  Gravitational waves provide a novel way to probe axions or axion-like
particles coupled to a dark photon field, even in the absence of couplings to
Standard Model particles. In the conventional misalignment mechanism, the
generation of an observable stochastic gravitational wave background, however,
requires large axion decay constants. We here investigate the gravitational
wave signal generated within the kinetic misalignment scenario, where the axion
is assumed to have a large initial velocity. Its kinetic energy then provides a
sufficiently high energy budget to generate a detectable gravitational wave
signal also at lower values of the decay constant. We obtain an analytic
estimate as well as perform numerical simulations of the corresponding
gravitational wave signal, and evaluate its detectability at current and future
gravitational wave observatories. We further present the corresponding
projected constraints on the parameter space of the model, along with the
parameter regions in which the dark photon or axion constitute dark matter, or
in which the baryon asymmetry of the Universe is generated via the axiogenesis
mechanism. Finally we compute the GW production from the fragmentation of
rotating axions, which is however difficult to observe experimentally.
