B.3 Calculation of k_ρ, m and n as a function of k_R, k_Z and k_ϕ

The vector k is projected onto the covariant basis

(129)

such that

(130)

If k is expressed in coordinates as k = k_R + k_ZẐ + k_ϕ or in coordinates as k = k_r + k_θ+ k_ϕ we get

(131)

where

(132)

Note that we retrieve

(133)

since

(134)