NDLI: The range of validity of the Rayleigh hypothesis

Content Provider	IEEE Xplore Digital Library
Author	Watanabe, T. Choyal, Y. Minami, K. Granatstein, V.L.
Copyright Year	2004
Description	Author affiliation: Theor. & Data Anal. Div., Nat. Inst. for Fusion Sci., Toki, Japan (Watanabe, T.)
Abstract	Summary form only given. The parameter range over which the Rayleigh hypothesis (RH) for optical gratings might be validly applied to analysis of high power backward wave oscillators (BWOs) has been investigated numerically. A widely used method to analyze high power backward wave oscillators (BWO's) is to represent the electromagnetic (EM) fields in axisymmetric slow wave structure (SWS) in terms of a Floquet harmonic expansion (FHE). EM fields, E and B, are expressed in a form as, [E B]=/spl Sigma//sub n=-N//sup N/[E/sub n/(r) B/sub n/(r)]exp i(k/sub zn/z+l/spl theta/-/spl omega/t) where k/sub zn/=k/sub z/+nK/sub 0/, K/sub 0/ is wavenumber of SWS periodicity, and n=0, /spl plusmn/1, /spl plusmn/2,.../spl plusmn/N is the Floquet harmonic number. Expansion similar to (1) was firstly introduced by Lord Rayleigh for diffraction of waves from planar grating. He assumed that the expansion was applicable both outside and inside the corrugation, and this assumption is called as RH. It was argued by some mathematician that our numerical analysis was applied to deep corrugation of hK/sub 0/=1.67 which was beyond the limiting value hK/sub 0/=0.448 for validity in RH for planar sinusoidal grating, consequently the results were invalid. Here, h is the amplitude of corrugation. To respond the doubt, EM fields and dispersion relation in the SWS are numerically analyzed with and without RH for a given set of size parameters. The field patterns and eigen frequency for the SWS are solved for a given k/sub z/ numerically by using finite difference code HIDM (Higher Order Implicit Difference Method) that is free from RH. The results are compared with those using (1). For a deep corrugation, hK/sub 0/=5/spl times/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.
Sponsorship	Plasma Sci. and Applications Committee of the IEEE Nuclear and Plasma Sci. Soc
File Size	88405
File Format	PDF
ISBN	0780383346
ISSN	07309244
DOI	10.1109/PLASMA.2004.1340133
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2004-07-01
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Dispersion Oscillators Electromagnetic analysis Harmonic analysis Electromagnetic scattering Electromagnetic fields Power system harmonics Diffraction gratings Numerical analysis Frequency
Content Type	Text
Resource Type	Article
Subject	Atomic and Molecular Physics, and Optics Condensed Matter Physics Electrical and Electronic Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in