4.6 Specular reflection at the plasma edge

Sometimes a wave is to be reflected within the scrape-off layer, which is outside the domain of application of the code. In this case, a specular reflection is enforced just before the last closed flux-surface at the location (ρ ,θ ,ϕ )
  1  1  1 where the incident wave vector is (k  ,m  ,n )
  ρ1   1  1. The condition for the specular reflection is

(58)

with the contravariant basis ej = (             )
          ^θ--^ϕ
  ∥∇ ρ∥ρ^, r,R such that

(59)

and (??) becomes

(60)

such that m and n are conserved through the reflection and

(61)

We should verify that the dispersion relation is satisfied for the outgoing wave. We have (??), (??)

(62)

such that

(63)

and the dispersion relation is satisfied.