Contents

1 Introduction
2 Linear wave theory in an infinite uniform plasma
 2.1 Maxwell’s equations
 2.2 Constitutive relation
 2.3 Fourier transform
 2.4 Linear wave equation
 2.5 Dispersion relation
 2.6 Weak damping approximation
3 Ray tracing in a slowly varying plasma
 3.1 WKB Approximation
 3.2 Ray equations
4 Canonical coordinates in an axisymmetric toroidal plasma
 4.1 Flux coordinate system
 4.2 Ray equations
 4.3 Parallel index of refraction
 4.4 Perpendicular index of refraction
 4.5 Derivatives
 4.6 Specular reflection at the plasma edge
 4.7 Inward propagating ray
5 Numerical algorithms
 5.1 Magnetic equilibrium interpolation
 5.2 Runge-Kutta differential equation solver
6 Conclusion
A Explicit expressions
 A.1 Dispersion relation
 A.2 Derivatives of the equilibrium
B Various properties of the coordinates system
 B.1 Alternative calculation of the parallel index of refraction
 B.2 Calculation of kρ, m and/or n as a function of k and k
 B.3 Calculation of kρ, m and n as a function of kR, kZ and kϕ
 B.4 Wave scattering by fluctuations
  B.4.1 Calculation of the scattered wave vector
  B.4.2 Derivation of the wave kinetic equation
  B.4.3 Solution of the wave kinetic equation
 B.5 Calculation of ρ
C Susceptibility tensor and dispersion relation
 C.1 Cold plasma model
D Kinetic plasma model
E Benchmarking of C3PO
 E.1 JET-like plasma
  E.1.1 Equilibrium
  E.1.2 Wave initial conditions
  E.1.3 Results
  E.1.4 Numerical performances
 E.2 VERSATOR II and PLT plasmas
  E.2.1 Equilibrium
  E.2.2 Wave initial conditions
  E.2.3 Results
 E.3 Propagation in toroidal vacuum device
  E.3.1 Magnetic configuration
  E.3.2 Wave initial conditions
  E.3.3 Results
 E.4 Reverse field pinch plasma
  E.4.1 Equilibrium
  E.4.2 Wave initial conditions
  E.4.3 Results