No monochromatic ($\Delta {\omega }_x/{\omega }_x<1\%$), high peak brightness [$>{10}^{20}\mathrm{photons}/(\mathrm{m}{\mathrm{m}}^2\times {\mathrm{mrad}}^2\times \mathrm{s}\times 0.1\%\mathrm{bandwidth})$], tunable light sources currently exist above 100 keV. Important applications that would benefit from such new hard x-ray and $\gamma$-ray sources include the following: nuclear resonance fluorescence spectroscopy and isotopic imaging, time-resolved positron annihilation spectroscopy, and MeV flash radiography. In this paper, the peak brightness of Compton scattering light sources is derived for head-on collisions and found to scale quadratically with the normalized energy, $\gamma$; inversely with the electron beam duration, $\Delta \tau$, and the square of its normalized emittance, $\epsilon$; and linearly with the bunch charge, $e{N}_e$, and the number of photons in the laser pulse, $N_{\gamma }\mathrm{\text{:}}{\widehat{B}}_x\propto {\gamma }^2{N}_e{N}_{\gamma }/{\epsilon }^2\Delta \tau$. This ${\gamma }^2$ scaling shows that for low normalized emittance electron beams (1 nC, $1\mathrm{mm}·\mathrm{mrad}$, $<1\mathrm{ps}$, $>100\mathrm{MeV}$), and tabletop laser systems ($1–10\mathrm{J}$, 5 ps) the x-ray peak brightness can exceed ${10}^{23}\mathrm{photons}/(\mathrm{m}{\mathrm{m}}^2\times {\mathrm{mrad}}^2\times \mathrm{s}\times 0.1\%\mathrm{bandwidth})$ near $\hslash {\omega }_x=1\mathrm{MeV}$; this is confirmed by three-dimensional codes that have been benchmarked against Compton scattering experiments performed at Lawrence Livermore National Laboratory. The interaction geometry under consideration is head-on collisions, where the x-ray flash duration is shown to be equal to that of the electron bunch, and which produce the highest peak brightness for compressed electron beams. Important nonlinear effects, including spectral broadening, are also taken into account in our analysis; they show that there is an optimum laser pulse duration in this geometry, of the order of a few picoseconds, in sharp contrast with the initial approach to laser-driven Compton scattering sources where femtosecond laser systems were thought to be mandatory. The analytical expression for the peak on-axis brightness derived here is a powerful tool to efficiently explore the 12-dimensional parameter space corresponding to the phase spaces of both the electron and incident laser beams and to determine optimum conditions for producing high-brightness x rays.

• Received 11 November 2004

DOI:https://doi.org/10.1103/PhysRevSTAB.8.100702

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