Range of validity of the Rayleigh hypothesis.
The parameter range over which the Rayleigh hypothesis (RH) for optical gratings might be validly applied to analysis of high power backward wave oscillators has been investigated numerically. It had been pointed out that from a rigorous mathematical viewpoint, RH was only valid for a shallow corrugation of slow wave structure (SWS) such that h K0 <0.448; here, h and K0 are, respectively, the amplitude and wave number of the periodicity in a sinusoidal planar grating. We numerically analyze the electromagnetic fields in the axisymmetric SWS with and without use of RH. The field patterns and eigenfrequency for the SWS are solved numerically for a given k(z) by using the code HIDM (higher order implicit difference method) that is free from the RH. It is found that, for a deep corrugation, h K0 =5 x 0.448, using RH is still valid for obtaining the dispersion relation, although the Floquet harmonic expansion (FHE) fails to correctly represent the field patterns inside the corrugation. Accordingly, there exists a discrepancy between the validity of using RH for obtaining dispersion relations and for an exact convergence of FHE everywhere in the SWS.
Watanabe
T
T
Theory and Data Analysis Division, National Institute for Fusion Science, Toki City 509-5292, Japan.
Choyal
Y
Y
Minami
K
K
Granatstein
V L
VL