Backward Wave Mode Research Articles

Multiple internal resonances of rotating composite cylindrical shells under varying temperature fields

Composite cylindrical shells, as key components, are widely employed in large rotating machines. However, due to the frequency bifurcations and dense frequency spectra caused by rotation, the nonlinear vibration usually has the behavior of complex multiple internal resonances. In addition, the varying temperature fields make the responses of the system further difficult to obtain. Therefore, the multiple internal resonances of composite cylindrical shells with porosities induced by rotation with varying temperature fields are studied in this paper. Three different types of the temperature fields, the Coriolis forces, and the centrifugal force are considered here. The Hamilton principle and the modified Donnell nonlinear shell theory are used to obtain the equilibrium equations of the system, which are transformed into the ordinary differential equations (ODEs) by the multi-mode Galerkin technique. Thereafter, the pseudo-arclength continuation method, which can identify the regions of instability, is introduced to obtain the numerical results. The detailed parametric analysis of the rotating composite shells is performed. Multiple internal resonances caused by the interaction between backward and forward wave modes and the energy transfer phenomenon are detected. Besides, the nonlinear amplitude-frequency response curves are different under different temperature fields.

Experimental visualization of dispersion characteristics of backward volume spin wave modes

Basing on the measurement of spatial spectra (spectra of wavenumbers), the dispersion characteristics of the first three modes of backward volume spin wave, propagating along the direction of a constant uniform magnetic field in a tangentially magnetized ferrite film, were visualized firstly. The study was carried out by microwave probing of spin waves with subsequent use of spatial Fourier analysis of the complex wave amplitude for a series of frequencies. It was found that experimental spatial spectrum of the backward volume spin wave modes has a fine structure and every m-th mode splits into n closely located satellite modes appearing due to the existence of layers with similar magnetic parameters in ferrite film. It was found that satellites of the first mode of this wave are excited most effectively, while satellites of the third mode - least effectively, and the effectiveness of satellites excitation decreases as the number n increases. It is found that the theoretical dispersion dependencies of the first three modes of the wave coincide well with the experimental dispersion dependencies of the satellite modes that are excited most effectively.

Regenerated amplification of terahertz spoof surface plasmon radiation

Regenerated amplification induced by a Fabry–Perot (F–P) cavity is introduced to enhance the interaction efficiency of the free-electron-driven spoof surface plasmon. A direct-current electron beam flies above the meta-grating surface and seeds noise-level plasmonic waves. This weak signal experiences multiple back-and-forth regenerated amplifications in the F–P cavity loaded grating system, and the system outputs a pulsed radiation when the signal leaves the cavity. When compared with the condition without the F–P cavity, the equivalent beam-wave interaction length is effectively extended, and the interaction efficiency is improved by orders of magnitude. The proof-of-principle scheme is verified in both backward-wave and forward-wave modes using the particle-in-cell simulation. This scheme is promising for developing high-efficient on-chip terahertz free-electron radiation sources.

On Travelling Wave Modes of Axially Moving String and Beam

The traditional vibrational standing‐wave modes of beams and strings show static overall contour with finite number of fixed nodes. The travelling wave modes are investigated in this study of axially moving string and beam although the solutions have been obtained in the literature. The travelling wave modes show time‐varying contour instead of static contour. In the model of an axially moving string, only backward travelling wave modes are found and verified by experiments. Although there are n − 1 fixed nodes in the nth order mode, similar to the vibration of traditional static strings, the presence of travelling wave phenomenon is still spotted between any two adjacent nodes. In contrast to the stationary nodes of string modes, the occurrence of galloping nodes of axially moving beams is discovered: the nodes oscillate periodically during modal motions. Both forward and backward travelling wave phenomena are detected for the axially moving beam case. It is found that the ranges of forward travelling wave modes increase with the axially moving speed. It is also concluded that backward travelling wave modes can transform to the forward travelling wave modes as the transport speed surpasses the buckling critical speed.

Coherent Cherenkov-cyclotron radiation excited by an electron beam in a two-spiral metamaterial waveguide

We present the analysis of a microwave generator that uses two-spiral metamaterial (MTM) plates in a below cutoff WR340 waveguide that interacts with a high-power electron beam, motivated by recent results obtained by researchers at MIT. Particle-in-cell simulations using the MAGIC code demonstrated that power levels of 12 MW are achieved in a backward wave mode at a frequency of 2.47 GHz from an anomalous Doppler instability using a 1 μs pulsed electron beam of energy 400 keV, current 82 A in a 415 G magnetic field. In addition, a backward wave with 9 MW output power is achieved at a frequency of 2.54 GHz attributed to a Cherenkov instability using a 1 μs pulsed electron beam of energy 400 keV, current 82 A in a 1200 G magnetic field. MAGIC simulations demonstrate that the beam-wave interaction electronic efficiency can be as high as 27.4%. Nonlinear simulations indicate that beam interception leads to secondary electron emission from surfaces, which makes the anomalous Doppler instability and Cherenkov instability more complicated by a shift in frequency. This work seeks to clarify some discrepancy between particle-in-cell simulations and experiments at MIT over a range of guide magnetic field.

Parasitic Oscillations in Smooth-Wall Circular Symmetric Gyrotron Beam Ducts

In order to study parasitic oscillation that may occur in a realistic beam duct upstream to the gyrotron cavity, the self-consistent linear and spectral code TWANGlinspec has been modified. The large inhomogeneities in the smooth-wall beam duct geometry or in the magnetic field profile required the implementation of a numerical approach using a hybrid finite element method. The new model permits to characterize a large number of potentially spurious TE modes. Compared to previous studies on gyrotron beam duct instabilities, an extended interaction space including also the gyrotron cavity has been considered. The role of the connecting part between the beam duct and the cavity, called spacer, is highlighted and it is shown that the gyro backward-wave TE modes excited in this region generally have their minimum starting current. The sensitivity of the minimum starting current on electron beam velocity spread is also evaluated.

Group Velocity and Backward-Wave Modes in Closed Anisotropic Waveguides

In this paper, the conditions of the existence of backward-wave modes in closed, lossless waveguides filled with inhomogeneous and anisotropic medium that has coupling between transverse and longitudinal field components are presented. In these waveguides, Maxwell’s equations are transformed into an infinite linear algebraic equation system by application of the Galerkin version of moment method. Propagation constants of the problem are found as the eigenvalues of the coefficient matrix of this infinite linear algebraic equation system. In this paper, the derivative of the eigenvalue is obtained analytically using the result expressions of moment method and group velocity is determined. It is utilized to reveal necessary and sufficient conditions for the existence of backward-wave mode. These conditions are adequate to determine whether this waveguide supports the backward-wave mode in a frequency range of interest.

High power long pulse microwave generation from a metamaterial structure with reverse symmetry

Experimental operation of a high power microwave source with a metamaterial (MTM) structure is reported at power levels to 2.9 MW at 2.4 GHz in full 1 μs pulses. The MTM structure is formed by a waveguide that is below cutoff for TM modes. The waveguide is loaded by two axial copper plates machined with complementary split ring resonators, allowing two backward wave modes to propagate in the S-Band. A pulsed electron beam of up to 490 kV, 84 A travels down the center of the waveguide, midway between the plates. The electron beam is generated by a Pierce gun and is focused by a lens into a solenoidal magnetic field. The MTM plates are mechanically identical but are placed in the waveguide with reverse symmetry. Theory indicates that both Cherenkov and Cherenkov-cyclotron beam-wave interactions can occur. High power microwave generation was studied by varying the operating parameters over a wide range, including the electron beam voltage, the lens magnetic field, and the solenoidal field. Frequency tuning with a magnetic field and beam voltage was studied to discriminate between operation in the Cherenkov mode and the Cherenkov-cyclotron mode. Both modes were observed, but pulses above 1 MW of output power were only seen in the Cherenkov-cyclotron mode. A pair of steering coils was installed prior to the interaction space to initiate the cyclotron motion of the electron beam and thus encourage the Cherenkov-cyclotron high power mode. This successfully increased the output power from 2.5 MW to 2.9 MW (450 kV, 74 A, 9% efficiency).

Spatial frequency maps of power flow in metamaterials and photonic crystals: Investigating backward-wave modes across the electromagnetic spectrum

We present spatial frequency maps of power flow in metamaterials and photonic crystals in order to provide insights into their electromagnetic responses and further our understanding of backward power in periodic structures. Since 2001, many different structures across the electromagnetic spectrum have been presented in the literature as exhibiting an isotropic negative effective index. Although these structures all exhibit circular or spherical equifrequency contours that resemble those of left-handed media, here we show through $k$-space diagrams that the distribution of power in the spatial frequency domain can vary considerably across these structures. In particular, we show that backward power arises from high-order right-handed harmonics in photonic crystals, magnetodielectric crystals, and across the layers of coupled-plasmonic-waveguide metamaterials, while arising from left-handed harmonic pairs in split-ring resonator and wire composites, plasmonic crystals, and along the layers of coupled-plasmonic-waveguide metamaterials. We also show that the fishnet structure exhibits the same left-handed harmonic pairs as the latter group. These observations allow us to categorize different metamaterials according to their spatial spectral source of backward power and identify the mechanism behind negative refraction at a given interface. Finally, we discuss how $k$-space maps of power flow can be used to explain the high or low transmittance of power into different metamaterial or photonic crystal structures.

Study of Electronic Switching Between Multiple Backward-Wave Modes in a W-Band Extended Interaction Oscillator

The performance of electronic switching between multiple backward-wave modes is studied in a designed extended interaction oscillator (EIO) based on a ladder circuit with finite number of periods to overcome electronic tuning range limits of EIOs operated in standing-wave mode. The dispersion characteristic of the circuit with finite number of periods, which is constructed by a series of discrete modes, is investigated. The mode separation is analyzed and reduced to support continuous switching between multiple different modes by increasing the number of periods as compared with the standing-wave EIO approach. An output circuit is designed to extract the power of backward wave. The electronic switching between nine backward-wave modes has been achieved by changing the beam voltage from 4.1 to 10.5 kV, where the maximum output power over 58 W is obtained at 5.3 kV from the simulation prediction. The EIO can operate over an electronic tuning range of 3.53 GHz from 89.65 to 93.18 GHz in ensuring the output power no less than 20 W. This technique can be extensively applied to increase operating band for extended interaction klystrons (EIKs) and electronic tuning range for EIOs, making them more suitable for many potential applications.

Propagation Properties of Backward Lamb Waves in Plate Investigated by Dynamic Photoelastic Technique**Supported by the National Natural Science Foundation of China under Grant Nos 11374325 and 11427809.

The dynamic photoelastic technique is employed to visualize and quantify the propagation properties of backward Lamb waves in a plate. Higher energy leakage of second-order symmetric backward wave mode S2b in contrast to third-order anti-symmetric backward mode A3b is shown by the dispersion curve of a plate immersed in water, and then verified by experiments. To avoid the considerable high leakage, the plate is placed in air, both group and phase velocities of modes S2b and A3b in the glass plate are experimentally measured. In comparison with the theoretical values, less than 5% errors are found in experiments.

Normal wave diffraction on a plate submerged in a liquid: Level gauge model, factorization method modification, and waveguide quasiresonances

An exact solution is obtained for onemore new diffraction problem whose transcendental difficulty has been known since Sommerfeld and Kirchhoff. The model of waveguide level gauge, where the main problem is the bulk diffraction of normal waves in a layered structure consisting of an elastic plate between two semi-infinite liquid layers, is investigated. The boundary value problem is solved by using a modification of the Wiener–Hopf factorization method; the factorization is used twice to solve two systems of underdetermined functional equations, and this is a specific characteristics of the problem and amethodological novelty. The proposed modification is acceptable for the class of such problems. The diffracted spectra are analyzed; the waveguide quasiresonances are physically treated; the effect of pure Lamb wave propagation under the liquid is established; the narrow-band backward-wave modes are determined.

Propagation characteristics of an extremely anisotropic metamaterial loaded helical guide.

In this study, we report slow wave propagation characteristics of an extremely anisotropic metamaterial loaded helical guide (EAMLHG). An analytical expression has been theoretically derived and numerically computed to get exact solutions of all possible guided modes of propagation. Anisotropy is defined in terms of positive longitudinal permittivity (ϵz > 0) and negatives transverse permittivity value (ϵt < 0). The waveguide supports hybrid (HE) mode propagation and possesses characteristics of backward wave (BW) mode, forward wave (FW) mode, zero-group velocity and mode-degeneracy. The large value of effective index of BW mode and mode-degeneracy mechanism leads to slowing and trapping of electromagnetic (EM) wave. Closed-form guided mode energy propagation expressions has been also derived and computed which exhibits zero power flow at mode degeneracy point. A comparative study is also carried out between extremely anisotropic metamaterial helical waveguide (EAMLHG) and conventional extremely anisotropic metamaterial cylindrical guide (EAMCG), which reveals enhanced slow wave behaviour. Engineering feasible design and analysis is also presented by combining alternate disks of silver and glass as an extremely anisotropic medium which exhibits lossy and dispersive properties. This type of waveguide can find applications as a filter, phase shifter, and delay lines in microwave to THz applications and, as an optical buffer in optoelectronics applications.

Coherent Cherenkov-Cyclotron Radiation Excited by an Electron Beam in a Metamaterial Waveguide.

An electron beam passing through a metamaterial structure is predicted to generate reversed Cherenkov radiation, an unusual and potentially very useful property. We present an experimental test of this phenomenon using an intense electron beam passing through a metamaterial loaded waveguide. Power levels of up to 5MW are observed in backward wave modes at a frequency of 2.40GHz using a one microsecond pulsed electron beam of 490keV, 84A in a 400G magnetic field. Contrary to expectations, the output power is not generated in the Cherenkov mode. Instead, the presence of the magnetic field, which is required to transport the electron beam, induces a Cherenkov-cyclotron (or anomalous Doppler) instability at a frequency equal to the Cherenkov frequency minus the cyclotron frequency. Nonlinear simulations indicate that the Cherenkov-cyclotron mode should dominate over the Cherenkov instability at a lower magnetic field where the highest output power is obtained.

Dispersion control of helical slow-wave structure by double-negative metamaterial loading

A helix supported by a double-negative metamaterial (DNG-MMT) surrounding it, in a metal envelope, was field-analyzed to show that the shape of the dispersion is more sensitive to the value of the relative permittivity of the metamaterial (MMT) than that of its relative permeability. The field analysis was validated against equivalent circuit analysis as well as against simulation. The values of the MMT support parameters were adjusted to obtain nearly flat, rather slightly negative, dispersion characteristics together with a high value of the interaction impedance of the structure as required for a wideband traveling-wave amplifier. Unlike in a conventional traveling-wave tube, the flow of power of RF wave supported by DNG-MMT loaded helix was found to be in a direction opposite to that of the RF phase velocity of the wave supported by the structure resulting in a negative value of the interaction impedance of the structure suggesting that the device using a helix with double-negative MMT supports would operate in the backward-wave mode analogously to a reversed Cherenkov amplifier.

Short-wave radiation generation by strip electron beams in the surface-wave excitation mode

The quasi-optical theory of short-wave Cherenkov oscillators, in operation of which surface waves are excited by relativistic electron beams moving above periodically corrugated structures, is constructed. π-mode oscillations characterized by the generation rate close to the Bragg frequency, as well as backward-wave tube modes in which generation rate is shifted downward from the Bragg frequency, are analyzed. It is demonstrated that surface-wave excitation can be employed to generate submillimeter radiation with multimegawatt power levels.

Investigation of Microstrip Meander-Line Traveling-Wave Tube Using EBG Ground Plane

A novel electromagnetic bandgap meander-line (EBG-ML) slow-wave structure (SWS) is proposed for improvement of the interaction impedance and reduction of circuit attenuation by in-phase reflection of EBG for traveling-wave tube applications. With high on-axis interaction impedance, the EBG-ML SWS can interact with a low-current-density electron beam. The backward-wave mode of EBG-ML SWS can be suppressed by the transmission stopband of EBG. Particle-in-cell simulations are carried out for the proposed structure with a sheet beam source. The simulation results show that a 50% improved interaction impedance and a 20% reduced circuit attenuation of EBG-ML SWS can be achieved, in comparison with those of traditional ML SWS. With a small input signal, the RF efficiency of EBG-ML is improved by 137.5% over that of the ML SWS.

Sub-wavelength waveguide loaded by a complementary electric metamaterial for vacuum electron devices

We report the electromagnetic properties of a waveguide loaded by complementary electric split ring resonators (CeSRRs) and the application of the waveguide in vacuum electronics. The S-parameters of the CeSRRs in free space are calculated using the HFSS code and are used to retrieve the effective permittivity and permeability in an effective medium theory. The dispersion relation of a waveguide loaded with the CeSRRs is calculated by two approaches: by direct calculation with HFSS and by calculation with the effective medium theory; the results are in good agreement. An improved agreement is obtained using a fitting procedure for the permittivity tensor in the effective medium theory. The gain of a backward wave mode of the CeSRR-loaded waveguide interacting with an electron beam is calculated by two methods: by using the HFSS model and traveling wave tube theory; and by using a dispersion relation derived in the effective medium model. Results of the two methods are in very good agreement. The proposed all-metal structure may be useful in miniaturized vacuum electron devices.

Broadband Unit-Cell Design for Highly Anisotropic Impedance Surfaces

A unit-cell design for highly anisotropic impedance surfaces is simulated and experimentally demonstrated. The unit cell consists of a grounded dielectric substrate with a metal patch and plated metal via. The design has a ring of metal removed from the patch so that the resonant effect of the via is reduced. The reduced resonance prevents backward-wave modes which are difficult to excite experimentally. On grounded dielectric substrates, the transverse-magnetic mode is fundamental and the transverse-electric (TE) mode is bound above a cutoff frequency. It is shown that highly anisotropic surface impedance can only be achieved below the TE cutoff frequency. The proposed unit cell is constructed using printed-circuit-board fabrication technology, and the result is a unit cell that obtains highly anisotropic impedance over a broader frequency range than traditional patch or mushroom unit cells.

Planar Slow-Wave Structure With Parasitic Mode Control

A planar sheath-like slow-wave structure with rectangular geometry is considered for use in a traveling-wave amplifier driven by a sheet electron beam. The sheath like structure provides a low-dispersion operating mode and hence potential for broad bandwidth. However, due to the large transverse dimension of the structure multiple backward-wave modes can interact with the beam. Both the operating mode and the parasitic modes are analyzed using field theories with the planar sheath approximation. These solutions are then compared with finite element computations. Suppression of backward waves is then considered by designing the structure to preferentially absorb these waves. The results show a good control of mode competition and high-primary mode gain.