
constant of the motion
2.6.3 Mirror
Trapping
2.6.4 Pitch Angle
θ
2.6.5 Other
Features of Mirror Motions
2.7 Time Varying B Field (E
inductive)
2.8 Time Varying Efield (E, B uniform)
2.8.1 Direct
Derivation of [(dE)/dt] effect:
`Polarization Drift'
2.9 Non Uniform E (Finite Larmor Radius)
2.10 Summary of Drifts
3
Collisions in Plasmas
3.1 Binary collisions between charged particles
3.1.1 Frames of
Reference
3.1.2 Scattering
Angle
3.2 Differential CrossSection for Scattering by Angle
3.3 Relaxation Processes
3.3.1 Energy Loss
3.3.2 Cutoffs
Estimates
3.3.3 Momentum Loss
3.3.4 `Random Walk'
in angle
3.3.5 Summary of
different types of collision
3.4 Thermal Distribution Collisions
3.4.1 e → i
3.4.2 i → e
3.4.3 i → i
3.4.4 e → e
3.4.5 Summary of
Thermal Collision Frequencies
3.5 Applications of Collision Analysis
3.5.1 Energetic
(`Runaway') Electrons
3.5.2 Plasma
Resistivity (DC)
3.5.3 Diffusion
3.5.4 Energy
Equilibration
3.6 Some Orders of Magnitude
4
Fluid Description of Plasma
4.1 Particle Conservation (In 3d Space)
4.2 Fluid Motion
4.2.1 Lagrangian
& Eulerian Viewpoints
4.2.2 Momentum
(Conservation) Equation
4.2.3 Pressure
Force
4.2.4 Momentum
Equation: Eulerian Viewpoint
4.2.5 Effect of
Collisions
4.3 The Key Question for Momentum Equation:
4.4 Summary of TwoFluid Equations
4.5 TwoFluid Equilibrium: Diamagnetic Current
4.6 Reduction of Fluid Approach to the Single Fluid Equations
4.6.1 Summary of
Single Fluid Equations: M.H.D.
4.6.2 Heuristic
Derivation/Explanation
4.6.3 Maxwell's
Equations for MHD Use
4.7 MHD Equilibria
4.7.1 θpinch
4.7.2 Zpinch
4.7.3 `Stabilized
Zpinch'
4.8 Some General Properties of MHD Equilibria
4.8.1 Pressure
& Tension
4.8.2 Magnetic
Surfaces
4.8.3 `Current
Surfaces'
4.8.4 Low β
equilibria: ForceFree Plasmas
4.9 Toroidal Equilibrium
4.10 Plasma Dynamics (MHD)
4.11 Flux Conservation
4.12 Field Line Motion
4.13 MHD Stability
4.14 General Perturbations of Cylindrical Equil.
4.15 General Principles Governing Instabilities
4.16 Quick and Simple Analysis of Pinches
5
Electromagnetic Waves in Plasmas
5.1 General Treatment of Linear Waves in Anisotropic Medium
5.1.1 Simple Case.
Isotropic Medium
5.1.2 General Case
(k in
zdirection)
5.2 High Frequency Plasma Conductivity
5.2.1 Zero Bfield
case
5.2.2 Meaning of
Negative N^{2}: Cut Off
5.3 Cold Plasma Waves
(Magnetized Plasma)
5.3.1 Derivation of
Dispersion Relation
5.3.2 Hybrid
Resonances Perpendicular Propagation
5.3.3 Whistlers
5.4 Thermal Effects on Plasma Waves
5.4.1 Refractive
Index Plot
5.4.2 Including the
ion response
5.5 Electrostatic Approximation for (Plasma) Waves
5.6 Simple Example of MHD Dynamics: Alfven Waves
5.7 NonUniform Plasmas and wave propagation
5.8 Two Stream Instability
5.9 Kinetic Theory of Plasma Waves
5.9.1 Vlasov
Equation
5.9.2 Linearized
Wave Solution of Vlasov Equation
5.9.3 Landau's
original approach. (1946)
5.9.4 Solution of
Dispersion Relation
5.9.5 Direct
Calculation of Collisionless Particle Heating
5.9.6 Physical
Picture
5.9.7 Damping
Mechanisms
5.9.8 Ion Acoustic
Waves and Landau Damping
5.9.9 Alternative
expressions of Dielectric Tensor Elements
5.9.10
Electromagnetic Waves in unmagnetized Vlasov Plasma
5.10 Experimental Verification of Landau Damping
1.1.1 What is Plasma?
1.1.1 An ionized gas
1.1.2 Plasmas are QuasiNeutral
1.2 Plasma Shielding
1.2.1 Elementary Derivation of the Boltzmann Distribution
1.2.2 Plasma Density in Electrostatic Potential
1.2.3 Debye Shielding
1.2.4 PlasmaSolid Boundaries (Elementary)
1.2.5 Thickness of the sheath
1.3 The `Plasma Parameter'
1.4 Summary
1.5 Occurrence of Plasmas
1.6 Different Descriptions of Plasma
1.6.1 Equations of Plasma Physics
1.6.2 Self Consistency
2 Motion of Charged Particles in Fields
2.1 Uniform B field, E = 0.
2.1.1 Qualitatively
2.1.2 By Vector Algebra
2.2 Uniform B and nonzero E
2.2.1 Drift due to Gravity or other Forces
2.3 NonUniform B Field
2.4 Curvature Drift
2.4.1 Vacuum Fields
2.5 Interlude: Toroidal Confinement of Single Particles
2.5.1 How to solve this problem?
2.5.2 The Solution: Rotational Transform
2.6 The Mirror Effect of Parallel Field Gradients: E = 0, ∇B B
2.6.1 Force on an Elementary Magnetic Moment Circuit
2.6.2 μ is a constant of the motion
2.6.3 Mirror Trapping
2.6.4 Pitch Angle θ
2.6.5 Other Features of Mirror Motions
2.7 Time Varying B Field (E inductive)
2.8 Time Varying Efield (E, B uniform)
2.8.1 Direct Derivation of [(dE)/dt] effect: `Polarization Drift'
2.9 Non Uniform E (Finite Larmor Radius)
2.10 Summary of Drifts
3 Collisions in Plasmas
3.1 Binary collisions between charged particles
3.1.1 Frames of Reference
3.1.2 Scattering Angle
3.2 Differential CrossSection for Scattering by Angle
3.3 Relaxation Processes
3.3.1 Energy Loss
3.3.2 Cutoffs Estimates
3.3.3 Momentum Loss
3.3.4 `Random Walk' in angle
3.3.5 Summary of different types of collision
3.4 Thermal Distribution Collisions
3.4.1 e → i
3.4.2 i → e
3.4.3 i → i
3.4.4 e → e
3.4.5 Summary of Thermal Collision Frequencies
3.5 Applications of Collision Analysis
3.5.1 Energetic (`Runaway') Electrons
3.5.2 Plasma Resistivity (DC)
3.5.3 Diffusion
3.5.4 Energy Equilibration
3.6 Some Orders of Magnitude
4 Fluid Description of Plasma
4.1 Particle Conservation (In 3d Space)
4.2 Fluid Motion
4.2.1 Lagrangian & Eulerian Viewpoints
4.2.2 Momentum (Conservation) Equation
4.2.3 Pressure Force
4.2.4 Momentum Equation: Eulerian Viewpoint
4.2.5 Effect of Collisions
4.3 The Key Question for Momentum Equation:
4.4 Summary of TwoFluid Equations
4.5 TwoFluid Equilibrium: Diamagnetic Current
4.6 Reduction of Fluid Approach to the Single Fluid Equations
4.6.1 Summary of Single Fluid Equations: M.H.D.
4.6.2 Heuristic Derivation/Explanation
4.6.3 Maxwell's Equations for MHD Use
4.7 MHD Equilibria
4.7.1 θpinch
4.7.2 Zpinch
4.7.3 `Stabilized Zpinch'
4.8 Some General Properties of MHD Equilibria
4.8.1 Pressure & Tension
4.8.2 Magnetic Surfaces
4.8.3 `Current Surfaces'
4.8.4 Low β equilibria: ForceFree Plasmas
4.9 Toroidal Equilibrium
4.10 Plasma Dynamics (MHD)
4.11 Flux Conservation
4.12 Field Line Motion
4.13 MHD Stability
4.14 General Perturbations of Cylindrical Equil.
4.15 General Principles Governing Instabilities
4.16 Quick and Simple Analysis of Pinches
5 Electromagnetic Waves in Plasmas
5.1 General Treatment of Linear Waves in Anisotropic Medium
5.1.1 Simple Case. Isotropic Medium
5.1.2 General Case (k in zdirection)
5.2 High Frequency Plasma Conductivity
5.2.1 Zero Bfield case
5.2.2 Meaning of Negative N^{2}: Cut Off
5.3 Cold Plasma Waves (Magnetized Plasma)
5.3.1 Derivation of Dispersion Relation
5.3.2 Hybrid Resonances Perpendicular Propagation
5.3.3 Whistlers
5.4 Thermal Effects on Plasma Waves
5.4.1 Refractive Index Plot
5.4.2 Including the ion response
5.5 Electrostatic Approximation for (Plasma) Waves
5.6 Simple Example of MHD Dynamics: Alfven Waves
5.7 NonUniform Plasmas and wave propagation
5.8 Two Stream Instability
5.9 Kinetic Theory of Plasma Waves
5.9.1 Vlasov Equation
5.9.2 Linearized Wave Solution of Vlasov Equation
5.9.3 Landau's original approach. (1946)
5.9.4 Solution of Dispersion Relation
5.9.5 Direct Calculation of Collisionless Particle Heating
5.9.6 Physical Picture
5.9.7 Damping Mechanisms
5.9.8 Ion Acoustic Waves and Landau Damping
5.9.9 Alternative expressions of Dielectric Tensor Elements
5.9.10 Electromagnetic Waves in unmagnetized Vlasov Plasma
5.10 Experimental Verification of Landau Damping
4th State Of Matter 
Contents
1.1What is a Plasma?
1.1.1 An ionized gas
 (1.1) 
1.2 Plasmas are QuasiNeutral
 (1.2) 
 (1.3) 
Example: Slab.

 (1.6) 
 (1.7) 
 (1.8) 
 (1.9) 
1.2 Plasma Shielding
1.2.1 Elementary Derivation of the Boltzmann Distribution
 (1.10) 

 (1.13) 
 (1.14) 
 (1.15) 
 (1.16) 
 (1.17) 
1.2.2 Plasma Density in Electrostatic Potential
 (1.18) 
1.2.3 Debye Shielding

 (1.21) 
 (1.22) 
 (1.23) 
 (1.24) 
1.2.4 PlasmaSolid Boundaries (Elementary)
 Plasma is normally charged positively with respect to the solid.
Figure 1.7: PlasmaSolid interface: Sheath  There is a relatively thin region called the "sheath", at the boundary of the plasma, where the main potential variation occurs.
 (1.25) 
 (1.26) 


1.2.5 Thickness of the sheath
 (1.31) 
 (1.32) 
 (1.33) 
1.3 The `Plasma Parameter'
 (1.34) 
 (1.35) 
1.4 Summary
 (1.36) 
1.5 Occurrence of Plasmas
1.6 Different Descriptions of Plasma
 Single Particle Approach. (Incomplete in itself). Eq. of Motion.
 Kinetic Theory. Boltzmann Equation.
⎡
⎣∂
+ v. ∂
+ a . ∂
⎤
⎦f = ∂f
⎞
⎠
col.(1.37)  Fluid Description. Moments, Velocity, Pressure, Currents, etc.
1.6.1 Equations of Plasma Physics
 (1.38) 
1.6.2 Self Consistency
 Calculate Plasma Response (to given E,B)
 Get currents & charge densities
 Calculate E & B for j, p.
TO BE CONTINUED...