A Method for Evaluating the Generation Power of Orotrons with a Two-Row Periodic Structure in the Frequency Range of 180–400 GHz

Abstract

A method for evaluating the generation power of orotron experimental models with a two-row periodic structure (TRPS), which operate with 2 × 10^–6-s duration pulses and a 0.02-s repetition period in the frequency range of 180–400 GHz, is described. To realize this method, a setup has been created for measuring the attenuation of the microwave path in a wide frequency interval (180–400 GHz) based on ОV-66 (180–260 GHz) and ОV-65 (260–360 GHz) backward-wave tubes (BWOs), which are not packed in a magnet focusing system, and the possibility of their operation in a pulse power-supply regime with a high off-duty factor is shown.

APPENDIX

Let us consider the issue of the influence of the microwave-path superdimensionality on the measurement of the radiation power of orotrons with a TRPS according to the proposed method in more detail. We assume that a fundamental-type H₁₀ wave is excited in a waveguide of the 2-mm range with a cross section of 0.8 × 1.6 mm² in both the 1-mm and submillimeter ranges.

Then, for a frequency of 400 GHz (λ = 0.75 mm), it is possible to calculate the wavelength in the waveguide for a type H₁₀ wave using the well-known formula. It was found to be 0.77 mm. For a waveguide with a cross section of 0.8 × 1.6 mm², this means that (1.6/0.77) = 2.077922 waves, i.e., approximately four half-waves, fit along the wide waveguide wall. Consequently, in the middle of the wide waveguide wall, the field amplitude value is close to 0. However, the detector diode, which is usually placed at the maximum of the RF field of the fundamental-type H₁₀ wave, has nonzero dimensions (or there is an inaccuracy of manufacture); therefore, we were able to register a generation power of 5 mW at this frequency. In fact, the generation power can be several times higher.

The same calculation gives a type H₁₀ wavelength equal to λ_w = 1.0527 mm in a waveguide for a wavelength of 1 mm in free space. Consequently, 1.6/1.0527 = 1.519 waves (i.e., approximately 1.5λ_w) fit along the length of the wide waveguide wall, and the RF field maximum is reached. Thus, for wavelengths in free space shorter than 1 mm, the detector readings decrease to 0 gradually, up to λ₀ = 0.75 mm, deviating from the readings that would correspond to the calibration. The same can be said about the behavior of the detector in the wavelength range from 1 mm to λ₀ = 1.43 mm (209.63 GHz), i.e., for λ_w = 1.6 mm, where an RF-field minimum of the H₁₀ wave must be observed. The next (last) field maximum will be observed at 0.5λ_w = 1.6 mm, i.e., λ_w = 3.2 mm, which corresponds to λ₀ = 2.26 mm (136.36 GHz), i.e., to the middle of the 2-mm range of 100–150 GHz.

This situation can be described by introducing the function in the form F(λ_w) = cos(π / (0.5b))λ_w, where b is the length of the wide waveguide wall of the 2-mm wavelength range and λ_w is the wavelength in the waveguide that corresponds to the measured wavelength in free space. This function is defined on the segment [0, 1]. The adjusted value of the power P_out measured by the proposed method (see formula (1)), i.e., using our calibration, should be calculated in this case according to the following formula:

$$~P_{{{\text{out}}}}^{{{\text{adj}}}} = {{P}_{{{\text{out}}}}}\left[ {1{\text{/}}F({{\lambda }_{{\text{w}}}})} \right] = {{P}_{{{\text{out}}}}}\left[ {1{\text{/cos}}(\pi {\text{/}}(0.5b)){{\lambda }_{{\text{w}}}}} \right].$$

However, in this case, for the λ_w values at which the function F(λ_w) turns to 0, the function $P_{{{\text{out}}}}^{{{\text{adj}}}}$ turns to infinity. Therefore, such an adjustment cannot be used. In this case, near the zero values of F(λ_w), it is necessary to determine the region in which such an adjustment is still possible. This is an independent task and has nothing to do with this study. However, near the maximum values of the function F(λ_w), such a correction is quite possible. To make sure of this, it is necessary to analyze the characteristics of various orotron prototypes we have already measured from this standpoint. This is the task for the next study.