Response to ‘Comment on “Boundary conditions for surface waves propagating along the interface of plasma flow and free space” ’

Abstract

Shoucri (1999) has commented on our paper (Lee and Cho 1997) in view of his relativistic calculation, and has stated that the boundary condition and the dispersion relation obtained there are incorrect. In this response, we reaffirm that all the results contained in Lee and Cho (1997) are correct in so far as one uses the nonrelativistic equation of motion. In particular, the boundary condition that we used (equation (57) in Lee and Cho 1997) is valid in both the nonrelativistic and the relativistic theory, and is equivalent to equation (11) of Shoucri (1999). Shoucri's hasty conclusion that our boundary condition (57) is incorrect appears to be due to his neglect of the fact that a boundary condition can be put into different forms depending upon problems under consideration.One way to derive a boundary condition for the surface-wave problem with a sharp boundary is to assume an inhomogeneous plasma having a varying density N(x) (in the notation of Lee and Cho 1997), integrate the inhomogeneous wave equation or the Maxwell equations across the infinitesimal transition layer, and specialize N(x) as a step function, as was done in Lee (1995). Starting from the Maxwell equations on p. 418 of Lee and Cho (1997) and calculating the currents relativistically, we find that the following three boundary conditions are equivalent, and any one of them is acceptable:(i) equation (57) in Lee and Cho (1997);(ii) equation (11) in Shoucri (1999);(iii) formula here(in the notation of Lee and Cho (1997), with γ as the relativistic factor).