1 Introduction
2 Tokamak geometry and particle dynamic
 2.1 Coordinate system
  2.1.1 Momentum Space
  2.1.2 Configuration Space
 2.2 Particle motion
  2.2.1 Arbitrary configuration
  2.2.2 Circular configuration
3 Kinetic description of electrons
 3.1 Boltzman equation; Gyro- and Wave-averaging
 3.2 Guiding-Center Drifts and Drift-Kinetic Equation
  3.2.1 Drift Velocity from the Conservation of Canonical Momentum
  3.2.2 Drift Velocity from the Expression of Single Particle Drift
  3.2.3 Case of Circular concentric flux-surfaces
  3.2.4 Steady-State Drift-Kinetic Equation
 3.3 Small drift approximation
  3.3.1 Small Drift Ordering
 3.4 Low collision limit and bounce averaging
  3.4.1 Fokker-Planck Equation
  3.4.2 Drift-Kinetic Equation
 3.5 Flux conservative representation
  3.5.1 General formulation
  3.5.2 Dynamics in Momentum Space
  3.5.3 Dynamics in Configuration Space
  3.5.4 Bounce-averaged flux calculation
  3.5.5 Up to first order term: the Drift Kinetic equation
 3.6 Moments of the distribution function
  3.6.1 Flux-surface Averaging
  3.6.2 Density
  3.6.3 Current Density
  3.6.4 Power Density Associated with a Flux
  3.6.5 Stream Function for Momentum Space fluxes
  3.6.6 Ohmic electric field
  3.6.7 Fraction of trapped electrons
  3.6.8 Runaway loss rate
  3.6.9 Magnetic ripple losses
  3.6.10 RF Wave induced cross-field transport
  3.6.11 Non-thermal bremsstrahlung
4 Detailed description of physical processes
 4.1 Coulomb collisions
  4.1.1 Small angle scattering
  4.1.2 Linearized collision operator
  4.1.3 Electron-electron collision operators
  4.1.4 Electron-ion collision operators
  4.1.5 Large angle scattering
  4.1.6 Bounce Averaged Fokker-Planck Equation
  4.1.7 Bounce Averaged Drift Kinetic Equation
 4.2 Ohmic electric field
  4.2.1 Conservative Form for the Ohmic Electric Field Operator
  4.2.2 Bounce Averaged Fokker-Planck Equation
  4.2.3 Bounce Averaged Drift Kinetic Equation
 4.3 Radio frequency waves
  4.3.1 Conservative formulation of the RF wave operator
  4.3.2 RF Diffusion coefficient for a Plane Wave
  4.3.3 Integration in k-space
  4.3.4 Incident Energy Flow Density
  4.3.5 Narrow Beam Approximation
  4.3.6 Normalized Diffusion Coefficient
  4.3.7 Bounce Averaged Fokker-Planck Equation
  4.3.8 Bounce Averaged Drift-Kinetic Equation
  4.3.9 Modeling of RF Waves
5 Numerical calculations
 5.1 Bounce integrals
 5.2 Grid definitions
  5.2.1 Momentum space
  5.2.2 Configuration space
  5.2.3 Time grid definition
 5.3 Discretization procedure
  5.3.1 Zero order term: Fokker-Planck equation
  5.3.2 First order term: Drift kinetic equation
 5.4 Zero order term: the Fokker-Planck equation
  5.4.1 Momentum dynamics
  5.4.2 Spatial dynamics
  5.4.3 Grid interpolation
  5.4.4 Discrete description of physical processes
  5.4.5 Collisions
  5.4.6 Ohmic electric field
 5.5 Up to first order term: the Drift Kinetic equation
  5.5.1 Grid interpolation
  5.5.2 Momentum dynamics
  5.5.3 Discrete description of physical processes
 5.6 Initial solution
  5.6.1 Zero order term: the Fokker-Planck equation
  5.6.2 Up to first order term: the Drift Kinetic equation
 5.7 Boundary conditions
  5.7.1 Zero order term: the Fokker-Planck equation
  5.7.2 Up to first order term: the Drift Kinetic equation
 5.8 Moments of the Distribution Function
  5.8.1 Flux discretization for moment calculations
  5.8.2 Numerical integrals for moment calculations
6 Algorithm
 6.1 Matrix representation
  6.1.1 Zero order term: the Fokker-Planck equation
  6.1.2 Up to first order term: the Drift Kinetic equation
 6.2 Inversion procedure
  6.2.1 Incomplete matrix factorization
  6.2.2 Zero order term: the Fokker-Planck equation
  6.2.3 Up to first order term: the Drift Kinetic equation
 6.3 Normalization and definitions
  6.3.1 Temperature, density and effective charge
  6.3.2 Coulomb Logarithm
  6.3.3 Time
  6.3.4 Momentum, velocity, and kinetic energy
  6.3.5 Maxwellian electron momentum distribution
  6.3.6 Poloidal flux coordinate
  6.3.7 Drift kinetic coefficient
  6.3.8 Momentum convection and diffusion
  6.3.9 Radial convection and diffusion
  6.3.10 Fluxes
  6.3.11 Current density
  6.3.12 Power density
  6.3.13 Electron runaway rate
  6.3.14 Electron magnetic ripple loss rate
  6.3.15 Units
7 Examples
 7.1 Ohmic conductivity
 7.2 Runaway losses
 7.3 Lower Hybrid Current drive
 7.4 Electron Cyclotron Current drive
  7.4.1 Introduction
  7.4.2 Grid size effects
  7.4.3 Electron trapping effects
  7.4.4 Momentum-space dynamics
  7.4.5 Coupling to propagation models
  7.4.6 Conclusion
 7.5 Fast electron radial transport
 7.6 Fast electron magnetic ripple losses
 7.7 Maxwellian bootstrap current
8 Conclusion
9 Acknowledgements
A Curvilinear Coordinate Systems
 A.1 General Case (u¹,u²,u³)
  A.1.1 Vector Algebra
  A.1.2 Tensor Algebra
 A.2 Configuration space
  A.2.1 System (R,Z,ϕ)
  A.2.2 System (r,θ,ϕ)
  A.2.3 System (ψ,s,ϕ)
  A.2.4 System (ψ,θ,ϕ)
 A.3 Momentum Space
  A.3.1 System ( p_∥,p_⊥,φ)
  A.3.2 System (p,ξ,φ)
B Calculation of Bounce Coefficients for Circular Concentric FS
C Effective trapped fraction for Circular Concentric FS
D Cold Plasma Model for RF Waves
 D.1 Cold Plasma Model
  D.1.1 Wave Equation and Dispersion Tensor
  D.1.2 Dispersion Relation
  D.1.3 Polarization components
  D.1.4 Power flow
  D.1.5 Conclusion
 D.2 Lower Hybrid Current Drive
  D.2.1 Electrostatic Dispersion Relation
  D.2.2 Cold Plasma Limit
  D.2.3 Lower Hybrid Waves
  D.2.4 Polarization
  D.2.5 Determination of Θ_k^b,LH
  D.2.6 Determination of Φ_bP ^LH
  D.2.7 Determination of Φ_bT ^LH
  D.2.8 LH Diffusion Coefficient
 D.3 Electron Cyclotron Current Drive
  D.3.1 Polarization
  D.3.2 Determination of Θ_k^b,EC
  D.3.3 Determination of Φ_b^EC in the low density limit.
  D.3.4 EC Diffusion Coefficient
E Large pitch-angle collisions
F Alternative discrete cross-derivatives coefficients
G MatLab File List