Narrow-Band Emission in Thomson Sources Operating in the High-Field Regime

We present a novel and quite general analysis of the interaction of a high-field chirped laser pulse and a relativistic electron, in which exquisite control of the spectral brilliance of the up-shifted Thomson-scattered photon is shown to be possible. Normally, when Thomson scattering occurs at high field strengths, there is ponderomotive line broadening in the scattered radiation. This effect makes the bandwidth too large for some applications and reduces the spectral brilliance. We show that such broadening can be corrected and eliminated by suitable frequency modulation of the incident laser pulse. Furthermore, we suggest a practical realization of this compensation idea in terms of a chirped-beam-driven free electron laser oscillator configuration and show that significant compensation can occur, even with the imperfect matching to be expected in these conditions.

Figure 1

Thomson scattering for a chirped laser pulse. Chirping the electron bunch before it passes through an oscillator FEL produces a chirped laser pulse. Thomson scattering occurs as the laser pulse collides with an electron. Narrow-band emission of the resulting backscattered radiation is recovered through frequency chirping.

Figure 2

(a) Normalized spectra of scattered radiation for the case without FM (green line), FM from Eq. (3) (black line), FM from optimal $f_{\mathrm{GA}}$($\xi$; $b$, $c$) (blue line), and the exact FM from Eq. (4) (red line). The shapes of the spectra—both nonmodulated and modulated—are independent on the scattering electron’s energy. (b) Complete correction of spectral width is demonstrated by this comparison of the case with no FM (green line), the Fourier transform of the amplitude function (blue line), and the case with exact FM (red line). In both panels, a Gaussian envelope is used with $a_0=0.587$ and electron’s $\gamma =100$ as in Fig. 2 of Ref. [9].

Figure 3

Narrowing the radiation spectra by exact FM. Scattered spectral distributions calculated with no FM (green line), the GSU FM as in Eq. (5) (blue line), and the exact FM given in Eq. (6) (red line). A Gaussian envelope is used with $a_0=0.865$ as in Fig. 6 of Ref. [11]. Note the linear scale and that only data in the first harmonic is displayed for both panels. The top $x$ axis denotes photon energies for the case of $E_{\text{beam}}=300\mathrm{MeV}$, $\lambda =800\mathrm{nm}$, FWHM pulse duration of 90 fs, as in Fig. 6 of Ref. [11].