A scheme for fast, compact and controllable acceleration of heavy particles in vacuum has been recently proposed (Peano F et al 2008 New J. Phys.10 033028), wherein two counterpropagating laser beams with variable frequencies drive a beat-wave structure with variable phase velocity, leading to particle trapping and acceleration. The technique allows for fine control over the energy distribution and the total charge of the accelerated beam to be obtained via tuning of the frequency variation. Here, the theoretical bases of the acceleration scheme are described, and the possibility of applications to ultrafast muon acceleration and to the prompt extraction of cold-muon beams is discussed.