Kinetic analysis of the sideband instability in a helical wiggler free-electron laser for electrons trapped near the bottom of the ponderomotive potential

1991

Phys. Rev. A

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The motion of a relativistic test electron in a free electron laser can be altered significantly by the equilibrium self-field effects produced by the beam space charge and current and by the transverse spatial inhomogeneities in a realizable magnetic wiggler field. In a field configuration consisting of an ideal (constant-amplitude) helical wiggler field and a uniform axial guide field, it is shown that the inclusion of self-field effects destroys the integrability of the particle equations of motion. Consequently, the Group-I orbits and the Group-II orbits become chaotic at sufficiently high beam density. An analytical estimate of the threshold value of the self-field parameter F, = wg/ckw for the onset of chaoticity is obtained and found to be in good agreement with computer simulations. In addition, the effects of transverse spatial gradients in a realizable helical wiggler field with three-dimensional spatial variations are investigated in the absence of an axial guide field, but including self-field effects. For a thin electron beam (k 2r2 < 1) and small wiggler field amplitude (a, < yb 2 ), it is shown that the motion is regular and confined radially provided E, < ybaw/(1 + al). However, because of the intrinsic nonintegrability of the motion, the regular region in phase space diminishes in size as the wiggler amplitude is increased. The threshold value of the wiggler amplitude for the onset of chaoticity is estimated analytically and confirmed by computer simulations for the special case where self-field effects are negligibly small. Moreover, it is shown that the particle motion becomes chaotic on a time scale comparable with the beam transit time through one wiggler period.

mentioning

confidence: 99%

Chaotic particle dynamics in free-electron lasers

Chen

1991

Phys. Rev. A

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“…(20), (24), (25) and (35), it is assumed that all electrons have zero transverse canonical momentum, i.e., P' .= 0 = P' .…”

Section: Ks + K0mentioning

confidence: 99%

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

Wurtele

1987

The Physics of Fluids

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Use is made of the single-particle orbit equations together with Maxwell's equations and appropriate statistical averages to investigate detailed properties of the sideband instability for a helical-wiggler free electron laser with wiggler wavelength x0 = 2w/k 0 = const. and normalized wiggler amplitude aw = eBw/mc 2 k 0 = const.The model describes the nonlinear evolution of a right-circularly-polarized primary electromagnetic wave with frequency ws, wavenumber ks, and slowly varying amplitude as(z,t) and phase s (z,t) (Eikonal approximation). The orbit and wave equations are analysed in the ponderomotive frame ("primed" variables) moving with velocity v = Ws/(ks + k 0 ) relative to the laboratory. Detailed properties of the sideband instability are investigated for small-amplitude perturbations about a quasi-steady equilibrium state characterized by a = const. (independent of z' and t'). Two cases are treated. The first case assumes constant equilibrium wave phase ss = const., which requires (for self-consistency) both untrapped-and trapped-electron populations satisfying N exp[ik'zJ0(t') + i6 ] /y,> =0. Here, k' = (ks + k 0 )/y p is the wavenumber of the ponderomotive potential; zjO(t') is the equilibrium orbit; and y mc is the electron energy. The second case assumes that all of the electrons are deeply trapped, which requires a slow spatial variation of the equilibrium wave phase, 30 /az0 2r ( rck/ 2 k 0. The resulting dispersion relations and des 0O0OOBp tailed stability properties are found to be quite different in the two cases. Both the weak-pump and strong-pump regimes are considered.

“…Another topic of considerable practical importance is the sideband instability'-" 21 In circumstances where the trapped electrons are localized near the bottom of the ponderomotive potential, it was found that the detailed stability properties are relatively insensitive to the form of the distribution of trapped electrons. In a subsequent analysis, 22 the detailed dependence of the sideband instability on 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.…”

Section: Introductionmentioning

confidence: 99%

Macroclump model of the nonlinear evolution of the sideband instability in a helical wiggler free-electron laser

Yang

Physics of Fluids B: Plasma Physics

1990

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The nonlinear evolution of a helical wiggler free electron laser is investigated within the framework of a macroclump model for the trapped electrons. The model describes the nonlinear evolution of a right-circularly polarized electromagnetic wave with frequency w, and wavenumber k,, and slowly varying amplitude &,(z, t) and phase 8 ,(z, t) (eikonal approximation). The model further assumes that the trapped electrons can be treated as tightly bunched macroclumps that interact coherently with the radiation field. The analysis is carried out in the ponderomotive frame, which leads to a substantial simplification in both the analytical and numerical studies. As a first application, the nonlinear evolution of the primary signal is examined when 98' = 0 (no spatial variation of the wave amplitude and phase). The evolution equations are reduced to quadrature, and the maximum excursion of the wave amplitude a,, is calculated analytically. Subsequently, the nonlinear evolution of the sideband instability is investigated, making use of the equations describing the self-consistent evolution of the wave amplitude &, and phase 8,, which vary slowly with both space and time, together with the macroclump orbit equation. In the present analysis, the sideband signals are treated as perturbations (not necessarily small) about a constant-amplitude (&0 = const) primary electromagnetic wave with slowly varying phase 6'(z'). The coupled orbit and field equations are investigated analytically and numerically over a wide range of system parameters to determine detailed scaling properties of the sideband instability. The results of the present analysis suggest that free electron lasers operating with system parameters corresponding to the strong-pump regime [(f'/I, )'/4 > 1] are least vulnerable to the sideband instability. Moreover, the nonlinear evolution of the sideband instability is investigated numerically for system parameters corresponding to the Los Alamos free electron laser experiment. In several aspects, the numerical results are found to be in good qualitative agreement with the experimental results.