Exploring new traveling wave solutions by solving the nonlinear space-time fractal Fornberg-Whitham equation.

Complex and nonlinear fractal equations are ubiquitous in natural phenomena. This research employs the fractal Euler-Lagrange and semi-inverse methods to derive the nonlinear space-time fractal Fornberg-Whitham equation. This derivation provides an in-depth comprehension of traveling wave propagation. Consequently, the nonlinear space-time fractal Fornberg-Whitham equation is pivotal in elucidating fundamental phenomena across applied sciences. A novel analytical technique, the generalized Kudryashov method, is presented to address the space-time fractal Fornberg-Whitham equation. This method combines the fractional complex approach with the modified Kudryashov method to enhance its effectiveness. We derive an analytical solution for the space-time fractal Fornberg-Whitham equation to elucidate how various parameters influence the propagation of new traveling wave solutions. Furthermore, Figures 1 through 6 analyze the impact of parameters α , ß , b 1 , and k on these new traveling wave solutions. Our results show that the solitary wave solutions remain intact for both case 1 and case 2, regardless of the time fractional orders ß . At the end, the manuscript discusses the implications of these findings for understanding complex wave phenomena, paving the way for further exploration and applications in wave propagation studies.

Presence and infestation waves of hematophagous arthropod species.

The invasion of hematophagous arthropod species in human settlements represents a threat, not only to the economy but also to the health system in general. Recent examples of this phenomenon were seen in Paris and Mexico City, evidencing the importance of understanding these dynamics. In this work, we present a reaction-diffusion model to describe the invasion dynamics of hematophagous arthropod species. The proposed model considers a denso-dependent growth rate and parameters related to the control of the invasive species. Our results illustrate the existence of two invasion levels (presence and infestation) within a region, depending on control parameter values. We also prove analytically the existence of the presence and infestation waves and show different theoretical types of invasion waves that result from varying control parameters. In addition, we present a condition threshold that determines whether or not an infestation occurs. Finally, we illustrate some results when considering the case of bedbugs and brown dog ticks as invasion species.

A Symmetrical Quasi-Synchronous Step-Transition Folded Waveguide Slow Wave Structure for 650 GHz Traveling Wave Tubes.

For the purpose of improving performance and reducing the fabrication difficulty of terahertz traveling wave tubes (TWTs), this paper proposes a novel single-section high-gain slow wave structure (SWS), which is named the symmetrical quasi-synchronous step-transition (SQSST) folded waveguide (FW). The SQSST-FW SWS has an artificially designed quasi-synchronous region (QSR) to suppress self-oscillations for sustaining a high gain in an untruncated circuit. Simultaneously, a symmetrical design can improve the efficiency performance to some extent. A prototype of the SQSST-FW SWS for 650 GHz TWTs is designed based on small-signal analysis and numerical simulation. The simulation results indicate that the maximum saturation gain of the designed 650 GHz SQSST-FW TWT is 39.1 dB in a 34.3 mm slow wave circuit, occurring at the 645 GHz point when a 25.4 kV 15 mA electron beam and a 0.43 mW sinusoidal input signal are applied. In addition, a maximum output power exceeding 4 W is observed at the 648 GHz point using the same beam with an increased input power of around 2.8 mW.

Dynamics of the epidemiological Predator-Prey system in advective environments.

This paper aims to establish the existence of traveling wave solutions connecting different equilibria for a spatial eco-epidemiological predator-prey system in advective environments. After applying the traveling wave coordinates, these solutions correspond to heteroclinic orbits in phase space. We investigate the existence of the traveling wave solution connecting from a boundary equilibrium to a co-existence equilibrium by using a shooting method. Different from the techniques introduced by Huang, we directly prove the convergence of the solution to a co-existence equilibrium by constructing a special bounded set. Furthermore, the Lyapunov-type function we constructed does not need the condition of bounded below. Our approach provides a different way to study the existence of traveling wave solutions about the co-existence equilibrium. The existence of traveling wave solutions between co-existence equilibria are proved by utilizing the qualitative theory and the geometric singular perturbation theory. Some other open questions of interest are also discussed in the paper.

Biological invasion with a porous medium type diffusion in a heterogeneous space.

The knowledge of traveling wave solutions is the main tool in the study of wave propagation. However, in a spatially heterogeneous environment, traveling wave solutions do not exist, and a different approach is needed. In this paper, we study the generation and the propagation of hyperbolic scale singular limits of a KPP-type reaction-diffusion equation when the carrying capacity is spatially heterogeneous and the diffusion is of a porous medium equation type. We show that the interface propagation speed varies according to the carrying capacity.

Elucidating the Gas-Phase Behavior of Nitazene Analog Protomers Using Structures for Lossless Ion Manipulations Ion Mobility-Orbitrap Mass Spectrometry.

2-Benzylbenzimidazoles, or "nitazenes", are a class of novel synthetic opioids (NSOs) that are increasingly being detected alongside fentanyl analogs and other opioids in drug overdose cases. Nitazenes can be 20× more potent than fentanyl but are not routinely tested for during postmortem or clinical toxicology drug screens; thus, their prevalence in drug overdose cases may be under-reported. Traditional analytical workflows utilizing liquid chromatography-tandem mass spectrometry (LC-MS/MS) often require additional confirmation with authentic reference standards to identify a novel nitazene. However, additional analytical measurements with ion mobility spectrometry (IMS) may provide a path toward reference-free identification, which would greatly accelerate NSO identification rates in toxicology laboratories. Presented here are the first IMS and collision cross section (CCS) measurements on a set of fourteen nitazene analogs using a structures for lossless ion manipulations (SLIM)-orbitrap MS. All nitazenes exhibited two high intensity baseline-separated IMS distributions, which fentanyls and other drug and druglike compounds also exhibit. Incorporating water into the electrospray ionization (ESI) solution caused the intensities of the higher mobility IMS distributions to increase and the intensities of the lower mobility IMS distributions to decrease. Nitazenes lacking a nitro group at the R1 position exhibited the greatest shifts in signal intensities due to water. Furthermore, IMS-MS/MS experiments showed that the higher mobility IMS distributions of all nitazenes possessing a triethylamine group produced fragment ions with m/z 72, 100, and other low intensity fragments while the lower mobility IMS distributions only produced fragment ions with m/z 72 and 100. The IMS, solvent, and fragmentation studies provide experimental evidence that nitazenes potentially exhibit three gas-phase protomers. The cyclic IMS capability of SLIM was also employed to partially resolve four sets of structurally similar nitazene isomers (e.g., protonitazene/isotonitazene, butonitazene/isobutonitazene/secbutonitazene), showcasing the potential of using high-resolution IMS separations in MS-based workflows for reference-free identification of emerging nitazenes and other NSOs.

A Staggered Vane-Shaped Slot-Line Slow-Wave Structure for W-Band Dual-Sheet Electron-Beam-Traveling Wave Tubes.

A staggered vane-shaped slot-line slow-wave structure (SV-SL SWS) for application in W-band traveling wave tubes (TWTs) is proposed in this article. In contrast to the conventional slot-line SWSs with dielectric substrates, the proposed SWS consists only of a thin metal sheet inscribed with periodic grooves and two half-metal enclosures, which means it can be easily manufactured and assembled and has the potential for mass production. This SWS not only solves the problem of the dielectric loading effect but also improves the heat dissipation capability of such structures. Meanwhile, the SWS design presented here covers a -15 dB S11 frequency range from 87.5 to 95 GHz. The 3-D simulation for a TWT based on the suggested SWS is also investigated. Under dual-electron injection conditions with a total voltage of 17.2 kV and a total current of 0.3 A, the maximum output power at 90 GHz is 200 W, with a 3 dB bandwidth up to 4 GHz. With a good potential for fabrication using microfabrication techniques, this structure can be a good candidate for millimeter-wave TWT applications.

Measurement of very low-molecular weight metabolites by traveling wave ion mobility and its use in human urine samples.

The collision cross-sections (CCS) measurement using ion mobility spectrometry (IMS) in combination with mass spectrometry (MS) offers a great opportunity to increase confidence in metabolite identification. However, owing to the lack of sensitivity and resolution, IMS has an analytical challenge in studying the CCS values of very low-molecular-weight metabolites (VLMs ≤ 250 Da). Here, we describe an analytical method using ultrahigh-performance liquid chromatography (UPLC) coupled to a traveling wave ion mobility-quadrupole-time-of-flight mass spectrometer optimized for the measurement of VLMs in human urine samples. The experimental CCS values, along with mass spectral properties, were reported for the 174 metabolites. The experimental data included the mass-to-charge ratio (m/z), retention time (RT), tandem MS (MS/MS) spectra, and CCS values. Among the studied metabolites, 263 traveling wave ion mobility spectrometry (TWIMS)-derived CCS values (TWCCSN2) were reported for the first time, and more than 70% of these were CCS values of VLMs. The TWCCSN2 values were highly repeatable, with inter-day variations of <1% relative standard deviation (RSD). The developed method revealed excellent TWCCSN2 accuracy with a CCS difference (ΔCCS) within ±2% of the reported drift tube IMS (DTIMS) and TWIMS CCS values. The complexity of the urine matrix did not affect the precision of the method, as evidenced by ΔCCS within ±1.92%. According to the Metabolomics Standards Initiative, 55 urinary metabolites were identified with a confidence level of 1. Among these 55 metabolites, 53 (96%) were VLMs. The larger number of confirmed compounds found in this study was a result of the addition of TWCCSN2 values, which clearly increased metabolite identification confidence.

Interictal discharge traveling waves recorded from stereoelectroencephalography electrodes.

OBJECTIVE: Interictal epileptiform discharges (IEDs) are intermittent high-amplitude electrical signals that occur between seizures. They have been shown to propagate through the brain as traveling waves when recorded with epicortical grid-type electrodes and small penetrating microelectrode arrays. However, little work has been done to translate experimental IED analyses to more clinically relevant platforms such as stereoelectroencephalography (SEEG). In this pilot study, the authors aimed to define a computational method to identify and characterize IEDs recorded from clinical SEEG electrodes and leverage the directionality of IED traveling waves to localize the seizure onset zone (SOZ). METHODS: Continuous SEEG recordings from 15 patients with medically refractory epilepsy were collected, and IEDs were detected by identifying overlapping peaks of a minimum prominence. IED pathways of propagation were defined and compared to the SOZ location determined by a clinical neurologist based on the ictal recordings. For further analysis of the IED pathways of propagation, IED detections were divided into triplets, defined as a set of 3 consecutive contacts within the same IED detection. Univariate and multivariate linear regression models were employed to associate IED characteristics with colocalization to the SOZ. RESULTS: A median (range) of 22.6 (4.4-183.9) IEDs were detected per hour from 15 patients over a mean of 23.2 hours of recording. Depending on the definition of the SOZ, a median (range) of 20.8% (0.0%-54.5%) to 62.1% (19.2%-99.4%) of IEDs per patient traversed the SOZ. IEDs passing through the SOZ followed discrete pathways that had little overlap with those of the IEDs passing outside the SOZ. Contact triplets that occurred more than once were significantly more likely to be detected in an IED passing through the SOZ (p < 0.001). Per our multivariate model, patients with a greater proportion of IED traveling waves had a significantly greater proportion of IEDs that localized to the SOZ (ß = 0.64, 95% CI 0.01-1.27, p = 0.045). CONCLUSIONS: By using computational methods, IEDs can be meaningfully detected from clinical-grade SEEG recordings of patients with epilepsy. In some patients, a high proportion of IEDs are traveling waves according to multiple metrics that colocalize to the SOZ, offering hope that IED detection, with further refinement, could serve as an alternative method for SOZ localization.

Spread and persistence for integro-difference equations with shifting habitat and strong Allee effect.

We study an integro-difference equation model that describes the spatial dynamics of a species with a strong Allee effect in a shifting habitat. We examine the case of a shifting semi-infinite bad habitat connected to a semi-infinite good habitat. In this case we rigorously establish species persistence (non-persistence) if the habitat shift speed is less (greater) than the asymptotic spreading speed of the species in the good habitat. We also examine the case of a finite shifting patch of hospitable habitat, and find that the habitat shift speed must be less than the asymptotic spreading speed associated with the habitat and there is a critical patch size for species persistence. Spreading speeds and traveling waves are established to address species persistence. Our numerical simulations demonstrate the theoretical results and show the dependence of the critical patch size on the shift speed.

Investigation of the dynamical structures of double-chain deoxyribonucleic acid model in biological sciences.

The present research investigates the double-chain deoxyribonucleic acid model, which is important for the transfer and retention of genetic material in biological domains. This model is composed of two lengthy uniformly elastic filaments, that stand in for a pair of polynucleotide chains of the deoxyribonucleic acid molecule joined by hydrogen bonds among the bottom combination, demonstrating the hydrogen bonds formed within the chain's base pairs. The modified extended Fan sub equation method effectively used to explain the exact travelling wave solutions for the double-chain deoxyribonucleic acid model. Compared to the earlier, now in use methods, the previously described modified extended Fan sub equation method provide more innovative, comprehensive solutions and are relatively straightforward to implement. This method transforms a non-linear partial differential equation into an ODE by using a travelling wave transformation. Additionally, the study yields both single and mixed non-degenerate Jacobi elliptic function type solutions. The complexiton, kink wave, dark or anti-bell, V, anti-Z and singular wave shapes soliton solutions are a few of the creative solutions that have been constructed utilizing modified extended Fan sub equation method that can offer details on the transversal and longitudinal moves inside the DNA helix by freely chosen parameters. Solitons propagate at a consistent rate and retain their original shape. They are widely used in nonlinear models and can be found everywhere in nature. To help in understanding the physical significance of the double-chain deoxyribonucleic acid model, several solutions are shown with graphics in the form of contour, 2D and 3D graphs using computer software Mathematica 13.2. All of the requisite constraint factors that are required for the completed solutions to exist appear to be met. Therefore, our method of strengthening symbolic computations offers a powerful and effective mathematical tool for resolving various moderate nonlinear wave problems. The findings demonstrate the system's potentially very rich precise wave forms with biological significance. The fundamentals of double-chain deoxyribonucleic acid model diffusion and processing are demonstrated by this work, which marks a substantial development in our knowledge of double-chain deoxyribonucleic acid model movements.

Fuzzy analysis of 2-D wave equation through Hukuhara differentiability coupled with AOS technique.

The research article in hand provides a new mechanism that deals with the investigation of the triangular analytical fuzzy solutions (TAFS) of the two-dimensional fuzzy fractional order wave equation (2-D FFWE) through the Hukuhara conformable fractional derivative (HCFD) along with the concept of [gH] and [gH-p] differentiability. The mechanism consists of a fuzzy traveling wave method coupled with additive operating splitting (AOS). The procedure for the aforesaid mechanism starts with the extension of the HCFD to the fuzzy conformable fractional derivative (FCFD). Furthermore, some properties of FCFD that play a vital role in this study like, ([i-gH],[ii-gH],[i-p],[ii-p])-differentiability, switching point, fuzzy chain rule, and traveling wave method are discussed in detail. Further, fuzzy traveling wave method coupled with the procedure of the additive operating splitting (AOS) method is adopted to investigate the triangular analytical fuzzy solution of the Two-dimensional fuzzy wave equation (2-D FWE). Finally, some examples are provided that support our arguments.

Identification of Unique Fragmentation Patterns of Fentanyl Analog Protomers Using Structures for Lossless Ion Manipulations Ion Mobility-Orbitrap Mass Spectrometry.

The opioid crisis in the United States is being fueled by the rapid emergence of new fentanyl analogs and precursors that can elude traditional library-based screening methods, which require data from known reference compounds. Since reference compounds are unavailable for new fentanyl analogs, we examined if fentanyls (fentanyl + fentanyl analogs) could be identified in a reference-free manner using a combination of electrospray ionization (ESI), high-resolution ion mobility (IM) spectrometry, high-resolution mass spectrometry (MS), and higher-energy collision-induced dissociation (MS/MS). We analyzed a mixture containing nine fentanyls and W-15 (a structurally similar molecule) and found that the protonated forms of all fentanyls exhibited two baseline-separated IM distributions that produced different MS/MS patterns. Upon fragmentation, both IM distributions of all fentanyls produced two high intensity fragments, resulting from amine site cleavages. The higher mobility distributions of all fentanyls also produced several low intensity fragments, but surprisingly, these same fragments exhibited much greater intensities in the lower mobility distributions. This observation demonstrates that many fragments of fentanyls predominantly originate from one of two different gas-phase structures (suggestive of protomers). Furthermore, increasing the water concentration in the ESI solution increased the intensity of the lower mobility distribution relative to the higher mobility distribution, which further supports that fentanyls exist as two gas-phase protomers. Our observations on the IM and MS/MS properties of fentanyls can be exploited to positively differentiate fentanyls from other compounds without requiring reference libraries and will hopefully assist first responders and law enforcement in combating new and emerging fentanyls.

A switching method for traveling/standing wave transportation modes in two-dimensional acoustic fields using a dual-transducer support structure.

The dual-transducer support structure discussed has the advantages of a simple structure and low cost, as well as allowing for the use of both Traveling-Wave (TW) and Standing-Wave (SW) acoustic transportation, supporting its use in pharmaceutical and biochemical analysis, for example. By adjusting the distance between the vibrating plate and the reflector which forms SW field in the y direction, the control of the position of the SW nodes or the TW component along the x direction allows the formation of a Two-Dimensional Standing Wave (2D-SW) or a Traveling Wave (TW) acoustic field, and these could be used for transportation in the x direction. It has been found that the x position of the SW nodes can be adjusted through changing the temporal phase shift, θ, which permits multiple objects to be transported using the 2D-SW mode. By comparison, TWs in the opposite direction could be generated at a pair of specific temporal phase shifts, allowing fast transportation using the TW mode. In this research work, an experiment has been carried out to transport polystyrene spheres using the two modes by programming the temporal phase shift, θ, this illustrating that precise position control of the multiple objects transported was possible using the 2D-SW mode, while high-speed transportation (up to 540 mm/s) was realized using the TW mode, showing that the dual-transducer support structure could be used effectively for accurate and fast transportation. As a fully non-contact method, the dual-transducer support structure can be seen to work in the 2D-SW mode for reaction synthesis or detection applications, and also in TW mode for rapid sample transportation applications.

Forced Traveling Waves in a Reaction-Diffusion Equation with Strong Allee Effect and Shifting Habitat.

We study a reaction-diffusion equation that describes the growth of a population with a strong Allee effect in a bounded habitat which shifts at a speed [Formula: see text]. We demonstrate that the existence of forced positive traveling waves depends on habitat size L, and [Formula: see text], the speed of traveling wave for the corresponding reaction-diffusion equation with the same growth function all over the entire unbounded spatial domain. It is shown that for [Formula: see text] there exists a positive number [Formula: see text] such that for [Formula: see text] there are two positive traveling waves and for [Formula: see text] there is no positive traveling wave. It is also shown if [Formula: see text] for any [Formula: see text] there is no positive traveling wave. The dynamics of the equation are further explored through numerical simulations.

Pile Damage Detection Using Machine Learning with the Multipoint Traveling Wave Decomposition Method.

The in-hole multipoint traveling wave decomposition (MPTWD) method is developed for detecting and characterizing the damage of cast in situ reinforced concrete (RC) piles. Compared with the results of MPTWD, the results of the in-hole MPTWD reconstruction technique are found ideal for evaluating the lower-part pile integrity and are further utilized to establish a data-driven machine-learning framework to detect and quantify the degree of damage. Considering the relatively small number of field test samples of the in-hole MPTWD method at this stage, an analytical solution is employed to generate sufficient samples to verify the feasibility and optimize the performance of the machine learning modeling framework. Two types of features extracted by the distributed sampling and statistical and signal processing techniques are applied to three machine-learning classifiers, i.e., logistic regression (LR), extreme gradient boosting (XGBoost) and multilayer perceptron (MLP). The performance of the data-driven machine-learning framework is then evaluated through a specific case study. The results demonstrate that all three classifiers perform better when employing the statistical and signal processing techniques, and the total of 24 extracted features are sufficient for the machine-learning algorithms.

Traveling-wave based fault location estimation in FACTS compensated transmission system: Recent status, challenges and future research directions.

This article presents a recent literature review on traveling wave-based fault location estimation in flexible alternating current transmission system (FACTS) compensated transmission system. The review aims to provide an overview of the current state-of-the-art in traveling wave-based fault location methods and their applications in FACTS compensated power systems. Firstly, the importance of fault location techniques and their classification are discussed. Secondly, the basic theory behind traveling-wave based fault location methods is presented. Further, the effects of presence of different FACTS devices are presented to highlight the challenges in developing efficient fault location methods for FACTS compensated transmission system. The survey covers reported traveling-wave based fault location techniques and highlights the current status and challenges. Additionally, the survey reviews recent advancements in the field and identifies future research directions. The study concludes by summarizing the main findings and providing recommendations for further research. The presented literature review provides valuable insights for researchers, engineers, and practitioners in the field of power system protection and control.

Design and Development of a Traveling Wave Ferro-Microfluidic Device and System Rig for Potential Magnetophoretic Cell Separation and Sorting in a Water-Based Ferrofluid.

The timely detection and diagnosis of diseases and accurate monitoring of specific genetic conditions require rapid and accurate separation, sorting, and direction of target cell types toward a sensor device surface. In that regard, cellular manipulation, separation, and sorting are progressively finding application potential within various bioassay applications such as medical disease diagnosis, pathogen detection, and medical testing. The aim of this paper is to present the design and development of a simple traveling wave ferro-microfluidic device and system rig purposed for the potential manipulation and magnetophoretic separation of cells in water-based ferrofluids. This paper details in full: (1) a method for tailoring cobalt ferrite nanoparticles for specific diameter size ranges (10-20 nm), (2) the development of a ferro-microfluidic device for potentially separating cells and magnetic nanoparticles, (3) the development of a water-based ferrofluid with magnetic nanoparticles and non-magnetic microparticles, and (4) the design and development of a system rig for producing the electric field within the ferro-microfluidic channel device for magnetizing and manipulating nonmagnetic particles in the ferro-microfluidic channel. The results reported in this work demonstrate a proof of concept for magnetophoretic manipulation and separation of magnetic and non-magnetic particles in a simple ferro-microfluidic device. This work is a design and proof-of-concept study. The design reported in this model is an improvement over existing magnetic excitation microfluidic system designs in that heat is efficiently removed from the circuit board to allow a range of input currents and frequencies to manipulate non-magnetic particles. Although this work did not analyze the separation of cells from magnetic particles, the results demonstrate that non-magnetic (surrogates for cellular materials) and magnetic entities can be separated and, in some cases, continuously pushed through the channel based on amperage, size, frequency, and electrode spacing. The results reported in this work establish that the developed ferro-microfluidic device may potentially be used as an effective platform for microparticle and cellular manipulation and sorting.

Numerical Solution of the Electric Field and Dielectrophoresis Force of Electrostatic Traveling Wave System.

Electrostatic traveling wave (ETW) methods have shown promising performance in dust mitigation of solar panels, particle transport and separation in in situ space resource utilization, cell manipulation, and separation in biology. The ETW field distribution is required to analyze the forces applied to particles and to evaluate ETW design parameters. This study presents the numerical results of the ETW field distribution generated by a parallel electrode array using both the charge simulation method (CSM) and the boundary element method (BEM). A low accumulated error of the CSM is achieved by properly arranging the positions and numbers of contour points and fictitious charges. The BEM can avoid the inconvenience of the charge position required in the CSM. The numerical results show extremely close agreement between the CSM and BEM. For simplification, the method of images is introduced in the implementation of the CSM and BEM. Moreover, analytical formulas are obtained for the integral of Green's function along boundary elements. For further validation, the results are cross-checked using the finite element method (FEM). It is found that discrepancies occur at the ends of the electrode array. Finally, analyses are provided of the electric field and dielectrophoretic (DEP) components. Emphasis is given to the regions close to the electrode surfaces. These results provide guidance for the fabrication of ETW systems for various applications.

A Novel Staggered Double-Segmented Grating Slow-Wave Structure for 340 GHz Traveling-Wave Tube.

In this paper, a novel staggered double-segmented grating slow-wave structure (SDSG-SWS) is developed for wide-band high-power submillimeter wave traveling-wave tubes (TWTs). The SDSG-SWS can be considered as a combination of the sine waveguide (SW) SWS and the staggered double-grating (SDG) SWS; that is, it is obtained by introducing the rectangular geometric ridges of the SDG-SWS into the SW-SWS. Thus, the SDSG-SWS has the advantages of the wide operating band, high interaction impedance, low ohmic loss, low reflection, and ease of fabrication. The analysis for high-frequency characteristics shows that, compared with the SW-SWS, the SDSG-SWS has higher interaction impedance when their dispersions are at the same level, while the ohmic loss for the two SWSs remains basically unchanged. Furthermore, the calculation results of beam-wave interaction show that the output power is above 16.4 W for the TWT using the SDSG-SWS in the range of 316 GHz-405 GHz with a maximum power of 32.8 W occurring at 340 GHz, whose corresponding maximum electron efficiency is 2.84%, when the operating voltage is 19.2 kV and the current is 60 mA.