Telescopic zoom system for electron acceleration with lasers: general design and tests

Both the size of the focal spot and the Rayleigh range of laser beams are increasing with the focal length of a focusing system. When preparing experiments for accelerating electron with lasers, people are considering focal lengths that can range from a few meters up to tens of meters. Telescopic zoom systems made of three spherical mirrors can be designed for such purpose. After a first attempt to design such system based on simple “a priori” parameters, a general algebraic theory has been investigated and shows that there are always solutions with no spherical aberration. When all mirrors are placed off-axis to avoid obscuration of the beam, it is possible to show that there are still solutions that minimize aberrations. When changing the distance between the mirrors, we can obtain a focal excursion of the system while the final focal spot is fixed. Of course, the goal of the study is to find what are the solutions that minimize aberrations for a given numerical aperture over a given zoom range. I have built and tested three zoom systems based on different solutions and I have been able to show that there are simple alignment procedures for generating a fixed focal spot over the zoom range. In this paper, a step-by-step analysis including damage fluence considerations for designing the 3-mirror zoom system will be detailed.