Accession Number:

AD0260403

Title:

PHASE RELATIONSHIPS IN A NONLINEAR VELOCITY-MODULATED ELECTRON BEAM

Descriptive Note:

Corporate Author:

CORNELL UNIV ITHACA N Y

Personal Author(s):

Report Date:

1961-01-31

Pagination or Media Count:

1.0

Abstract:

The fundamental differential equation describing the polarization of an electron in an infinitely wide electron beam is derived. The modified fundamental differential equation is formulated into a fourth-degree non-linear partial differential equation. Terms involving the polarization raised to powers higher than the third are neglected and the remaining third-degree equation is separated into 3 linear differential equations by successive approximations. The solution to the differential equation for the first-degree polarization is substituted into the equation for the second-degree polarization to yield the driving terms of that equation. The second-degree polarization is composed of dc and first-harmonic frequency terms. The procedure is repeated and the fundamental-frequency terms of the third-degree polarization are computed. The component of the third-degree fundamental-frequency polarization in quadrature with the first-degree polarization describes the nonlinear phase shift behavior of the electron beam. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE