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

Do you design and build vacuum electron devices, or work with the systems that use them? Quickly develop a solid understanding of how these devices work with this authoritative guide, written by an author with over fifty years of experience in the field. Rigorous in its approach, it focuses on the theory and design of commercially significant types of gridded, linear-beam, crossed-field and fast-wave tubes. Essential components such as waveguides, resonators, slow-wave structures, electron guns, beams, magnets and collectors are also covered, as well as the integration and reliable operation of devices in microwave and RF systems. Complex mathematical analysis is kept to a minimum, and Mathcad worksheets supporting the book online aid understanding of key concepts and connect the theory with practice. Including coverage of primary sources and current research trends, this is essential reading for researchers, practitioners and graduate students working on vacuum electron devices.

Microwave and RF Vacuum Electronic Power Sources

This paper presents a low-profile and wideband metamaterial-lens (metalens) antenna based on high-refractive-index metasurface. A novel three-layer nonresonant metamaterial unit cell is introduced and analyzed by the full-wave simulation tool. The proposed unit cell is a stacking configuration of four H-shaped lines realized by multiple microwave laminates. It can achieve a large refractive index variation range of 4.76 (from 1.5 to 6.26). In addition, two impedance matching layers based on the proposed unit cell are developed to provide better transmission for incident waves passing through the metalens antenna. The attractiveness of this new metalens antenna is its low-profile thickness of $0.26~\lambda _{0}$ , where $\lambda _{0}$ is the wavelength at 10 GHz. To validate the performance of the metalens antenna, a wideband stub-loaded horn antenna with stable radiation patterns in E- and H-planes is adopted as the feeding antenna source. The measured results demonstrate a wide impedance bandwidth of 66% (7.2–14.3 GHz) and a high aperture efficiency of up to 65%. Moreover, its sidelobe and cross-polarization levels are less than −17 and −25 dB across the entire bandwidth, respectively.

A Low-Profile and Wideband Lens Antenna Based on High-Refractive-Index Metasurface

This letter proposes an ultrawideband and high-gain antipodal tapered slot antenna (ATSA) with a gradient refractive index (GRIN) lens. The GRIN lens consisting six metamaterial lenses is placed in the maximum radiation direction of the ATSA to greatly enhance its radiation capability. We found that the proposed GRIN lens antenna has a wide impedance bandwidth of 175.7% (0.84–13 GHz) and −3 dB gain bandwidth of 65.8% (5.86–11.6 GHz). Its gain is averagely increased by 4.81 dB in the whole operating band, and the maximum gain reaches 20.55 dBi at 9.5 GHz. The simulation and measured results demonstrate that the designed GRIN lens antenna has an excellent performance and is suitable for short-pulse ground penetrating radar systems.

Ultrawideband Antipodal Tapered Slot Antenna With Gradient Refractive Index Metamaterial Lens

A rectangular tape helix slow-wave structure with infinitesimal thickness and finite width in free space is investigated. With the expansion of surface currents in the helix and the applications of the modified Marcatili’s method, as well as average power flow matching method at the boundaries, the dispersion properties and the interaction impedance for transverse antisymmetric modes in a rectangular tape helix immersed in free space are obtained. It is shown that, compared with the results of the simplified sheath model by previous researchers, higher accuracy has been obtained between the calculation results of the present theory and the data obtained from HFSS, and the validity of the present theory is further demonstrated by comparison with experiments. The improved characteristic equations hold scientific and practical significance in the design and performance evaluation of such plane slow-wave structure in the application of compact traveling-wave tubes. The distribution characteristics on the cross section of the longitudinal electric field fundamental component are also discussed based on this theory.

Dispersion Equations of a Rectangular Tape Helix Slow-Wave Structure

A volumetric metamaterial lens exhibiting a negative refractive index (NRI) at C-band is designed and its free-space focusing properties are experimentally verified. The designed lens employs a multilayer geometry and its unit cells are loaded using metal–insulator–metal (MIM) capacitors and dual-arm spiral inductors in a biplanar configuration. These elements, although fully printed and without vias, provide strong reactive loading that enables a unit cell size of $\lambda_0/11$ and allows the metamaterial’s dispersion properties to be accurately modeled in the effective-medium regime using an equivalent-circuit approach. It is also conducive to implementation at high frequencies, where surface-mount components are unusable. The focusing properties of the fabricated lens are confirmed for a band of frequencies around 5.0 GHz in an anechoic chamber using a free-space field probing system consisting of electrically small shielded-loop antennas affixed to a computer-controlled scanner.

Free-Space Focusing at C-Band Using a Flat Fully Printed Multilayer Metamaterial Lens

The homogeneous boundary value problem arising in the propagation of electromagnetic waves guided by an open tape helix modelled to be of infinitesimal tape thickness and infinite tape-material conductivity is shown to be inherently ill posed. It is demonstrated how the ill posed problem may be regularised using the mollification method. The regularised boundary value problem is then solved to yield the approximate dispersion equation which takes the form of the solvability condition for an infinite system of linear homogeneous algebraic equations viz., the determinant of the infinite-order coefficient matrix is zero. For the numerical computation of the dispersion characteristic, all the entries of the symmetrically truncated version of the coefficient matrix are estimated by summing an adequate number of the rapidly converging (after regularisation) series for them. The tape-current distribution is estimated from the null-space vector of the truncated coefficient matrix corresponding to a specified root of the dispersion equation. A comparison of the numerical results with those for the anisotropically conducting model (that neglects the component of the tape-current density perpendicular to the winding direction) of the tape helix reveals that the propagation characteristic computed on the basis of the anisotropically conducting model could be substantially in error even for moderately wide tapes.

Perfectly conducting tape-helix model for guided electromagnetic wave propagation

The approximate distribution of the current density induced on the tape surface by guided electromagnetic waves supported by an inflnite open tape helix is estimated from an exact solution of a homogenous boundary value problem for Maxwell's equations. It is shown that the magnitude of the surface current density component perpendicular to the winding direction is at least three orders of magnitude smaller than that of the surface current density component parallel to the winding direction everywhere on the tape surface. Also, the magnitude and phase distribution for the surface current density components parallel and perpendicular to the winding direction are seen to be nearly uniform at all frequencies corresponding to real values of the propagation constant.

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On the Distribution of Current on an Open Tape Helix

The dispersion equation for free electromagnetic waves guided by an anisotropically conducting open tape helix is derived from the exact solution of a homogenous boundary value problem for Maxwell's equations without invoking any a priori assumption about the tape-current distribution. The approximate dispersion curve tends to be close to the dominant-mode sheath-helix dispersion curve in the middle portion of first two allowed regions exhibiting a marked downward deviation everywhere from the sheath-helix dispersion curve in the third allowed region. The dispersion curve tends to slope downward towards the forbidden-region boundaries in all the three allowed regions. The magnitude plot of the current distribution on the tape surface exhibits a maximum along the center line of the tape irrespective of the width of the tape. The phase of the surface current distribution on the other hand exhibits a nearly linear variation across the entire width of the tape.

Propagation of electromagnetic waves guided by an open tape helix

The practically important case of dielectric loaded tape helix enclosed in a perfectly conducting coaxial conductor is analysed in this paper. The dispersion equation for the infinitesimally thin and anisotropically conducting tape is derived from an exact solution of a homogeneous boundary value problem for Maxwell's equation. The boundary value problem is solved to yield the dispersion equation which takes the form of the solvability condition viz., the determinant of the infinite-order coefficient matrix is zero. For the numerical computation of the approximate dispersion characteristics, all the entries of the symmetrically truncated version of the coefficient matrix are estimated by summing an adequate number of the rapidly converging series for them. The numerical computation of dispersion characteristics and phase speed variations for different values of b/a (outer conductor to inner helix radius) and effective dielectric permittivity is presented.

G. Naveen Babu

Papers

Free-Space Focusing at C-Band Using a Flat Fully Printed Multilayer Metamaterial Lens

Perfectly conducting tape-helix model for guided electromagnetic wave propagation

On the Distribution of Current on an Open Tape Helix

Propagation of electromagnetic waves guided by an open tape helix

Wave propagation characteristics in anisotropically conducting dielectric loaded tape helix slow wave structures