Principles of Operation of Gyrodevices

The operation of gyrodevices is based on the cyclotron maser instability. This instability originates from the relativistic dependence of the cyclotron frequency of electrons gyrating in an external magnetic field on their energy. So this effect has a purely relativistic nature, although it can be well pronounced also in electron beams moving with rather small velocities.

The process of interaction between gyrating electrons and electromagnetic (EM) waves can be subdivided into three stages. First, an EM wave modulates electron energies (modulation stage). This causes small changes in the cyclotron frequencies of electrons, thus some particles start to gyrate faster while others slower, which results in the formation of an electron bunch on a gyro-orbit (bunching stage). Note that, after initial modulation, this bunching may evolve even in the absence of an EM wave. Finally, when the bunch is formed in the decelerating phase with respect to the wave, this bunch can be decelerated by the wave, which will result in a decrease of electron orbital velocities (decelerating stage).

Such a subdivision of the interaction process clearly indicates that, in a certain sense, gyrodevices can be treated as conventional klystrons driven by linear electron beams. However, this analogy can be made in a much more general way because, as follows from the Table, for each microwave source driven by a linear beam its counterpart among gyrodevices can be found.

The interaction between EM waves and gyrating electrons is most efficient when the wave frequency, w, is close to the electron cyclotron frequency, W, or its harmonic sW (s is the harmonic number). In the reference frame with the origin on the gyration axis, such resonance fields have a multipole structure with the order of multipole equal to the resonant harmonic number, as shown in the figure.

Since an electron bunching is a nonlinear process, in multi-stage gyrodevices (e.g., gyroklystrons or gyrotwystrons shown in the Table) the modulation of electron energies in the input stage at the signal frequency may cause the appearance of harmonics of this frequency in the electron current density. Then, the output stage of the device can be excited by one of such harmonics. So, multi-stage gyrodevices can operate in the regime of frequency multiplication.