Relativistic Nonlinear Electrodynamics by Hamlet Karo Avetissian

Author:Hamlet Karo Avetissian
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(8.142)

where is a slowly varying envelope and is the coordinate along the electron beam propagation. Taking into account (8.140), the rate of energy exchange between the electrons and probe wave can be expressed in the form

(8.143)

where

(8.144)

Then, the coherence condition, at which the bremsstrahlung emitted from various crystal centers along the electron path interfere constructively, is the following:

(8.145)

which represents the general resonance condition for the forward radiation. Though the consideration can be easily generalized to higher harmonics, we will consider the fundamental resonance and keep only the resonant term () in (8.143). For the formulation of the Maxwell–Vlasov equations it is convenient to change the independent variables from () to (, ) and the conjugate variable to will be

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