Single-particle analysis of the free-electron laser sideband instability for primary electromagnetic wave with constant phase and slowly varying phase

Nuclear Instruments and Methods in Physics Research Section A:

1990

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It is shown that the inclusion of the equilibrium self fields of the electron beam results in chaotic electron motion in the field configuration consisting of a constant-amplitude helical wiggler magnetic field and a uniform axial guide field. The threshold value of the self-field parameter e = w/4Q' is determined for the onset of chaoticity in the Group-I and Group-II orbits for the parameter regime corresponding to moderately high beam current (and density). The time scale for self-field-induced changes in the particle orbits is found to be of the order of beam-transit time through one wiggler period.

Section: T =-Z T" (17)mentioning

confidence: 99%

Self-field-induced chaotic electron motion in free electron lasers

Chen

Nuclear Instruments and Methods in Physics Research Section A:

1990

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“…Finally, for future reference, we introduce the small dimensionless parameter r defined by 23 , 37 1 a 2…”

Section: )mentioning

confidence: 99%

“…II) is based on the single-particle orbit equations together with Maxwell's equations and appropriate statistical averages. 36 , 37 Like our recent treatment 37 of the sideband instability (which neglects the effects of untrapped electrons), the present analysis is carried out in the ponderomotive frame, which leads to a substantial simplification in the analysis.…”

Section: Introductionmentioning

confidence: 99%

Influence of untrapped electrons on the sideband instability in a helical wiggler free electron laser

Wurtele

1987

The Physics of Fluids

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The detailed influence of an untrapped-electron population on the sideband instability in a helical wiggler free electron laser is investigated for smallamplitude perturbations about a constant-amplitude (as = const.) primary electromagnetic wave with slowly varying equilibrium phase 6 . A simple model is adopted in which all of the trapped electrons are deeply trapped, and the equilibrium motion of the untrapped electrons (assumed monoenergetic) is only weakly modulated by the ponderomotive potential. The theoretical model is based on the single-particle orbit equations together with Maxwell's equations and appropriate statistical averages. Moreover, the stability analysis is carried out in the ponderomotive frame, which leads to a substantial simplification in deriving the dispersion relation. Detailed stability properties are investigated over a wide range of dimensionless pump strength B /rbck0 and fraction of untrapped electrons f = Au b. When both trapped and untrapped electrons are present, there are generally two types of unstable modes, referred to as the sideband mode, and the untrapped-electron mode. For fu = 0, only the sideband instability is present. As fu is increased, the growth rate of the sideband instability decreases, whereas the growth rate of the untrapped-electron mode increases until only the untrapped-electron mode is unstable for fu = 1. It is found that the characteristic maximum growth rate of the most unstable mode varies by only a small amount over the entire range of f u from fu = 0 (no untrapped electrons) to fu = 1 (no trapped electrons). This suggests that it is a serious oversight to neglect an untrapped-electron component when calculating the detailed linear and nonlinear evolution of the beam electrons and the radiation field.Permanent address:

“…In a subsequent analysis, 2 2 the detailed dependence of the sideband instability on the system parameters was examined. Moreover, Davidson and Wurtele 24 have developed a single-particle model (with appropriate statistical averages) to analyze the sideband instability in the ponderomotive frame. The effects of the untrapped electrons have also been considered.…”

Section: Introductionmentioning

confidence: 99%

Influence of the trapped-electron distribution on the sideband instability in a helical wiggler free-electron laser

Yang

Physics of Fluids B: Plasma Physics

1990

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Use is made of the Vlasov-Maxwell equations to investigate detailed properties of the sideband instability for a helical wiggler free-electron laser with wiggler wavelength A, = 27r/ko =const and normalized wiggler amplitude a, = eB./mc 2 ko =const. The model describes the nonlinear evolution of a right-circularly polarized primary electromagnetic wave with frequency w,, wavenumber k,, and slowly varying amplitude a,(z, t) and phase 8,(z,t) (eikonal approximation). The coupled Vlasov and field-evolution equations are analyzed in the ponderomotive frame ("primed" variables) moving with velocity v, = w,/(k, -+-ko) relative to the laboratory. Detailed properties of the sideband instability are investigated for small-amplitude perturbations about a quasi-steady state characterized by an equilibrium electron distribution f'(-yb) and a primary electromagnetic wave with constant amplitude a' =const (independent of z' and t') and slowly varying phase 60(z'). A formal dispersion relation is derived for perturbations about a general equilibrium distribution f 0 (ys) which may include both trapped and untrapped electrons. For the case where only trapped electrons are present, the dispersion relation is reduced to a simple analytical form. Detailed properties of the sideband instability are investigated for the case where the trapped electrons uniformly populate the ponderomotive potential up to an energy 7's < +, where j is the energy at the separatrix. Analysis of the dispersion relation shows that the maximum energy of the trapped-electron population (4') significantly affects detailed stability properties in the strong-pump and intermediate-pump regimes.