Optimizing the interaction geometry of inverse Compton scattering x-ray sources
Inverse Compton scattering (ICS) is a promising method for generating coherent and tunable x-rays in a compact setup. In this paper, we present a theoretical framework describing the output of an ICS x-ray source for arbitrary interaction angles between pulsed electron and laser beams, in the Thomson regime. This allows for analytic optimization of the x-ray beam properties by varying the parameters defining the geometry. In general, different x-ray applications require optimization of different x-ray beam properties, such as energy spread for x-ray spectroscopy and angular spread for x-ray scattering measurements. In this paper, we restrict ourselves to optimization of the x-ray brilliance, which is a comprehensive figure of merit for x-ray beam quality. The framework can be used, however, to optimize other x-ray properties. We investigate two specific ICS interaction geometries in particular: head-on scattering of a laser beam off an electron beam; and scattering of a laser beam off an electron beam in a co-propagating geometry, interacting under a grazing angle. For head-on scattering we show that a tightly focused, cylindrically symmetric laser pulse, which balances laser intensity and interaction time, optimizes the x-ray brilliance. For a co-propagating, grazing angle geometry, an elliptical focus of the laser pulse is required to mitigate the geometric reduction of the interaction time. We find that the latter geometry is especially useful for soft x-ray generation.