Abstract: Apparatus and method are provided for causing different groups of particles from an accelerated electron or positron beam to interact exclusively in different sections of a free electron laser. The sections may be one or several amplifiers and an oscillator. The electron beam of a single accelerator used to excite a free electron laser is directed to traverse first an amplifier section or a sequence of amplifier sections and thereafter is directed into an oscillator section where the electron beam induces lasing. If the beam source is pulsed, this invention produces the proper time synchronization of electron and laser pulses. Specifically, delay times between optical pulses are employed among the oscillator and the amplifier or amplifiers to cause the laser to oscillate on the appropriate subharmonic or subharmonics of the accelerator repetition rate so that the intervening electron pulses are used only in the amplifier or amplifiers.