Equation (274) indicates that, for the differential equation (270), there is a resonant response to a perturbation ei(m𝜃−nζ) on a magnetic surface with m − nq = 0. Therefore, the magnetic surface with q = m∕n is called the “resonant surface” for the perturbation ei(m𝜃−nζ).
The phase change of the perturbation ei(m𝜃−nζ) along a magnetic field is given by mΔ𝜃 − nΔζ, which can be written as Δ𝜃(m−nq). Since m−nq = 0 on a resonant surface, this indicates that there is no phase change along a magnetic field line on a resonant surface, i.e., the parallel wavenumber k∥ is zero on a resonant surface.