Optimizing the interaction geometry of inverse Compton scattering x-ray sources

TL;DR

The paper develops an analytical, covariant framework for inverse Compton scattering x-ray sources that works for arbitrary electron–laser interaction angles. It shows that tightly focused, geometry-specific laser spots and proper electron energy are crucial to maximize x-ray brilliance, deriving closed-form expressions for head-on and grazing-angle configurations. The grazing-angle approach, particularly with elliptical (line-focused) laser focusing, yields significant gains in soft x-ray brightness, and the authors validate the theory against simulations while outlining practical design guidelines. The results offer a path toward university-lab scale, tunable, coherent x-ray sources with lab-scale laser and electron-beam systems. The framework paves the way for compact, high-brilliance ICS sources by directly linking geometry, beam parameters, and x-ray performance.

Abstract

Inverse Compton scattering is developing to be a promising method to generate coherent and tunable x-rays. In this paper we present a theoretical framework to describe an inverse Compton scattering x-ray source for arbitrary interaction angles between the electron and laser pulse. Importantly the divergence of a tightly focused laser pulse will have a significant impact of the number of scattered x-rays. The parameters of the interaction geometry are optimized for two specific cases: head-on scattering; and a grazing co-propagating interaction angle. For head-on scattering we show that a tight symmetrically focused laser pulse, that balances laser intensity and interaction time, optimizes the x-ray brilliance. For a grazing angle geometry an elliptical focus of the laser pulse is required to mitigate a reduced interaction time. We find that the latter geometry is especially useful for soft x-ray generation.

Figures (11)

• Figure 1: a) Schematic representation of ICS. An electron (green) interacts with a laser pulse (red) under an angle $\theta_L$, generating an x-ray with emission angle $\theta_\mathrm{x}$. b) shows the angular radiation distribution, which becomes symmetrical for $\theta_\mathrm{x} \ll 1/\gamma$. Here the vertical axis is in the direction of the laser polarization. c) shows the spectral angular density, with $\omega_0 = \omega_L (1-\beta \cos\theta_L)/(1-\beta)$ is the on-axis x-ray frequency.
• Figure 2: Four illustrations of the geometries considered throughout this paper. In each geometry the electron bunch (green) with velocity $\boldsymbol\beta$ and laser pulse (red) with wave vector $\boldsymbol k_L$ are shown at three different times up until the collision. The top figures show the pencil beam (1) and focused laser beam (2) description in a head-on geometry. The bottom figures the pencil beam (3) and focused laser beam (4) description in a grazing angle geometry. The relevant r.m.s. pulse dimensions are also indicated
• Figure 3: Illustration of how the laser divergence effects the interaction time when the pulse length becomes comparable to the interaction length. The bottom graph shows the product of the electron and laser density as a function of time for a tight and loose focus.
• Figure 4: Plots of the function $g(u)$ for $\chi =0$ (green) and $\chi = 5$ (blue). The inset shows value of $u_\mathrm{max}$ for varying values of $\chi$. The green curve shows the function $1/u$ corresponding to the brilliance scaling of the pencil beam limit.
• Figure 5: X-ray brilliance in for 10 keV x-ray generation in a head-on geometry for varying bunch charge and matched electron and laser spot sizes. The analytical result of Eq. \ref{['eq:BrillianceDivergence1']} (solid curve) agrees well with simulation results (dots). The arrow marks the theoretical optimized bunch charge according to Eq. \ref{['eq:Qopt']}