Conditions for self-excitation of a cyclotron resonance maser with a nonresonant electrodynamic system

Conclusions

Despite the complexity of the linearized equations for a CRM having a high-frequency field of nonfixed structure, many of the most important characteristics of the starting regime in systems with arbitrary Q can be obtained analytically by the prescribed-field method or the dispersion-equation method. Where necessary, more exact results may be obtained by numerical investigation (1)–(3). Analysis of the self-excitation conditions for elementary systems (Fig. 1) on the basis of these methods leads to the following results.

• 1) The starting current (all other parameters being equal) is determined by the ratio of resonator Q to the minimum diffractional Q and depends weakly on the specific methods used to create wave reflection (contraction or expansion of the waveguide at the ends of the working space).

• 2) When the adjustment of the magnetostatic field is varied, the structure of the high-frequency field is continuously deformed, since there is an increase in the number of longitudinal variations as the field strenght H₀ rises. In a CRM with a high-Q (Q≪Q^*) resonator, the greatest changes in field structure take place in tuning regions where self-excitation is impossible according to the prescribed-field approximation.

• 3) The self-excitation of parasitic modes having the same transverse field structure as the working mode will be excluded if the electron-beam current is less than the starting current of the mode having q =1 for amplifiers of the CRM-klystron or CRM-twistron type and of the mode having q=2 for a CRM monotron. The starting-current ratio for modes with q=1 and q=2 in a CRM with a low-Q electrodynamic system is of the order of 4–7.

• 4) The greatest danger in low-Q systems is the excitation of competing modes having lower critical frequencies than that of the working mode, since the value of starting current rises slowly on the high-frequency branches of the I(δ) curves and rapidly on the low-frequency branches (in the first case, there is continuous fine tuning to resonance with the opposed wave as the magnetic field increases, ω+hv∥-nω_H≈0; in the second case, the condition for resonance interaction with either the opposed or cotraveling wave is rapidly violated).