Optimizing Light-Shining-through-a-Wall Experiments for Axion and other WISP Searches

One of the prime tools to search for new light bosons interacting very weakly with photons -- prominent examples are axions, axion-like particles and extra ``hidden'' U(1) gauge bosons -- are light-shining-through-a-wall (LSW) experiments. With the current generation of these experiments finishing data taking it is time to plan for the next and search for an optimal setup. The main challenges are clear: on the one hand we want to improve the sensitivity towards smaller couplings, on the other hand we also want to increase the mass range to which the experiments are sensitive. Our main example are axion(-like particle)s but we also discuss implications for other WISPs (weakly interacting slim particles) such as hidden U(1) gauge bosons. To improve the sensitivity for axions towards smaller couplings one can use multiple magnets to increase the length of the interaction region. However, naively the price to pay is that the mass range is limited to smaller masses. We discuss how one can optimize the arrangement of magnets (both in field direction as well as allowing for possible gaps in between) to ameliorate this problem. Moreover, future experiments will include resonant, high quality optical cavities in both the production and the regeneration region. To achieve the necessary high quality of the cavities we need to avoid too high diffraction losses. This leads to minimum requirements on the diameter of the laser beam and therefore on the aperture of the cavity. We investigate what can be achieved with currently available magnets and desirable features for future ones.