Generation and growth rates of nonlinear distortions in a traveling wave tube

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 5, 2002, Pages 5-

  Wöhlbier, John G ^a   Dobson, Ian ^a   Booske, John H ^a  

^a Wisconsin Electric Machines and Power Electronics Consortium   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EULERIAN EQUATIONS; INTERMODULATION FREQUENCIES; NONLINEAR DISTORTIONS; NONLINEAR PHYSICS;

BANDWIDTH; COMPUTER SIMULATION; DIFFERENCE EQUATIONS; ELECTRIC FIELD EFFECTS; ELECTRON BEAMS; INTERMODULATION; MATHEMATICAL MODELS; VELOCITY MEASUREMENT;

TRAVELING WAVE TUBES;

ARTICLE;

EID: 41349123685     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.056504     Document Type: Article

References (10)

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2. C. Armstrong (private communication).
3. J.G. Wöhlbier, J.H. Booske, and I. Dobson, IEEE Trans. Plasma Sci. (to be published).
4. R.G.E. Hutter, Beam and Wave Electronics in Microwave Tubes (Van Nostrand, Princeton, 1960).
5. E.A. Coddington and N. Levinson, Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1955), p. 78.
6. M.A. Wirth, A. Singh, J.E. Scharer, and J.H. Booske, IEEE Trans. Electron Devices 49, 1082 (2002).
7. T.M. Antonsen, Jr. and B. Levush, IEEE Trans. Electron Devices 26, 774 (1998).
8. The series solution of Eq. (7) can be obtained by setting (Formula presented) expanding in a power series in the parameter (Formula presented) and applying the method of small parameters; see e.g., S.G. Mikhlin and K.L. Smolitskiy, Approximate Methods for Solution of Differential and Integral Equations (American Elsevier, New York, 1967), p. 17.
9. In general, (Formula presented) is a vector of polynomials in z, i.e., there are “secular” terms in the solution. We assume that (Formula presented) is a constant vector, i.e., the term containing the maximum growth rate never has a factor of z multiplying the complex exponential. The secular terms arise in the special case of exact “resonance” of eigenvalues of (Formula presented) for different values of (Formula presented) For example, to have a leading secular term in the harmonic solution, the dominant eigenvalue at the harmonic must be exactly equal to two times the dominant eigenvalue at the fundamental. For general dispersion, there is a zero probability of having such an eigenvalue resonance. However, in a dispersionless model secular terms must be accounted for and the present theory would need to be modified.
10. Since we measure growth rates from power vs axial position data, we actually compare two times Eq. (20) to the data. However, we do not make this distinction in the text of the paper.