Open AccessANALYTIC RESEARCH ON THE DISPERSION RELATION AND FIELD DISTRIBUTION OF THE RESON ANT CAVITY CHAIN
Author(s) -
Zhongwei Fan,
Qingxiang Liu
Publication year - 2000
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.49.1249
Subject(s) - physics , dispersion relation , field (mathematics) , scalar field , boundary value problem , helmholtz free energy , analytic function , classical mechanics , quantum electrodynamics , mathematical analysis , optics , quantum mechanics , mathematics , pure mathematics
Starting from homogeneous scalar Helmholtz's equations associated with Borgnis p otential function in a cylindrical coordinate system, and based on the standing wave concept of slow-wave introduced in the paper, the analytic expressions of the dispersion relation and field distribution for azimuthally symmetric transverse magnetic modes in the resonant cavity chain with full-cavity terminations are derived, by using boundary conditions for Borgnis potential function in conjunction with field matching conditions at the common interface between adjacent sub regions. The resonance frequency of the four-cavity transit-time tube oscillator calculated by this analytic method is compared with that measured in experiment s and it is found that they are in agreement quite well. The field distribution of the oscillator developed by this analytic method is agreeable to that simula ted by numerical code.