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Analytic Criteria for Stability of Beam Loaded R.F. Systems
BibTeX
@MISC{Triumf_analyticcriteria,
author = {Shane Koscielniak Triumf and Shane R. Koscielniak and Triumf Vancouver and B. C. Canada and I T (t)e},
title = {Analytic Criteria for Stability of Beam Loaded R.F. Systems},
year = {}
}
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Abstract
This paper presents the instability analysis of a beamloaded radio-frequency system with beam phase-loop and cavity tuning-loop for both accelerating and nonaccelerating beams. The case of voltage-proportional feedback around the cavity is also included. The symbolic manipulation program SMP [1] was used to expand and simplify the Routh determinantal conditions for a fifth order characteristic polynomial. The paper is a much abridged version of an internal design note [2]. I. Beam Loading Equations The disposition of steady state phasors is as shown above. We adopt the notation of Reference [2]. The cavity voltage is V(t)e j!t and the total current driving the cavity is I T (t)e j!t , where t indicates time and ! is the drive angular frequency. Bold face indicates complex quantities, and ordinary type denotes scalars. We employ dot notation for time derivatives. The cavity fundamental resonance is modelled as a parallel resonance LCR circuit. Let \Omega res = 1= p LC be the re...
Keyphrases
analytic criterion beam loaded r.f. system nonaccelerating beam drive angular frequency beam phase-loop dot notation steady state phasors fifth order characteristic polynomial cavity tuning-loop internal design note bold face cavity voltage symbolic manipulation program smp cavity fundamental resonance instability analysis parallel resonance lcr circuit routh determinantal condition complex quantity radio-frequency system ordinary type beam loading equation time derivative voltage-proportional feedback
