Status of and upgrade concepts for HALHF: the hybrid, asymmetric, linear Higgs factory

This contribution outlines the HALHF concept, which combines the high gradients achievable in plasma-wakefield acceleration with conventional radio-frequency acceleration. In HALHF, beam-driven plasma-wakefield cells are used to accelerate electrons to high energy. Because plasma-based acceleration of positrons is problematic, conventional RF acceleration is used but to much lower energy. The HALHF concept utilises not only asymmetric energies but also asymmetric bunch charges and asymmetric transverse emittances, leading to comparable luminosity to conventional facilities but much lower capital cost. Possible upgrades to the HALHF facility are discussed, in particular to the $\rm{t\bar{t}}$ threshold and to 550 GeV, where the Higgs self-coupling and $\rm{t\bar{t}}H$ coupling can be measured. Other upgrades include the provision of two interaction points, to implement a $\gamma$$\unicode{x2013}$$\gamma$ collider of two possible types and finally a symmetric high-energy collider if the problem of plasma-based positron acceleration can be solved.