Optimizing Laser Pulses for Narrow-Band Inverse Compton Sources in the High-Intensity Regime

Scattering of ultraintense short laser pulses off relativistic electrons allows one to generate a large number of X- or gamma-ray photons with the expense of the spectral width—temporal pulsing of the laser inevitable leads to considerable spectral broadening. In this Letter, we describe a simple method to generate optimized laser pulses that compensate the nonlinear spectrum broadening and can be thought of as a superposition of two oppositely linearly chirped pulses delayed with respect to each other. We develop a simple analytical model that allows us to predict the optimal parameters of such a two-pulse—the delay, amount of chirp, and relative phase—for generation of a narrow-band $\gamma$-ray spectrum. Our predictions are confirmed by numerical optimization and simulations including three-dimensional effects.

Figure 1

Schematic sketch of the two-pulse model for generating optimized laser pulses for narrow-band nonlinear ICS (a). Wigner function of the recombined two-pulse for $\mathit{B}=\{1.4,4.5,-4.6\}$ (b). The black curve is the analytical expression for the instantaneous frequency ${\omega }_L(\phi )$, and the green dashed curve is the analytical instantaneous $1+a^2(\phi )$.

Figure 2

(a) On-axis scattered photon spectra for $a_0=2$, $\mathrm{\Delta }{\omega }_L/{\omega }_0=0.1$ for different values of parameters $\mathit{B}$. The spectrum for the unchirped case with $\mathit{B}=\mathbf{0}$ is drawn with a dashed black line. Note, that for visibility, the spectrum has been multiplied by 5. The case of the optimal set of parameters $\mathit{B}=\{1.4,4.5,-4.6\}$ is shown with a blue curve. The red cure demonstrates the on-axis scattered photon spectrum for the matched unchirped Gaussian pulse (described in the text). (b) Corresponding amplitudes $a(\phi )$ of the normalized laser vector potential.

Figure 3

(a) Optimal chirp parameters $B_0$ (red diamonds), $B_1$ (green squares), and $B_2$ (blue circles) that lead to the narrowest on-axis scattered photon spectrum and obtained from simulations, as functions of $a_0$ for $\mathrm{\Delta }{\omega }_L/{\omega }_0=0.1$. Shaded areas of corresponding colors are the model predictions, Eq. (8). (b) Relative rms bandwidth of the on-axis photon spectrum for the optimally chirped pulse. (c) Peak spectral brightness (psb) of the on-axis scattered photons as a function of $a_0$ for the optimally chirped pulse (purple diamonds) and compared to matched Gaussian (orange squares) and unoptimized cases (cyan circles). The black dotted curve represents a fit $f(a_0)=637a_0^{2.8}$ of the optimized case, the shaded area corresponds to peak spectral brightness predicted using model parameters just like in (a).

Figure 4

Simulated spectral-angular Compton photon distribution for a 50 pC realistic electron beam interacting with a focused laser pulse. The green curve is an on-axis lineout.