# Radiation force corrections to planar wiggler FEL gain

B. W J McNeil, W J Firth

Research output: Contribution to journalArticle

### 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 445-448 4 Nuclear Inst. and Methods in Physics Research, A 250 1-2 Published - 1 Sep 1986

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pendulums
electrons
Bessel functions
Lorentz force
spontaneous emission
deflection
derivation
inclusions
harmonics
cross sections
products
magnetic fields

### Cite this

McNeil, B. W J ; Firth, W J. / Radiation force corrections to planar wiggler FEL gain. In: Nuclear Inst. and Methods in Physics Research, A. 1986 ; Vol. 250, No. 1-2. pp. 445-448.
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title = "Radiation force corrections to planar wiggler FEL gain",
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. {\circledC} 1986.",
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Radiation force corrections to planar wiggler FEL gain. / McNeil, B. W J; Firth, W J.

In: Nuclear Inst. and Methods in Physics Research, A, Vol. 250, No. 1-2, 01.09.1986, p. 445-448.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Radiation force corrections to planar wiggler FEL gain

AU - McNeil, B. W J

AU - Firth, W J

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N2 - 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.

AB - 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.

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