Theoretical analysis of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator

Abstract

The basic theory of cross-talking signals between counter-streaming electron beams in a vacuum tube oscillator consisting of two two-cavity klystron amplifiers reversely coupled through input/output slots is theoretically investigated. Application of Kirchhoff’s laws to the coupled equivalent RLC circuit model of the device provides four nonlinear coupled equations, which are the first-order time-delayed differential equations. Analytical solutions obtained through linearization of the equations provide oscillation frequencies and thresholds of four fundamental eigenstates, symmetric/antisymmetric 0∕π modes. Time-dependent output signals are numerically analyzed with variation of the beam current, and a self-modulation mechanism and transition to chaos scenario are examined. The oscillator shows a much stronger multistability compared to a delayed feedback klystron oscillator owing to the competitions among more diverse eigenmodes. A fully developed chaos region also appears at a relatively lower beam current, ∼3.5Ist, compared to typical vacuum tube oscillators (10-100Ist), where Ist is a start-oscillation current.

Synchronization of two coupled multimode oscillators with time-delayed feedback

“…2(e)). Such a behavior is in good agreement with the picture described in [43,44] for the two-stage klystron oscillator. , phase portraits (center) and spectra (right) demonstrating symmetry breaking and transition to chaos for the two-stage oscillator (8).…”

Theory and simulation of a two-stage W-band multiple cavity klystron oscillator

“…At higher values of current, non-stationary selfmodulation regimes are observed (c.f. [4,5]). Thus, the three-cavity two-stage oscillator can provide over 100 W output power in W band at substantially reduced level of the beam current (0.2-0.3 A).…”

“…The output cavity of one klystron is coupled through couplingslots with the input cavity of another one and vice versa. In [4], an elementary theory of the oscillator has been developed and basic pattern of oscillation modes arising with the increase of the electron beam current was analyzed. However, in [4] a simplified model of the oscillator described by a system of delay-differential equations has been considered.…”

“…In [4], an elementary theory of the oscillator has been developed and basic pattern of oscillation modes arising with the increase of the electron beam current was analyzed. However, in [4] a simplified model of the oscillator described by a system of delay-differential equations has been considered. Recently we studied a twostage double-cavity oscillator shown in Fig.…”

Nonstationary Simulation of Electron Beam Interaction with Coupled Resonant Microwave Oscillators

“…A CSEBO is comprised of a couple of two-cavity klystrons, running in parallel and pierced by electron beams moving in opposite directions. The output cavity of each klystron is 3 coupled with the input cavity of another one and visa versa3. The second one is a coupled-cavity TWT with parameters similar to the device described in Ref 4. The results of PIC simulations are compared with the data obtained earlier by simulation of simplified models, as well as with experimental studies35.…”