Nonlinear Brightness Optimization in Compton Scattering

In Compton scattering light sources, a laser pulse is scattered by a relativistic electron beam to generate tunable $x$ and gamma rays. Because of the inhomogeneous nature of the incident radiation, the relativistic Lorentz boost of the electrons is modulated by the ponderomotive force during the interaction, leading to intrinsic spectral broadening and brightness limitations. These effects are discussed, along with an optimization strategy to properly balance the laser bandwidth, diffraction, and nonlinear ponderomotive force.

Figure 1

Quadratic sinc spectra in the linear limit and with nonlinear dephasing.

Figure 2

Top: linear spectra of a Gaussian-Lorentzian pulse for different balances between bandwidth and diffraction. Bottom: following the maximum angular and spectral brightness as function of $\eta =\sqrt{\Delta \varphi }/k_0{w}_0$, for a fixed total energy, in the linear regime.

Figure 3

Top: nonlinear spectra for $\Delta \varphi ={10}^5$, and $\eta =1.7087$; the spectra are divided by ${\alpha }^2\overline{W_0}/{\pi }^2$ for comparison. Middle: following the maximum brightness as a function of $W_0$ for $\Delta \varphi ={10}^3$ (dashed line) and $\Delta \varphi ={10}^6$ (solid line), and 3 values of $\eta$. The energy and brightness scales correspond to the long pulse; they have to be multiplied by ${10}^{-3}$ for the short pulse. Bottom: optimized nonlinear Gaussian-Lorentzian parameters as a function of available laser energy: $A_0^{*2}$ (dashed line); $w_0$ (dotted line); $\Delta t$ (dashed-dotted line); and $B_x^{*}$ (solid line), for $\rho =7.6009$ ($\gamma ={10}^3$).