Emittance growth analysis of laser-driven broad energy spectral proton beams

With the rapid development of high-gradient laser plasma acceleration, implementing it in practical applications has become a priority. However, to go from “acceleration” to “accelerator,” a beam line system is required to accurately control the beam parameters according to different irradiation requirements. The laser-accelerated proton beam is characterized by a micron-scale original source size and a small emittance as low as 0.004 mm mrad [T. E. Cowan et al., Phys. Rev. Lett. 92, 204801 (2004)]. However, due to the broad energy spread and large divergence, its initial ultralow emittance will increase rapidly in the subsequent transmission process. This indicates that designing a beamline for laser-driven protons is challenging and differs significantly from that of a conventional accelerator. As a fundamental parameter for beam line design, we have theoretically derived the emittance growth law for laser-driven protons in both drift space and in a focusing element. The results demonstrate that the beam emittance deteriorates sharply with the energy spread and the square of the divergence angle. These theoretical calculations have been verified both in experiments and simulations. This work is helpful for designing subsequent beam lines that pursue high transmission efficiency and achromatic ability.