
Accession Number : AD0763091
Title : Utility of the Method of Steepest Descents in Analysis of Traveling Wave Instabilities.
Descriptive Note : Master's thesis,
Corporate Author : AIR FORCE INST OF TECH WRIGHTPATTERSON AFB OHIO SCHOOL OF ENGINEERING
Personal Author(s) : Johnson,David L.
Report Date : JUN 1973
Pagination or Media Count : 74
Abstract : The report analyzes some simple traveling wave instabilities which are mathematically similar to the instabilities found in electron beam tubes. The differential equation describing the system is solved by applying the Laplace transform over time and the Fourier transform over space. The resulting equation in transformed variables is solved algebraically and the inverse double transform obtained to yield the desired solution in space and time. The calculus of residues is used to obtain the inverse Fourier transform. The inverse Laplace transform cannot always be obtained exactly however. When this is the case, the method of steepest descents is used to obtain a closed form approximation to the inverse Laplace transform which will asymptotically approach the inverse Laplace transform for late times. The method of steepest descents not only provides an asymptotic approximation in closed form, but does so in a manner that facilitates a physical interpretation of the results obtained. (Modified author abstract)
Descriptors : (*ELECTROMAGNETIC RADIATION, STABILITY), STEEPEST DESCENT METHOD, INTEGRAL TRANSFORMS, FOURIER ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, COMPLEX VARIABLES, ANALYTIC FUNCTIONS, PLASMAS(PHYSICS), TRAVELING WAVE TUBES, THESES
Subject Categories : Radiofrequency Wave Propagation
Distribution Statement : APPROVED FOR PUBLIC RELEASE