Laboratoire Leprince-Ringuet
l’infiniment petit Plasma-wakefield acceleration promises orders of magnitude higher gradients than can be achieved via conventional radio-frequency cavities. It is now starting to be proposed for use in e.g. photon-science facilities. However, its application to particle-physics colliders has always been complicated by the difficulty in accelerating positrons. I will introduce the basics of plasma wakefield acceleration and explain the difficulty with accelerating positrons. HALHF avoids this by using a conventional linac to accelerate positrons, resulting in an asymmetric-energy, hybrid linear facility which is much smaller, greener and cheaper than any other Higgsfactory proposal. I will outline the original HALHF layout and principles, possible upgrades from the Higgs factory, recent design progress and the R&D path to making it a reality.