Wave Beam Research Articles

Simulation investigation of a Ka-band phase-locked klystron-type coaxial relativistic Cherenkov generator

To achieve coherent power combination of Ka-band high-power microwave (HPM), a phase-locked klystron-type coaxial relativistic Cherenkov generator (PKC-RCG), which combines the advantageous characteristics of weak dimensional sensitivity of RCG and low input power ratio of relativistic triaxial klystron amplifier (TKA), is proposed and investigated in this paper. The PKC-RCG is composed of two parts: a pre-modulation region adapted from TKA and an energy exchange region adapted from RCG. The pre-modulation region is used for initial speed modulation of intense relativistic electron beams (IREB), ensuring that the output frequency is consistent with the input frequency. The energy exchange region is used for deep clustering of the IREB and achieving efficient beam–wave energy conversion. Phase locking of the output HPM is accomplished through phase delivery of the modulated IREB. Specially designed reflectors and cascaded single-gap bunching cavities with active suppression of asymmetric TM mode are employed in the pre-modulation region to suppress energy coupling and achieve a lower input power ratio. Disk-loaded slow-wave structure with smooth inner conductor is employed in the energy exchange region to further decrease the dimensional sensitivity of RCG. By the proposed Ka-band PKC-RCG, an HPM with a power of 550 MW and a frequency of 29.0 GHz is obtained with ohmic loss being taken into account. Moreover, the input power ratio and phase-locking bandwidth of the proposed Ka-band PKC-RCG are −51.4 dB and 30 MHz, respectively.

Concept of a Diagnostic System for Measuring the Electron Temperature Profile of Plasma from the Intensity of Electron Cyclotron Emission for the TRT Facility

The paper presents a concept of the ECE diagnostic for the TRT facility and estimates the achievable measurement parameters in the baseline scenario. The target spectral region for the diagnostic corresponds to the first harmonic of the ECR frequency in ordinary polarization (O1) and the second harmonic in extraordinary polarization (X2). It is proposed to carry out measurements from the low-field side along two lines of sight: radial and toroidally oblique. The accessible spectral region in terms of the normalized radial coordinate is approximately estimated as –0.9 to 0.9 and –0.1 to 0.9. It is proposed to shape the input wave beam by means of a quasi-optical focusing system that provides a transverse size of the resolved region of approximately 3—5 cm for O1 and 1.2—3 cm for X2. For measurements, it is proposed to use Fourier transform spectrometers with a time resolution of about 10 ms and multichannel heterodyne receivers with a time resolution of about 1 μs. The minimum radial size of the resolved region is estimated to be 3—5 cm for O1 and 2—4 cm for X2, depending on the coordinate.

Dispersive properties of metamaterial beams with rod-like resonators: A coupled axial-flexural analysis

This paper addresses the propagation of coupled axial-flexural waves in metamaterial beams with rod-like resonators. Utilizing an exact frequency-dependent stiffness method, based on Euler–Bernoulli beam assumption for rods and host beam, and fully accounting for axial-flexural coupling phenomena, several adimensional parametric analyses are performed for investigating the dispersive properties of the metamaterial beams. The analyses reveal novel and relevant aspects unaddressed in previous studies. Firstly, they show that certain rod configurations lead to significant interference between flexural resonance and the band gaps opened by axial resonance, whereas other configurations enable flexural resonance to open substantial band gaps without interference from axial resonance. Results are complemented by 3D finite element analyses proving evidence of the findings and validating the method. Additional analyses demonstrate that adding a tip mass to the rods, while keeping the total mass of the resonator unchanged, can significantly reduce the opening frequency of the band gaps and can attenuate or remove the interference caused by flexural resonance within the band gaps opened by axial resonance; the rotational inertia of the tip mass can also play a significant role in removing flexural resonance interference. Notably, the paper also reveals that the attenuation phenomena for the coupled problem with a single set of rods are governed by the opening of weak band gaps, rather than by traditional band gaps; this aspect is elucidated by showing Bloch mode shapes of the infinite metamaterial beam and frequency response of the corresponding finite beam. Results and proposed design prove to be useful and promising for locally resonant beams featuring rod-like resonators, both as an alternative to traditional beam-like resonators and for their applicability in the 3D printing process of locally resonant structures, where rods serve as elastic elements in constructing the resonators.

Lagrangian Manifolds in the Theory of Wave Beams and Solutions of the Helmholtz Equation

Lagrangian Manifolds in the Theory of Wave Beams and Solutions of the Helmholtz Equation

Coherent propagation of high-power wave beams in hollow gas-filled daisy-shaped waveguides

Coherent propagation of high-power wave beams in hollow gas-filled daisy-shaped waveguides

Transient resonant triads: An examination of turbulent patches injected into finite-width internal wave fields

This article presents an experimental investigation into the interaction of a freely evolving turbulent structure with a steadily forced, finite-width internal gravity wave beam. Specifically, a vortex ring is used as the simplified prototype for a propagating turbulent structure and we present an exploration into how it's passage affects the linear stability of the imposed (or forced) wave field. We use the term "vortex ring" to describe an initially axisymmetric, toroidal fluid structure with azimuthal vorticity. We first examine both the vortex ring and the imposed internal gravity wave beam separately and present how they develop in a quiescent, stratified environment. In the absence of any vortex ring, we find—in agreement with many previous studies—there is an amplitude threshold that the wave beam must surpass before it becomes linearly unstable by a process known as triadic resonance instability (TRI). In the absence of an imposed wave field, we present the propagation and collapse of a coherent vortex ring into a turbulent patch, and measure the transient spectrum of internal waves produced. We then combine these two phenomena and investigate how each impacts the other. While we find that the preexisting internal wave beam has no significant influence on the evolution of the incident vortex ring, we do find that the propagation and subsequent collapse of the ring provokes a response from the internal wave beam. This response allows us to demonstrate two key findings relating to the internal wave beams pathway to triadic resonance. First, the passage of a vortex ring propagating through a forced wave field can provide a nonlinear trigger for the transition to a triadic state when the amplitude of the imposed wave field is itself too small for the spontaneous growth of such a triadic state through TRI. Second, we find that in some cases the triadic states induced by this interaction are not self-sustaining and eventually decay, prompting the terminology "transient triads." These surprising findings are further confirmed by the unintentional release of trapped air arising from under our "magic carpet" wavemaker. These air bubbles turbulently propagate vertically through the imposed beam and, in some cases, induce similar triadic state transitions to those of the vortex ring. Our analysis leads to a discussion on the beam's pathway to instability and to question the structure of the underlying dynamical system arising from the distribution of spectral power in a finite-width beam. Published by the American Physical Society 2024

Design and analysis of a hundred-watt G-band traveling wave tube

In this paper, a hundred-watt level traveling wave tube operating in the G-band is designed and analyzed. A non-semi-arc folded waveguide (FW) slow wave structure (SWS) is adopted to achieve high output power. Compared with the conventional FW, this structure has a higher coupling impedance, which is beneficial for beam–wave interaction. To further improve the efficiency of beam–wave interaction, phase velocity taper technology is adopted in SWS. A diamond pill-box output window is designed for electromagnetic wave input and output in SWS. In addition, the electron optics including a Pierce electron gun and a periodic permanent magnet focusing system are designed for emitting and constraining the electron beam. Using CST PIC solver for simulation, the results show that under a 23 kV and 80 mA electron beam, the maximum output power of the SWS is 132.7 W and the saturated gain is 36.5 dB. The bandwidth for output power greater than 100 W is 12 GHz. A pill-box window is designed and fabricated, and experimentally measured S11 is better than −13 dB and S21 is better than −1.3 dB in 213–229.5 GHz. The electron optics generate 79 mA current at 23 kV voltage.

Variational Analysis: Collapse of the Static Soliton Wave Beams in a One-Dimensional Discrete System

A system that experiences sudden state changes at specific times is said to be discrete. The majority of systems that are studied in operations research and management science, such as transportation or communication studies, are under the application of discrete systems. This study investigates the analytical study of the static soliton for Cubic-Quintic Discrete Nonlinear Schrödinger Equation (DNLSE) in discrete system. Subsequently, static soliton, that is often used to characterize specific self-action regime in a continuous one-dimensional problem, is defined as a self-reinforcing wave packet that keeps its form and velocity while it travels in a medium. Moreover, it is well-known that the NLSE is a known integrable equation of partial differential equation. Therefore, the variational approximation method is applied to transform the partial differential equation of the main equation into ordinary differential equations, thus, to derive the equations for soliton parameters evolution during the interaction process. The method is used to qualitatively study the Discrete NLSE and characterize self-action modes. It is shown that in discrete media, both wide and narrow wave beams (relative to the grating scale) experience weakened diffraction, resulting in the “collapse” of the one-dimensional wave field when the power is greater than the critical threshold. As a result, the central fiber is able to self-channel radiation.

Tuneable vibration control of beams using granular multilayer composite

We explore a passive control solution of bending waves in beams, which takes advantage of the dissipative properties of granular media. It consists in a layer of particles confined between two beams and interacting with each other through their contacts. The inter-particles contacts are intrinsically dissipative due to friction, which efficiently works under shear. In practice, the mechanical response of such a multilayer inherit Hertz contact mechanics, thus conferring confining pressure dependent elasticity and dissipation. Previous work have shown that the hysteretic shear behaviour of a granular medium confined in a box can be reasonably captured by a single DOF model using Dahl model fed by an effective medium theory of granular media. Using this reduced model together with finite element method, we simulate the dynamic response of a three-layer composite beam whose core is made of confined frictional particles. This model makes it possible to characterize its elastic and damping properties, revealing in particular a high and tuneable loss factor with respect to shear strain amplitude and confining pressure, suitable for vibro-acoustics applications.

Herschel-Quincke filters adapted to bending waves in beams and plates

A Herschel-Quincke (HQ) filter is a device for controlling the transmission of guided waves: by adding one or more auxiliary branches to a waveguide, it is possible to construct delay lines, which induce destructive interference effects and consequently zero-transmission phenomena at targeted frequencies. We explore the use of this principle in the context of elastic waves in beams.The dispersive nature of bending waves and their coupling with longitudinal waves introduces complexity into the tuning of the zero transmission frequencies. A model, developed within the framework of Timoshenko's beam theory, provides the scattering matrix of an HQ filter composed of several branches. The model is confirmed by FE and thus demonstrates the interest of the approach for the control of vibrations. The architecture of the HQ device and the modelling approach are extended to a 3 branches configuration. The properties of the filter are analysed, leading to a discussion of the advantages and disadvantages of the HQ strategy.

Multi-objective model predictive control for ship roll motion with gyrostabilizers

Ships are prone to significant roll motion while sailing in adverse conditions, posing a serious threat to ship safety and maneuverability. Therefore, effective ship motion control is crucial. Integrating the MPC control algorithm with a gyrostabilizer can effectively achieve this goal. To evaluate and compare control strategies, a multi-objective model predictive control is proposed that integrates considerations of ship motion, safety, and energy consumption to conduct the operation concurrently. By assigning different weights to these factors, the study aims to discern the varying impacts on control effectiveness. The response of ship roll motion in beam waves is evaluated through roll hydrodynamic modelling, accounting for wave memory effects. A state-space model of ship and gyrostabilizers is proposed to represent their dynamic interaction and response to external moment. Subsequently, the influence of different weightings in the multi-objective model predictive control is compared, and the control performances of a frigate under different wave conditions are analyzed respectively. The multi-objective model predictive control, with varied weight assignments, leads to distinct reductions in roll motions. This investigation offers valuable insights into controlling roll motion in beam wave conditions, effectively reducing motion under varying sea conditions, and providing alternative guidance tailored to user preferences.

Lie symmetry analysis, traveling wave solutions and conservation laws of a Zabolotskaya-Khokholov dynamical model in plasma physics

This article analyzes the analytic and solitary wave solutions of the one-dimensional Zabolotskaya-Khokholov (ZK) dynamical model which provides information about the propagation of sound beam or confined wave beam in nonlinear media and studies of beam deformation. By the Lie symmetry analysis method, we acquire the vector fields, commutation relations, optimal system, reduction, and analytic solutions to the specified equation by exerting the Lie group method. Moreover, the solitary wave solutions of the ZK model are procured by exerting the new auxiliary equation method (NAEM). The behavior of the acquired outcomes for several cases is exhibited graphically through two and three-dimensional dynamical wave profiles. Furthermore, the conservation laws of the ZK model are acquired by Ibragimov’s new conservation theorem.

A frequency steerable electromagnetic acoustic transducer

Abstract Electromagnetic acoustic transducers (EMATs) are convenient for non-destructive evaluation of plate-like structures since they can generate, without the need for contact with the medium under test, different types of ultrasonic guided waves. Guided-wave EMATs usually generate waves omnidirectionally or in a principal propagation direction. Beam steering is desirable in several applications, such as in inspections of large-area structures. This is usually achieved with several independently controlled elements forming a phased array. Alternatively, mono-element transducers with directional-dependent spectral content can steer the generated wave beam by altering the frequency of the excitation signal. A piezoelectric transducer with this characteristic, namely a frequency steerable acoustic transducer, was previously proposed. Its design was addressed in the wavenumber domain, leading to unconventional transducer shapes, but still reproducible with a piezoelectric patch, albeit unfeasible to implement as an EMAT. Here, we propose a new kind of EMAT, namely, frequency steerable EMAT (FSEMAT), whose design is addressed in the spatial domain in order to ensure its physical realization with a coil-magnet arrangement whilst still effectively presenting steering capability. The novel EMAT was designed to generate the A 0 Lamb wave mode in a frequency range from approximately 100 to 600 kHz. The FSEMAT was fabricated and experimentally evaluated in an aluminium plate at different frequencies within the designed frequency range, where each frequency corresponded to a specific propagating direction with high directivity, assessed by half-power beam widths of approximately 10 degrees. Furthermore, its theoretical directivity was computed by means of a wavenumber spectrum-based model, and showed good agreement with experimental results. The new transducer allows great flexibility effectively providing beam steering with a single EMAT.

Phase and amplitude simultaneously coding metasurface with multi-frequency and multifunctional electromagnetic modulations

The integration of multiple functionalities into a single, planar, ultra-compact metasurface has presented significant opportunities for enhancing capacity and performance within compact 5G/6G communication systems. Recent advances in multifunctional metasurfaces have unveiled comprehensive wavefront manipulations utilizing phase, polarization transmission/reflection, and coding apertures. Despite these developments, there remains a critical need for multifunctional metasurfaces with expanded channel capabilities, including multiple operational frequencies, minimal crosstalk, and high-efficiency computable array factors. This study introduces a multifunctional metasurface that integrates phase- and amplitude simultaneous coding meta-atoms at dual frequencies. By altering the polarization of electromagnetic (EM) waves, it is possible to reshape the wave-fronts of reflected waves at these frequencies. The coding metasurface proficiently manipulates both x and y linearly polarized waves through phase and amplitude coding at dual frequencies, thereby enabling distinct functionalities such as anomalous reflection, reflection imaging, and vortex wave beam generation. Both theoretical analysis and full-wave simulation confirm the anticipated functionalities of the designed devices, paving the way for advancements in integrated communication systems with diverse functionalities.

An X-band coaxial relativistic klystron oscillator with a novel diode structure packaged with permanent magnet

To achieve compactness and miniaturization for high-power microwave devices, this paper proposes an X-band permanent magnet-packaged coaxial relativistic klystron oscillator (RKO) with a novel diode structure featuring a stair-step cathode. First, by adopting a large-radius anode structure, the emission of beam currents from the side of the cathode surface is diminished, thereby reducing the proportion of the backward current in the beam current from 10% to 7%. Second, a stair-step cathode is used to inhibit the return flow of electron beams from striking the anode and generating plasma. Concurrently, a radially non-uniform coaxial resonant cavity structure is employed to enhance the fundamental wave modulation depth of the electron beam and improve the beam–wave interaction's efficiency. The experimental results show that the novel device outputs a microwave with a frequency of 9.46 GHz and a pulse width of 55 ns. It generates a power output of 1.5 GW with an efficiency of approximately 30.5%, in the case in which the diode voltage is 505 kV, the beam current is 9.7 kA, and the guiding magnetic flux density is 0.4 T. This novel structure surpasses traditional diode configurations by enhancing the beam-to-wave conversion efficiency by roughly 10%, thereby offering substantial support for the compactness and miniaturization of RKO.

Flexural wave propagation in canonical quasicrystalline-generated waveguides

We investigate the propagation of harmonic flexural waves in periodic two-phase phononic multi-supported continuous beams whose elementary cells are designed according to the quasicrystalline standard Fibonacci substitution rule. The resulting dynamic frequency spectra are studied with the aid of a trace-map formalism which provides a geometrical interpretation of the recursive rule governing traces of the relevant transmission matrices: the traces of three consecutive elementary cells can be represented as a point on the surface defined by an invariant function of the square root of the circular frequency, and the recursivity implies the description of a discrete orbit on the surface. In analogy with the companion axial problem, we show that, for specific layouts of the elementary cell (the canonical configurations), the orbits are almost periodic. Likewise, for the same layouts, the stop-/pass-band diagrams along the frequency domain are almost periodic. Several periodic orbits exist and each corresponds to a self-similar portion of the dynamic spectra whose scaling law can be investigated by linearising the trace map in the neighbourhood of the orbit. The obtained results provide a new piece of theory to better understand the dynamic behaviour of two-phase flexural periodic waveguides whose elementary cell is obtained from quasicrystalline generation rules.

Qualitative validation on a numerical model for the direct stability assessment of surf-riding and broaching

A previously developed numerical model for surf-riding and broaching is qualitatively validated based on the criteria of direct stability assessment (DSA) proposed in SDC 7. Roll decay tests are conducted to obtain roll backbone curves, which are compared with calculated GZ curve to demonstrate their consistency. Then, roll response curves under different wave frequencies in regular beam wave are obtained. It is verified that roll response curve “fold around” the newly defined “peak backbone curve”. Cases with fixed yaw under different Fn are chosen to demonstrate the numerical model's capability of reproducing surf-riding equilibrium. Turning circle test is conduced to demonstrate correct modelling of maneuvering forces and the capability to reproduce heel due to ship turning. Wave surging forces are calculated under different wave numbers and amplitudes. The correct tendency of phase difference between wave surging force and the incident wave is observed, which reveals the correct modelling of wave forces in the model. Moreover, a preliminary quantitative validation is conducted under various cases. Through comparison with experimental results, it is recommended that the wave diffraction correction of the wave surging forces should be included in the simulation model in order to avoid overestimation of surf-riding and broaching.

Tunable Photonic Hook Design Based on Anisotropic Cutting Liquid Crystal Microcylinder

The selective control and manipulation of nanoparticles require developing and researching new methods for designing optical tweeters, mainly based on a photonic hooks (PHs) effect. This paper first proposes a tunable PH in which a structured beam illuminates an anisotropic cutting liquid crystal microcylinder based on the Finite-DifferenceTime-Domain (FDTD) method. The PHs generated by plane wave, Gaussian, and Bessel beam are analyzed and compared. The impact of beams and LC particle parameters on the PHs are discussed. Where the influence of the extraordinary refractive index (ne) on PHs is emphasized. Our results reveal that introducing birefringence can change the bending direction of PH. Besides, the maximum intensity of the PHs increases as ne increases regardless of the beam type. The PH generated by a plane wave has a higher maximum intensity and smaller FWHM than that generated by the Gaussian and Bessel beams. The smallest FWHM and maximum intensity of the PHs generated by the Gaussian falls between that generated by the plane wave and the Bessel beam. The PH generated by a Bessel beam has the minor maximum intensity and the largest FWHM. Still, it exceeds the diffraction limit and exhibits bending twice due to its self-recovery property. This paper provides a new way to modulate PH. This work offers novel theoretical models and the degree of freedom for the design of PHs, which is beneficial for the selective manipulation of nanoparticles. It has promising applications in Mesotronics and biomedicine.

Travelling waves in beam-like structures submerged in water

There are many examples in nature of travelling waves used for propulsion purposes, e.g., micro-organisms and sea creatures. Structural travelling waves can be used to induce momentum in a surrounding media creating a net propelling force. Recent research has tried to capture this interaction in engineering devices. Nonetheless, some challenges remain to fully exploit this phenomenon so that travelling-waves propelled devices can be optimally designed. One such challenge is that the interaction between the structure and the surrounding fluid heavily influences the amplitude of the waves and how they travel through the structure. This paper proposes a systematic qualitative and quantitative analysis of travelling waves in a slender cantilever beam submerged in water. The novelty of this work is demonstrated through two key aspects: The application of the Euler-Bernoulli beam equation combined with the Galerkin approximation, enabling a deeper understanding of how travelling waves form at resonant frequencies rather than non-resonant ones; and An analytical approach using a Galerkin approximation to characterise the nonlinear fluid-structure interaction, followed by linearisation for a comprehensive parametric study of the problem. In this investigation, the contributions of the first five vibration modes are considered in relation to the travelling waves observed near the resonant peaks. Experimental tests validate the analytical results and assess the accuracy of the proposed models. The results demonstrate that the model presented effectively characterises the travelling waves, making a suitable tool for the design of travelling-wave propelled devices.

Broadband controllable defect state of longitudinal waves in one-dimensional pillared phononic crystal beams

Broadband controllable defect state of longitudinal waves in one-dimensional pillared phononic crystal beams