Foundations For Microwave Engineering

This paper presents a comprehensive theory of the cyclotron resonance maser (CRM) interaction in a circular waveguide. The kinetic theory is used to derive the dispersion relationships for both TE and TM modes. The TE mode case has been investigated by several authors, but there has been comparatively little work on the TM mode case. However, the TM mode interaction competes effectively with the TE mode interaction at relativistic electron energies. The conditions for maximum temporal and spatial growth rates are shown. The TM mode growth rates are found to vanish when the RF wave group velocity equals the beam axial velocity (‘grazing incidence’). The single particle theory is used to derive a compact set of self-consistent non-linear equations for the TE and TM mode interactions. These equations are particularly appropriate for the cyclotron auto-resonance maser (CARM) regime but applicability extends to other regimes as well. The conditions for optimum efficiency are investigated for oscillator and amp...

Linear and nonlinear theory of the Doppler-shifted cyclotron resonance maser based on TE and TM waveguide modes

We present the theory of a new amplification regime in traveling wave tubes (TWTs) composed of a slow wave periodic structure that supports multiple electromagnetic modes that can all be synchronized with the electron beam. The interaction between the multimodal slow wave structure and the electron beam is quantified using a multi-transmission line (MTL) approach based on a generalized Pierce model and transfer matrix analysis, leading to the identification of modes with complex Bloch wavenumber. In particular, we address a new possible operation condition for TWTs based on the supersynchronism between an electron beam and four modes exhibiting a degeneracy condition near a band edge of the periodic slow wave MTL. We show a phenomenological change in the band structure of a periodic MTL, where we observe at least two growing modal cooperating solutions as opposed to a uniform MTL, interacting with an electron beam where there is rigorously only one growing modal solution. We discuss the advantage of using such a degeneracy condition in TWTs that leads to larger gain conditions in amplifier regimes and also to very low starting beam current in high-power oscillators.

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Theory and New Amplification Regime in Periodic Multimodal Slow Wave Structures With Degeneracy Interacting With an Electron Beam

In this paper, we describe the design and experimental results from the rebuild of a 250 GHz gyrotron used for Dynamic Nuclear Polarization enhanced Nuclear Magnetic Resonance spectroscopy on a 380 MHz spectrometer. Tuning bandwidth of approximately 2 GHz is easily achieved at a fixed magnetic field of 9.24 T and a beam current of 95 mA producing an average output power of >10 W over the entire tuning band. This tube incorporates a double disk output sapphire window in order to maximize the transmission at 250.58 GHz. DNP Signal enhancement of >125 is achieved on a 13C-Urea sample using this gyrotron.

Continuously Tunable 250 GHz Gyrotron with a Double Disk Window for DNP-NMR Spectroscopy

The effect of broadening the bandwidth with a dielectric load in a cylindrical gyrotron is investigated for a hollow electron beam. The linear dispersion relation for the azimuthally symmetric, transverse electric (TE) modes is obtained by the method of the wave impedance matching. It is found that the TE perturbations exhibit three unstable modes characterized by their phase velocities vph : one fast wave, the long wavelength mode (LWM, vph ≳c), and two slow waves, the intermediate (IWM, c≳vph ≳ce−1/2) and the short (SWM, vph <ce−1/2) wavelength modes. The optimum conditions for the wide band operation are obtained individually for each mode. Although the bandwidth in excess of 40% is possible for the slow waves (IWM, SWM) at a small axial momentum spread, it decreases rapidly as the spread increases. On the other hand, the LWM yields approximately 10% of the bandwidth insensitive to the spread. It is also shown that for a small spread (<5%), the slow wave (IWM) is preferable for the wide band operation,...

Analysis of the wide band gyrotron amplifier in a dielectric loaded waveguide

Loading the circular waveguide interaction structure of a gyro-traveling-wave tube (gyro-TWT) with chiral material was proposed to show the possibility of widening the device bandwidth. Outlines to obtain the dispersion relation of a circular waveguide enveloping a chiral-dielectric rod and a chiral-dielectric tube were presented, which further interpreted in special cases for the circular waveguides loaded with a chiral-dielectric coaxial rod (structure I) and with a chiral-dielectric wall-lining (structure II). A computer code was developed in MATLAB to solve the dispersion relations and the solutions were substituted into the Pierce-type small-signal gain equation of a gyro-TWT for the device-gain calculation. The electromagnetic analysis of the structure has been validated against simulation. The dispersion shaping and the broadbanding were presented for the two structures. The structure I was found to be more sensitive to chirality parameter than structure II.

Broadbanding a gyro-traveling-wave tube by chiral-dielectric material loading

A simple electromagnetic technique to estimate quickly the ohmic quality factor of a corrugated wall circular cavity was proposed by dividing the cavity into a numbers of cells of circular cross-section. Although, the technique is general, the sinusoidal radius profile was taken to demonstrate the results of the proposed technique. The result of the present analysis was compared to obtain ~ 4 % variation with those obtained using commercially available simulation softwares, CST Microwave Studio and Ansoft HFSS, however, in very less time than these simulation tools. It was observed that the ohmic quality factor initially increases, and after obtaining a maximum, it starts decreasing with increasing mean radius of the cavity in the sinusoidal radius profile. The value of the maximum ohmic quality factor decreases and shifts towards a lower value of mean radius of the radius profile with increasing amplitude of the radius profile and increasing frequency of operation. Increasing the length of the cavity in the sinusoidal profile produces the alternate maximum and minimum of the ohmic quality factor within the range of length up to few wavelengths (~10λ), and afterwards the ohmic quality factor converges to a constant value which shows that the ohmic quality factor is independent of periodicity of the sinusoidal radius profile for a length of cavity greater than 10λ.

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A Quick Estimate of the Ohmic Quality Factor of a Corrugated Wall Circular Cavity

The plane surface of a dielectric disk window is engineered in three different patterns to explore the possibility of widening the frequency bandwidth. The reference bandwidth is taken as that for plane disk window considered in two thicknesses. The material chosen for window is Teflon. The mode and frequency range, for which window is examined, are respectively TE1,1 and 20–60 GHz. The window bandwidths of 12.38 GHz (32.93%), 16.74 GHz (36.2%) and 21.18 GHz (45.06%) are obtained, respectively, for rectangular, circular and triangular tip bars for the circular TE1,1 mode at 20dB return loss. However, the bandwidth of plane disk window without surface modification is 2.65 GHz (5.68%).

Exploring the Meta-Surface for Broadband TE1,1-mode in Circular Window

A four-section beam compression unit (BCU) with copper and aluminum nitride–silicon carbide (AlN-SiC) annular disks was proposed for a $W$ -band gyrotron. Various dimensional parameters were calculated, based on which the BCU was modeled in a high-frequency structure simulator (HFSS), and the transmission characteristics were plotted for various sets of dimensional parameters. The dimensional parameters were optimized for achieving the attenuation of more than 60 dB over 85–105 GHz. It was further examined that the hollow electron beam radius over various sections of the BCU should not lead to beam–wave interaction, and if so, it should not propagate toward the interaction cavity. For this purpose, azimuthal electric field intensities in various azimuthally symmetric modes below the operating mode were plotted against the radial coordinate in various sections of the BCU and checked for the azimuthal electric field intensity values with the range of beam radius in the corresponding section. The electric field intensity maxima should be avoided within the range of beam radius in the corresponding section. Furthermore, the transient thermal analysis of the BCU was carried out considering temperature varying thermal conductivity in two proposed models: 1) with radially constant and 2) radially varying heat loads within AlN-SiC disks to predict the maximum temperature attained in the ceramic as 76.8 °C and 88.5 °C, respectively, taking 8-L/min flow rate of deionized water and ten heat load pulses.

RF and Thermal Analysis of Beam Compression Unit for a $W$ -Band Gyrotron

Thermal analyses were carried out for a millimeter-wave mirror taking three different ways of surface heat load: i) over the full front reflecting surface of the mirror, ii) over the circular cross section (diameter 63.5mm) similar to that of RF beam over the front reflecting surface of the mirror, and iii) over the circular cross section (diameter 63.5mm) in Gaussian profiled manner on the front reflecting surface of the mirror. The thermal images were analyzed and the values of highest temperature attained and their location over the mirror were monitored. The highest temperature attained in three cases of heat load are 348.72, 330.53 and 391.64°C, respectively. Under practical consideration of Gaussian heat load, the maximum temperature attained was found below the allowable maximum temperature limit of 400°C and thus the proposed cooling found to be adequate for the case of heat load of 5kW.

Vishal Kesari

Papers

Broadbanding a gyro-traveling-wave tube by chiral-dielectric material loading

A Quick Estimate of the Ohmic Quality Factor of a Corrugated Wall Circular Cavity

Exploring the Meta-Surface for Broadband TE1,1-mode in Circular Window

RF and Thermal Analysis of Beam Compression Unit for a $W$ -Band Gyrotron

Thermal Analysis for Effective Cooling of a Millimeter-wave Mirror