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Formulation of normalized nonlinear free electron laser equations

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2 Author(s)
Tang, C.M. ; Naval Research Laboratory, Washington, D. C. 20375 ; Sprangle, P.

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The general nonlinear self‐consistent equations describing the FEL in the steady‐state amplifying configuration is derived with the space‐charge effects and all the efficiency enhancement schemes: (i) a spatially varying wiggler amplitude and/or period and (ii) a dc electric field Edc (z) = [-∂ϕdc /∂z]êz. All the efficiency enhancement schemes are shown to be somewhat equivalent. For a variable period magnetic wiggler, the FEL equations can be appropriately normalized to a three‐parameter set of coupled equations. All operating regimes are covered by these normalized equations. The condition for space charge to be unimportant is given. In the absence of the space‐charge effects, the three‐parameter set of equations reduces to a two‐parameter set. The inclusion of additional efficiency enhancement schemes increases the number of parameters to describe the FEL. Curves showing the efficiency, radiation amplitude, and growth rate will be presented.

Published in:

Journal of Applied Physics  (Volume:53 ,  Issue: 2 )