### Abstract

The longitudinal electron dynamics in an FEL are governed by the coupling of the electrons transverse velocity, V_{?}, to the combined magnetic fields of the wiggler and radiation in the Lorentz force equation. The derivation of the "standard" gain expression neglects the radiation contribution to V_{?} and assumes V_{?} results from the wiggler field alone [1]. We show, however, that the radiation contribution to V_{?} couples with the wiggler field to produce a force of the same order as that from the wiggler field coupling with the radiation field [2]. When this former force, the "radiation force", is included in the electron dymanics, the "difference of Bessel function factor" in the pendulum equation differs significantly from that of the standard expression, being given by: 1 21+ 1 fJ_{ (f-1) 2}(f?)-1- 1 fJ_{ (f+1) 2}(f?)(-1)^{ (f-1) 2} instead of {J_{ (f-1) 2}(f?)-J_{ (f+1) 2}(f?)}(-1)^{ (f-1) 2}. The gain is then proportional to the product of these two factors, rather than the square of the latter. The corrections to the pendulum/gain expressions result in approximately a 20% increase in gain at the fundamental but a 20% decrease in gain at the third harmonic for deflection parameter K = 2. The standard expressions for helical wiggler gain and spontaneous emission cross-sections are unaffected by inclusion of the radiation force term. © 1986.

Original language | English |
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Pages (from-to) | 445-448 |

Number of pages | 4 |

Journal | Nuclear Inst. and Methods in Physics Research, A |

Volume | 250 |

Issue number | 1-2 |

Publication status | Published - 1 Sep 1986 |

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## Cite this

*Nuclear Inst. and Methods in Physics Research, A*,

*250*(1-2), 445-448.