Quasilinear theory of terahertz free-electron lasers based on Compton scattering of incoherent pump wave by intense relativistic electron beam

The use of incoherent broadband pump radiation for improving the electron efficiency in the free-electron lasers (FEL) based on stimulated backscattering is considered. On the basis of a quasilinear approach, it is shown that the efficiency increases in proportion to the width of the pump spectrum. The effect is owing to a broadening of the spectrum of synchronous combination waves and realization of a mechanism of stochastic particle deceleration. The injection of a monochromatic seed signal in a single pass FEL amplifier or the implementation of a selective high-Q resonator in an FEL oscillator makes the high-frequency scattered radiation be monochromatic in spite of an incoherent pumping. In the regime of stochastic particle deceleration, the efficiency only slightly depends on the spread of the beam parameters, which is beneficial for a terahertz FEL powered by intense relativistic electron beams.

Figure 1

Schematic of amplifier (a) and generator (b) with incoherent pump wave. (1) Electron beam; (2) waveguide; (3) Bragg reflectors.

Figure 2

Single-pass amplifier. (a) Mutual arrangement of electron distribution function $\stackrel{⌢}{F}(u)$ with initial energy dispersion $\delta =0.035$ and profile of pump spectrum (blue line) with a half-width $\sigma =0.07$ in the energy space. The shift between the center of the pump spectrum and the center of the electron distribution function is $ϵ=1-u_i=0.05$. (b) Dependence of spatial growth rate $\mathrm{\Lambda }$ on relative shift $ϵ$ for different values of the pump spectrum half-width $\sigma$ calculated for electron energy dispersion $\delta =0.035$.

Figure 3

(a) Spatial evolution of the electron distribution function $\stackrel{⌢}{F}(u,Z)$ for the initial electron energy dispersion $\delta =0.02$, pump spectrum half-width $\sigma =0.07$, and relative shift $ϵ=0.08$, which is optimal for efficiency. Pump spectrum profile is shown by the black line. (b) Dependences of the electron efficiency $\eta$ on the amplification length $Z$ for the different pump spectrum half-width $\sigma$ and the optimal relative shift $ϵ$.

Figure 4

Dependence of (a) spatial growth rate $\mathrm{\Lambda }$ and (b) the electron efficiency $\eta$ on the shift $ϵ$ between the center of the pump wave spectrum and the center of the electron distribution function for a fixed half-width of pump spectrum $\sigma =0.07$ but different values of electron energy dispersion $\delta$.

Figure 5

Oscillator with the high-Q resonator. Temporal evolution of the electron distribution function $\stackrel{⌢}{F}(u,\overline{\tau })$ for different resonator lengths (a) $\tilde{L}=0.25$, (b) $\tilde{L}=0.5$. Profile of pump spectrum is shown by the black line. (c) Corresponding dependences of electron efficiency on time $\overline{\tau }$: $\delta =0.035$, $\sigma =0.035$, $ϵ=0.05$.

Figure 6

Oscillator with the high-Q resonator. Temporal dependences of electron efficiency for the given values of the electron energy dispersion $\delta$ and the pump spectrum half-width $\sigma$ at the different values of relative shift $ϵ$; $\tilde{L}=0.5$. (a) $\delta =0.035,$ $\sigma =0.035$; (b) $\delta =0.02$, $\sigma =0.07$.