Simultaneous Amplification of Two Waves due to the Cyclotron Interaction with Ensemble of Nonresonant Electrons

A new regime of the parametric cyclotron interaction of the bichromatic field with ensemble of charged particles is discovered and investigated. In this regime the energy transfer from electrons to the field, accompanied by the simultaneous amplification of the field components, takes place. It is important that particles are not resonant to the monochromatic waves, but stay in synchronism with the beats wave during the process of interaction which is time limited. The mechanism of energy exchange in this process is investigated in the reference frame where field components have equal frequencies and differ from each other by longitudinal wave numbers. The motion of charged particle in the nonresonant monochromatic wave with spatial-dependent amplitude in the presence of constant magnetic field is accompanied by the change of its averaged kinetic energy. This result is well known for nonrelativistic motion. The sign of energy change is defined by the sign of gradient of the wave amplitude in the direction of particle motion. We have shown that for energy extraction from the electron ensemble it is necessary to co-ordinate the longitudinal motion of particles with spatial structure of the beats of two interacting waves. Such coordination is achieved by a preliminary (due to external sources) or self-consistent longitudinal modulation of the longitudinal velocity of electrons in ensemble. The energy extraction leads to simultaneous amplification of two waves. The analysis has shown that in the system with nonrelativistic particles the energy transmitted from the electrons to the amplified HF field cannot essentially exceed the power input necessary for excitation of the modulation of electron ensemble. Detailed analysis is carried out for more complicated schemes taking into account relativistic modifications. It is shown that the system with essentially relativistic particles close to the resonance with HF waves (but not resonant) is much more promising. It is shown that the effect of simultaneous amplification of two interacted waves can be observed at the stage of formation of the stationary nonlinear process of induced scattering.