1 Axisymmetric magnetic field
  1.1 Poloidal magnetic field
  1.2 Toroidal magnetic field
  1.3 General form of axisymmetric magnetic field
  1.4 Gauge transformation of Ψ
  1.5 Contours of Ψ in the poloidal plane
  1.6 Magnetic surfaces
  1.7 Relation of Ψ with the poloidal magnetic flux
  1.8 Measurement of poloidal magnetic flux
  1.9 Closed magnetic surfaces in tokamak
  1.10 Safety factor
  1.11 Non-axisymmetric magnetic perturbations
 2 Plasma current density in terms of Ψ and g
  2.1 Poloidal current density
  2.2 Toroidal current density
 3 Constraint of force-balance on magnetic field
  3.1 MHD momentum equation
  3.2 Force balance equation in tokamak plasmas: Grad-Shafranov equation
  3.3 Axisymmetric equilibrium magnetic field
  3.4 Axisymmetric equilibrium current density
  3.5 Vacuum magnetic field (not finished)
  3.6 Equilibrium scaling
  3.7 Free boundary equilibrium problem
  3.8 Fixed boundary equilibrium and choices of coordinates
 4 Curvilinear coordinate system
  4.1 Coordinates transformation
  4.2 Jacobian
  4.3 Orthogonality relation between two sets of basis vectors
  4.4 An example: (ψ,𝜃,ζ) coordinates
  4.5 Gradient and directional derivative in general coordinates (ψ,𝜃,ζ)
  4.6 Divergence operator in general coordinates (ψ,𝜃,ζ)
  4.7 Laplacian operator in general coordinates (ψ,𝜃,ζ)
  4.8 Curl operator in general coordinates (ψ,𝜃,ζ)
  4.9 Metric tensor for general coordinate system
 5 Covariant/contravariant representation of equilibrium magnetic field
 6 Magnetic surface coordinates (ψ,𝜃,ϕ)
  6.1 Local safety factor
  6.2 Global safety factor
  6.3 Relation between Jacobian and poloidal angle 𝜃
  6.4 Calculating poloidal angle
 7 Constructing magnetic surface coordinate system from discrete Ψ(R,Z) data
  7.1 Finding magnetic surfaces
  7.2 Expression of metric elements of magnetic coordinates (ψ,𝜃,ϕ)
 8 Constructing model tokamak magnetic field
 9 Magnetic surface averaging
  9.1 Definition
  9.2 Flux Surface Functions—to be deleted
 10 Magnetic coordinates (ψ,𝜃,ζ) with general toroidal angle ζ
  10.1 General toroidal angle ζ
  10.2 Contravariant form of magnetic field in (ψ,𝜃,ζ) coordinates
  10.3 Relation between the partial derivatives in (ψ,𝜃,ϕ) and (ψ,𝜃,ζ) coordinates
  10.4 Steps to construct a straight-line magnetic coordinate system
  10.5 Form of operator B ⋅∇ in (ψ,𝜃,ζ) coordinates
  10.6 Resonant surface of a perturbation
  10.7 Helical angle used in tearing mode theory
  10.8 Covariant form of magnetic field in (ψ,𝜃,ζ) coordinate system
  10.9 Form of operator (B ×∇ψ∕B²) ⋅∇ in (ψ,𝜃,ζ) coordinates
  10.10 Radial differential operator
 11 Field-line-following coordinates
  11.1 Definition of the field-line-following coordinates (ψ,𝜃,α)
  11.2 Some discussions
  11.3 Expression of ∇α
  11.4 Field-aligned coordinates in GEM[7] and GENE[13] codes
  11.5 Visualization of gridpoints in field aligned coordinate system
  11.6 Field-line-following mesh in gyrokinetic turbulence simulation codes
  11.7 Numerical verification of the field-aligned coordinates
 12 Concentric-circular magnetic configuration with a given safety factor profile
  12.1 Is the above B divergence-free?
  12.2 Is the above B a solution to the GS equation?
  12.3 Explicit expression for the generalized toroidal angle
  12.4 Metric elements
  12.5 Safety factor profile
 13 Fixed boundary tokamak equilibrium problem
  13.1 Toroidal elliptic operator in general coordinates
  13.2 Finite difference form of toroidal elliptic operator in general coordinate system
  13.3 Special treatment at coordinate origin, wrong! to be deleted
  13.4 Pressure and toroidal field function profile
  13.5 Boundary magnetic surface and initial coordinates
  13.6 Fixed boundary equilibrium numerical code
  13.7 Benchmark of the code
  13.8 Low-beta equilibrium vs. high-beta equilibrium
  13.9 Analytical form of Jacobian (need cleaning up)
  13.10 Grad-Shafranov equation with prescribed safety factor profile (to be finished)
 14 Misc contents
  14.1 Expression of current density
  14.2 Normalized internal inductance
  14.3 Cylindrical tokamak
  14.4 Coils system of EAST tokamak
  14.5 Comparison of major tokamaks in the world
  14.6 Miller’s formula for shaped flux surfaces
  14.7 Double transport barriers pressure profile
  14.8 Ballooning transformation
 A
  A.1 Solovév equilibrium
  A.2 Plasma rotation
  A.3 Poloidal plasma current
  A.4 Efficiency of tokamak magnetic field in confining plasma: Plasma beta
  A.5 Beta limit
  A.6 Why bigger tokamaks with larger plasma current are better at fusion?
  A.7 Density limit
  A.8 Relation of plasma current density to pressure gradient
  A.9 Discussion about the poloidal current function, check!
  A.10 tmp check!
  A.11 Radial coordinate to be deleted
  A.12 Toroidal elliptic operator in magnetic surface coordinate system
  A.13 Grad-Shafranov equation in (r,𝜃,ϕ) coordinates
  A.14 Large aspect ratio expansion
  A.15 (s,α) parameters
 B Computing magnetic field generated by coils
  B.1 Magnetic field
  B.2 Magnetic vector potential
  B.3 For wires in poloial plane
  B.4 For wires along toroidal direction
 C About this document
 References