gray/doc/4.implementation.md

Implementation

index_rt

The index_rt is a unique index assigned to each combination of beam propagation mode and number of passes into the plasma. Initially index_rt is 1 for the ordinary mode or 2 for the extraordinary mode. Due to the mode mixing, on subsequent passes each beam splits into two modes and the index_rt is updated as:

  index_rt = 2*index_rt + 1  ! for the O mode
  index_rt = 2*index_rt + 2  ! for the X mode

It follows that ordinary(extraordinary) modes respectively have odd(even) indices and the number of passes is given by $\lfloor \log₂(1 + \tt index_rt) \rfloor$. For example, an index_rt=19 denotes the following chain:

  \begin{aligned}
    \text{mode:}           && O &→ X → O → O  \\
    \text{\tt index\_rt:}  && 1 &→ 4 → 9 → 19
  \end{aligned}