Accelerator apparatus (100) for accelerating charged particles (2) with pulsed radiation includes horn-shaped coupling device (10) with at least one horn coupler (11, 15) having input aperture (12), electrically conductive walls (13) and output aperture (14), wherein pulsed radiation is received at input aperture and focused towards output aperture, and waveguide device (20) coupled with the output aperture and configured for receiving focused pulsed radiation. Waveguide device includes injection section (21) for providing charged particles and subjecting them to acceleration by pulsed radiation in injection section, and lateral output port (23) for releasing accelerated charged particles along particle acceleration direction. The at least one horn coupler receives linearly polarized single cycle pulses (1) including broadband frequency spectrum shaped as a linearly polarized plane wave and focuses linearly polarized single cycle pulses. Waveguide device has non-resonant broadband transmission characteristic. Furthermore, charged particle gun and method of accelerating charged particles are described.