Hooman Bahman Soltani, Habibollah Abiri,
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Critical oscillating condition for the EIO with N = 10: (a) SWS and the excited RF field, (b) the formed electron bunches, (c) RF voltage at the voltage monitor, and (d) the spectrum of the RF voltage.
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Extended Interaction Oscillators (EIOs) are high-frequency sources of millimeter wave and terahertz radiations. The dimensions of the EIO resonant structure should be smaller to generate higher frequency signals. However, due to the skin effect and decreasing the available beam surface area, the maximum obtainable oscillating frequency of any RF geometry of EIO is limited. Analytical relations for maximum attainable frequencies of resonant EIO geometries in the sense of beam-wave coupling are derived and presented in this paper. They are directly expressed in terms of the standing-wave profile of the RF resonant circuit in this work. The maximum frequencies are expressed in terms of a defined two-variable analytical function U for single-section resonant EIOs. Besides, an algebraic formula is derived for a critical unloaded frequency of an EIO geometry (fcr) in terms of the resonant circuit field distribution. A 4/5 power-law dependency is derived for a maximum oscillating frequency vs a number of periods of the RF circuit. For two completely different EIO geometries, the results of the obtained relations are compared with the outcomes of a particle-in-cell solver, showing acceptable agreement for both the structures. In addition to computational rapidity, the obtained relations present an analytical viewpoint to estimate and improve the high-frequency generation capability of terahertz extended interaction oscillators.
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