A principle of selection of modes and their spatial harmonics in periodic waveguides and, in particular, in spatially developed slowing systems for multibeam traveling-wave tubes (TWTs) is elaborated. The essence of the principle is in the following: varying along the length of the system its period and at least one more parameter that determines the phase shift per period, one can provide constant phase velocity of one spatial harmonic and destroy other spatial harmonics, i.e., reduce their amplitudes substantially. In this case, variations of the period may be significant, and the slowing system becomes nonuniform, or pseudoperiodic; namely, one of the spatial harmonics remains the same as in the initial periodic structure. Relationships are derived for the amplitudes of the spatial-wave harmonics, interaction coefficient, and coupling impedance of the pseudoperiodic system. The possibility of the mode selection in pseudoperiodic slowing systems when the synchronism condition is satisfied for the spatial harmonic of one mode is investigated. The efficiency of suppressing spurious spatial harmonics and modes for linear and abrupt variation of spacing is estimated. The elaborated principle of selection of spatial harmonics and modes is illustrated by an example of a two-section helical-waveguide slowing system.
The objective of this paper is to study how the selection of the coil and the frequency affects the received modes in
guided Lamb waves, with the objective of analyzing the best configuration for determining the depth of a given
defect in a metallic pipe with the minimum error. Studies of the size of the damages with all the extracted
parameters are then used to propose estimators of the residual thickness, considering amplitude and phase
information in one or several modes. Results demonstrate the suitability of the proposal, improving the estimation of
the residual thickness when two simultaneous modes are used, as well as the range of possibilities that the coil and
frequency selection offers.
Quantum Theory. Wave Particle Duality. Particle in a Box. Schrodinger wave equation. Quantum Numbers and Electron Orbitals. Principal Shells and Subshells. A Fourth Quantum Number. Effective nuclear charge
A generalized linear theory of the discrete electron–wave interaction in slow...Victor Solntsev
A linear theory of the discrete interaction of electron flows and electromagnetic waves in slow-wave structures (SWSs) is developed. The theory is based on the finite-difference equations of SWS excitation. The local coupling impedance entering these equations characterizes the field intensity excited by the electron flow in interaction gaps and has a finite value at SWS cutoff frequencies. The theory uniformly describes the electron–wave interaction in SWS passbands and stopbands without using equivalent circuits, a circumstance that allows considering the processes in the vicinity of cutoff frequencies and switching from the Cerenkov mechanism of interaction in a traveling-wave tube to the klystron mechanism when passing to SWS stopbands. The features of the equations of the discrete electron–wave interaction in pseudoperiodic SWSs are analyzed.
R,L,C, G parameters of a co-axial & 2-wire transmission line
Field solutions for TE and TM modes for a waveguide
Design and analysis of rectangular waveguide to support TE10 mode
Design and analysis of circular waveguide to support TE11 mode
Simulation of Nonstationary Processes in Backward-Wave Tube with the Self-Mod...Victor Solntsev
The equations that describe nonlinear nonstationary processes in carcinotrode (backward- wave tube with the emission modulation in the presence of the field of the output signal fed to the cathode via a feedback loop) are derived. An algorithm and the corresponding code are developed to solve the equations with allowance for the modulation of emission using nonuniform (with respect to time) large particles (electrons of equal charge) ejected from the cathode. The effect of the feedback parameter on the intensity and shape of the carcinotrode oscillations is analyzed. It is demonstrated that the carcinotrode efficiency can be increased to about 50% upon the generation of harmonic oscil- lations. A more significant increase in the efficiency to 70% is possible in the regime of the weak self- modulation of oscillations upon an increase in the feedback coefficient in the feedback loop involving the slow-wave structure and the cathode and a decrease in the cathode–grid static field.
The objective of this paper is to study how the selection of the coil and the frequency affects the received modes in
guided Lamb waves, with the objective of analyzing the best configuration for determining the depth of a given
defect in a metallic pipe with the minimum error. Studies of the size of the damages with all the extracted
parameters are then used to propose estimators of the residual thickness, considering amplitude and phase
information in one or several modes. Results demonstrate the suitability of the proposal, improving the estimation of
the residual thickness when two simultaneous modes are used, as well as the range of possibilities that the coil and
frequency selection offers.
Quantum Theory. Wave Particle Duality. Particle in a Box. Schrodinger wave equation. Quantum Numbers and Electron Orbitals. Principal Shells and Subshells. A Fourth Quantum Number. Effective nuclear charge
A generalized linear theory of the discrete electron–wave interaction in slow...Victor Solntsev
A linear theory of the discrete interaction of electron flows and electromagnetic waves in slow-wave structures (SWSs) is developed. The theory is based on the finite-difference equations of SWS excitation. The local coupling impedance entering these equations characterizes the field intensity excited by the electron flow in interaction gaps and has a finite value at SWS cutoff frequencies. The theory uniformly describes the electron–wave interaction in SWS passbands and stopbands without using equivalent circuits, a circumstance that allows considering the processes in the vicinity of cutoff frequencies and switching from the Cerenkov mechanism of interaction in a traveling-wave tube to the klystron mechanism when passing to SWS stopbands. The features of the equations of the discrete electron–wave interaction in pseudoperiodic SWSs are analyzed.
R,L,C, G parameters of a co-axial & 2-wire transmission line
Field solutions for TE and TM modes for a waveguide
Design and analysis of rectangular waveguide to support TE10 mode
Design and analysis of circular waveguide to support TE11 mode
Simulation of Nonstationary Processes in Backward-Wave Tube with the Self-Mod...Victor Solntsev
The equations that describe nonlinear nonstationary processes in carcinotrode (backward- wave tube with the emission modulation in the presence of the field of the output signal fed to the cathode via a feedback loop) are derived. An algorithm and the corresponding code are developed to solve the equations with allowance for the modulation of emission using nonuniform (with respect to time) large particles (electrons of equal charge) ejected from the cathode. The effect of the feedback parameter on the intensity and shape of the carcinotrode oscillations is analyzed. It is demonstrated that the carcinotrode efficiency can be increased to about 50% upon the generation of harmonic oscil- lations. A more significant increase in the efficiency to 70% is possible in the regime of the weak self- modulation of oscillations upon an increase in the feedback coefficient in the feedback loop involving the slow-wave structure and the cathode and a decrease in the cathode–grid static field.
Characteristic equation and properties of electron waves in periodic structuresVictor Solntsev
The difference theory of excitation of periodic waveguides is used to derive the characteristic equation for electron waves formed during interaction of an electron flow with forward and counter-propagating electromagnetic waves of periodic waveguides (slowﱹwave structures). The derived characteristic equation describes interaction of electrons and waves in passbands and stopbands of periodic waveguides and contains known solutions for “smooth” slow-wave structures and resonator slow-wave structures near cutoff frequencies as particular cases. Several analytical solutions allowing comparison of amplification and propagation properties of electron waves inside and at the edges of passbands and stopbands of periodic waveguides are found.
This paper was published by my former Supervisor and involves partly my calculations and the concepts used during my MSci Thesis at University College London.
Ultrasonic guided wave techniques have great potential for structural health monitoring applications. Appropriate mode and frequency selection is the basis for achieving optimised damage monitoring performance.
In this paper, several important guided wave mode attributes are
introduced in addition to the commonly used phase velocity and group velocity dispersion curves while using the general corrosion problem as an example. We first derive a simple and generic wave excitability function based on the theory of normal mode expansion and the reciprocity theorem. A sensitivity dispersion curve is formulated based on the group velocity dispersion curve. Both excitability and sensitivity dispersion curves are verified with finite element simulations. Finally, a
goodness dispersion curve concept is introduced to evaluate the tradeoffs between multiple mode selection objectives based on the wave velocity, excitability and sensitivity.
Planar spiral systems with waves of constant radial phase velocityVictor Solntsev
Planar spiral systems are shown to exist, in which a cylindrical wave has a constant radial phase velocity. The equation of such spirals is derived and its solution is obtained in elementary functions. It is established that these spirals include the logarithmic spirals as a special case; in the general case, however, they have a large variety of forms and in particular they have a limiting inside or outside radius. This makes it possible to use such spirals for building new slow-wave structures and antennas.
Characteristic equation and properties of electron waves in periodic structuresVictor Solntsev
The difference theory of excitation of periodic waveguides is used to derive the characteristic equation for electron waves formed during interaction of an electron flow with forward and counter-propagating electromagnetic waves of periodic waveguides (slowﱹwave structures). The derived characteristic equation describes interaction of electrons and waves in passbands and stopbands of periodic waveguides and contains known solutions for “smooth” slow-wave structures and resonator slow-wave structures near cutoff frequencies as particular cases. Several analytical solutions allowing comparison of amplification and propagation properties of electron waves inside and at the edges of passbands and stopbands of periodic waveguides are found.
This paper was published by my former Supervisor and involves partly my calculations and the concepts used during my MSci Thesis at University College London.
Ultrasonic guided wave techniques have great potential for structural health monitoring applications. Appropriate mode and frequency selection is the basis for achieving optimised damage monitoring performance.
In this paper, several important guided wave mode attributes are
introduced in addition to the commonly used phase velocity and group velocity dispersion curves while using the general corrosion problem as an example. We first derive a simple and generic wave excitability function based on the theory of normal mode expansion and the reciprocity theorem. A sensitivity dispersion curve is formulated based on the group velocity dispersion curve. Both excitability and sensitivity dispersion curves are verified with finite element simulations. Finally, a
goodness dispersion curve concept is introduced to evaluate the tradeoffs between multiple mode selection objectives based on the wave velocity, excitability and sensitivity.
Planar spiral systems with waves of constant radial phase velocityVictor Solntsev
Planar spiral systems are shown to exist, in which a cylindrical wave has a constant radial phase velocity. The equation of such spirals is derived and its solution is obtained in elementary functions. It is established that these spirals include the logarithmic spirals as a special case; in the general case, however, they have a large variety of forms and in particular they have a limiting inside or outside radius. This makes it possible to use such spirals for building new slow-wave structures and antennas.
Spatially adiabatic frequency conversion in opto-electro-mechanical arraysOndrej Cernotik
Optoelectromechanical systems offer a promising route towards frequency conversion between microwaves and light and towards building quantum networks of superconducting circuits. Current theoretical and experimental efforts focus on approaches based on either optomechanically induced transparency or adiabatic passage. The former has the advantage of working with time-independent control but only in a limited bandwidth (typically much smaller than the cavity linewidth); the latter can, in principle, be used to increase the bandwidth but at the expense of working with time-dependent control fields and with strong optomechanical coupling. In my presentation, I will show that an array of optoelectromechanical transducers can overcome this limitation and reach a bandwidth that is larger than the cavity linewidth. The coupling rates are varied in space throughout the array so that a mechanically dark mode of the propagating fields adiabatically changes from microwave to optical or vice versa. This strategy also leads to significantly reduced thermal noise with the collective optomechanical cooperativity being the relevant figure of merit. I will also demonstrate that, remarkably, the bandwidth enhancement per transducer element is largest for small arrays. With these features the scheme is particularly relevant for improving the conversion bandwidth in state-of-the-art experimental setups.
The Propagation and Power Deposition of Electron Cyclotron Waves in Non-Circu...IJERA Editor
By solving the plasma equilibrium equation, ray equations, and quasi-linear Fokker-Planck equation, the ray
trajectories and power deposition of EC wave has been numerically simulated in non-circular HL-2A tokamak
plasma. The results show that shaping effect and temperature profile has little influence on ECRH, while plasma
density affect propagation and power deposition obviously. when the ordinary mode of EC waves are launched
from the mid-plane and low-field-side, ray trajectories are bended as the parallel refractive index increases and
even recurve to the low-field side when the parallel refractive index reaches to a certain value. Single absorption
decreases with increasing both poloidal and toroidal injection angle, and can be 100% when poloidal injection
angle is 180o and toroidal injection angle is less than 10o.
Investigation of the bandpass properties of the local impedance of slow wave ...Victor Solntsev
The properties of the local coupling impedance that determines the efficiency of the electron–wave interaction in periodic slow-wave structures are investigated. This impedance is determined (i) through the char- acteristics of the electromagnetic field in a slow-wave structure and (ii) through the parameters of a two-port chain simulating the structure. The continuous behavior of the local coupling impedance in the passbands of slow-wave structures, at the boundaries of the passbands, and beyond the passbands is confirmed with the help of a waveguide–resonator model.
Average Channel Capacity of Amplify-and-forward MIMO/FSO Systems Over Atmosph...IJECEIAES
In amplify-and-forward (AF) relay channel, when the direct link between source and destination terminals is deeply faded, the signal from the source terminal to the destination terminal propagates through the relay terminals, each of which relays a signal received from the previous terminal to the next terminal in series. This paper, we theoretically analyze the performance of multiple-input multiple-output (MIMO) AF free-space optical (FSO) systems. The AF-MIMO/FSO average channel capacity (ACC), which is expressed in terms of average spectral efficiency (ASE) is derived taking into account the atmospheric turbulence effects on the MIMO/FSO channel. They are modeled by log-normal and the gamma-gamma distributions for the cases of weak-to-strong turbulence conditions. We extract closed form mathematical expression for the evaluation of the ACC and we quantitatively discuss the influence of turbulence strength, link distance, different number of relay stations and different MIMO configurations on it.
Comparative detection and fault location in underground cables using Fourier...IJECEIAES
In this research, we create a single-phase to ground synthetic fault by the simulation of a three-phase cable system and identify the location using mathematical techniques of Fourier and modal transforms. Current and voltage signals are measured and analyzed for fault location by the reflection of the waves between the measured point and the fault location. By simulating the network and line modeling using alternative transient programs (ATP) and MATLAB software, two single-phase to ground faults are generated at different points of the line at times of 0.3 and 0.305 s. First, the fault waveforms are displayed in the ATP software, and then this waveform is transmitted to MATLAB and presented along with its phasor view over time. In addition to the waveforms, the detection and fault location indicators are presented in different states of fault. Fault resistances of 1, 100, and 1,000 ohms are considered for fault creation and modeling with low arch strength. The results show that the proposed method has an average fault of less than 0.25% to determine the fault location, which is perfectly correct. It is varied due to changing the conditions of time, resistance, location, and type of error but does not exceed the above value.
Theoretical and experimental analysis of electromagnetic coupling into microw...IJECEIAES
In this paper, our work is devoted to a time domain analysis of field-to-line coupling model. The latter is designed with a uniform microstrip multiconductor transmission line (MTL), connected with a mixed load which can be linear as a resistance, nonlinear like a diode or complex nonlinear as a Metal Semiconductor Field-Effect Transistor (MESFET). The finite difference time-domain technique (FDTD) is used to compute the expression of voltage and current at the line. The primary advantage of this method over many existing methods is that nonlinear terminations may be readily incorporated into the algorithm and the analysis. The numerical predictions using the proposed method show a good agreement with the GHz Transverse Electro Magnetic (GTEM) measurement.
Hybrid Time-power Switching Protocol of Energy Harvesting Bidirectional Relay...TELKOMNIKA JOURNAL
In this paper, we investigate system performance in term of throughput and ergodic capacity of the hybrid time-power switching protocol of energy harvesting bidirectional relaying network. In the first stage, the analytical expression of the system throughput and ergodic capacity of the model system is proposed and derived. In this analysis, both delay-limited and delay-tolerant transmission modes are presented and considered. After that, the effect of various system parameters on the proposed system is investigated and demonstrated by Monte-Carlo simulation. Finally, the results show that the analytical mathematical and simulated results match for all possible parameter values for both schemes.
A numerical wavefront solution for quantum transmission lines with charge discreteness is
proposed for the first time. The nonlinearity of the system becomes deeply related to charge discreteness. The
wavefront velocity is found to depend on the normalized (pseudo) flux variable. Finally we find the dispersion
relation for the normalized flux
0 / .
Accurate Evaluation of Interharmonics of a Six Pulse, Full Wave - Three Phase...idescitation
Interharmonics are the non-integral multiples of
the system’s fundamental frequency. The interharmonic
components can be apprehended as the intermodulation of
the fundamental and harmonic components of the system with
any other frequency components introduced by the load. These
loads include static frequency converters, cyclo-converters,
induction motors, arc furnaces and all the loads not pulsating
synchronously with the fundamental frequency of the system.
The harmonic and interharmonic components inflict common
damage to the system and apart from these damages the
interharmonics also cause light flickering, sideband torques
on motor/generator and adverse effects on transformer and
motor components. To
filter/compensate the interharmonic
components, their accurate evaluation is essential and to
achieve the same the Iterative algorithm has been proposed.
The main cause of spectral leakage errors is the truncation of
the time-domain signal. The proposed adaptive approach
calculates the immaculate window width, eliminating the
spectral leakage errors in the frequency domain and thereby
the interharmonics/harmonics can be calculated accurately.
The algorithm does not require any inputs regarding the
system frequency and interharmonic constituents of the
system. The only parameter required is the signal sequence
obtained by sampling the analog signal at equidistant sampling
interval.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
Welocme to ViralQR, your best QR code generator.ViralQR
Welcome to ViralQR, your best QR code generator available on the market!
At ViralQR, we design static and dynamic QR codes. Our mission is to make business operations easier and customer engagement more powerful through the use of QR technology. Be it a small-scale business or a huge enterprise, our easy-to-use platform provides multiple choices that can be tailored according to your company's branding and marketing strategies.
Our Vision
We are here to make the process of creating QR codes easy and smooth, thus enhancing customer interaction and making business more fluid. We very strongly believe in the ability of QR codes to change the world for businesses in their interaction with customers and are set on making that technology accessible and usable far and wide.
Our Achievements
Ever since its inception, we have successfully served many clients by offering QR codes in their marketing, service delivery, and collection of feedback across various industries. Our platform has been recognized for its ease of use and amazing features, which helped a business to make QR codes.
Our Services
At ViralQR, here is a comprehensive suite of services that caters to your very needs:
Static QR Codes: Create free static QR codes. These QR codes are able to store significant information such as URLs, vCards, plain text, emails and SMS, Wi-Fi credentials, and Bitcoin addresses.
Dynamic QR codes: These also have all the advanced features but are subscription-based. They can directly link to PDF files, images, micro-landing pages, social accounts, review forms, business pages, and applications. In addition, they can be branded with CTAs, frames, patterns, colors, and logos to enhance your branding.
Pricing and Packages
Additionally, there is a 14-day free offer to ViralQR, which is an exceptional opportunity for new users to take a feel of this platform. One can easily subscribe from there and experience the full dynamic of using QR codes. The subscription plans are not only meant for business; they are priced very flexibly so that literally every business could afford to benefit from our service.
Why choose us?
ViralQR will provide services for marketing, advertising, catering, retail, and the like. The QR codes can be posted on fliers, packaging, merchandise, and banners, as well as to substitute for cash and cards in a restaurant or coffee shop. With QR codes integrated into your business, improve customer engagement and streamline operations.
Comprehensive Analytics
Subscribers of ViralQR receive detailed analytics and tracking tools in light of having a view of the core values of QR code performance. Our analytics dashboard shows aggregate views and unique views, as well as detailed information about each impression, including time, device, browser, and estimated location by city and country.
So, thank you for choosing ViralQR; we have an offer of nothing but the best in terms of QR code services to meet business diversity!
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
Elevating Tactical DDD Patterns Through Object CalisthenicsDorra BARTAGUIZ
After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
91mobiles recently conducted a Smart TV Buyer Insights Survey in which we asked over 3,000 respondents about the TV they own, aspects they look at on a new TV, and their TV buying preferences.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
SAP Sapphire 2024 - ASUG301 building better apps with SAP Fiori.pdfPeter Spielvogel
Building better applications for business users with SAP Fiori.
• What is SAP Fiori and why it matters to you
• How a better user experience drives measurable business benefits
• How to get started with SAP Fiori today
• How SAP Fiori elements accelerates application development
• How SAP Build Code includes SAP Fiori tools and other generative artificial intelligence capabilities
• How SAP Fiori paves the way for using AI in SAP apps
2. To raise the output of relativistic devices, electron beams are applied that are
accelerated by the voltage U> 100 kV, as well as explosive-emission cathodes that
produce a large current. In such devices, one has to use large-current electron
accelerators to obtain high-power electron beams; therefore, they are manufactured
as large stationary installations.
Another method of raising the power output consists in increasing the electron-
beam current with the help of hot cathodes when the voltage U < 100 kV is
limited. The beam-current density is restricted by the capacity of the electron-
optical system; therefore, the beam cross section must be increased in order to
increase the current. In this case, cross-sectional dimensions may be much greater
than the wavelength in the slowing system. There may be a large number of modes
and spatial harmonics in such overdimensioned (or spatially developed) systems
that cause electron-field multimode interaction, as well as amplification and
oscillation instability. Thus, the selection becomes one of the major problems when
the electron-beam current and the device power output are to be increased.
At present, different techniques are used to suppress spurious oscillations and
modes, from the utilization of selective absorbers in TWTs and up to the
applicationof open resonators and open waveguides in orotrons, gyrotrons, and
free-electron lasers.
This paper addresses the principle of selection of spatial harmonics and modes
in periodic waveguides and slowing systems; in a general form, this principle was
formulated in [1, 2], and developed then in [3, 4]. The essence of the principle
consists in employing periodic electrodynamic systems with nonuniformly spaced
electron-field interaction gaps and a specified relation between the gap spacing and
the gap-field phase, which makes it possible to select one spatial harmonic or mode
and suppress the others.
The considered technique of selection in slowing systems is similar to the method
of suppressing the sidelobe maxima of nonuniform antenna arrays. Such
nonuniform systems may be considered as cryptoperi-odic or pseudoperiodic,
wherein the amplitudes of one or several harmonics remain the same as in the
initial periodic system, and the amplitudes of other spatial harmonics decrease. A
planar logarithmic spiral or the synchronous spirals considered in [2] represent
examples of pseudoperiodic systems. To some extent, one can assign to this class
two- or three-section systems with different spacing in the sections but with the
same phase velocity of one of the spatial harmonics in all the sections [5].
Generally, one can apply the considered principle of selection to slowing systems
of any type introducing the nonuniformity of both the spacing and the respective
phase shift over the spacing by varying the dimensions or configuration of the
system elements from one space to another (for instance, the dimensions of slots in
a comb-type structure, cross section of a helical waveguide, etc.). Here, we will
consider the influence of the distributions of spacings and the field phase over the
spacings on the amplitudes of spatial harmonics that determine the efficiency of
the electron-field interaction.
3. 1. AMPLITUDES OF SPATIAL HARMONICS AND THE
SYNCHRONISM CONDITION
To describe the electron-field interaction in pseudo-periodic systems, one can
use amplitudes of spatial harmonics and the interaction coefficients and coupling
impedance for the system as a whole or the local interaction coefficients for
individual gaps. Consider a general method of calculating these quantities.
Assume that it is given the longitudinal electric field distribution along the
system comprising Q spacings of different length , 1,2...qL q Q=
0
( ) ( )exp[ ( )]zE z E f z i zψ= (1)
Distribution of the real amplitude ( )f z and phase ( )zψ is determined by the
type of the system (uniform periodic or nonuniform).
Applying the Fourier transformation, we define the amplitudes ( )E h of spatial
harmonics by the relations
1
( ) ( )exp( )
2
zE z E h ihz dh
π
∞
−∞
= ∫
(2)
1
( ) ( )exp( )zE h E z ihz dz
l
∞
−∞
= −∫
In the general case, amplitudes ( )E h are continuous functions of the
wavenumber h and differ from the spectral density only by the factor 1/l, where
l is the length of the system. Let us represent them as a sum over the Q spacings of
the system:
1
1
( ) exp[ ( )]
Q
q q q q
q
E h U M i hz
l
ψ
=
= −∑ (3)
where ( )q qzψ ψ= is the average field phase at the qth spacing;
( )
/2
/2
1
( ) ( )exp ( )
q q
q q
z L
q q q
q q z L
M h f z z h z z dz
f d
ψ ψ
+
−
⎡ ⎤= − + −⎣ ⎦∫ (4)
is the local electron-field interaction coefficient;
/ 2
/ 2
1
( )
q q
q q
z L
q
q z L
f f z dz
d
+
−
= ∫
is the average value of the field amplitude at the qth spacing; 0
q q qU E f d= is the
rf voltage at the qth spacing; and q qz and d are the mean coordinate and
effective width of the qth gap. Note that for the gridless gaps, the choice of qd and
4. qf is to a certain extent arbitrary, because only their product is defined. Variation
of the voltage from one gap to another is determined, for the chosen form (1) of the
field representation, both by the distribution function ( )f z and losses in the
system. Formally, one may not separate these factors and take into account losses
from the very beginning using function ( )f z and assuming that ( )zψ is real.
This method is convenient in the presence of reflections in the system, when
( )zψ may be a complicated function. When calculating the interaction
coefficient (4), one may assume, as a rule, that within the qth gap, ( ) qzψ ψ≈ the
field is constant in the gap, ( ) qf z f= we obtain the familiar expression
sin /
2 2
q q
q
d d
M h h
⎛ ⎞
= ⎜ ⎟
⎝ ⎠
.
In the general case, the written relationships enable one to take into account the
distribution of the field amplitude and phase within one spacing. Usually, variation
of the field phase within a spacing can be ignored for slowing systems with
discrete electron-field interaction; then, the interaction coefficients are real and
positive, 0qM > . In this case, the maximal values of ( )E h can be obtained,
according to (3), for the wave-numbers mh h= that satisfy Q conditions:
2 ,m q qh z qmψ π= + 1,2....q Q= (5)
where the integer 0, 1...m = ± determines the number of the field spatial harmonic
with the maximal amplitude. Physically, conditions (5) mean the in-phase addition
of the electron radiation from individual gaps where interaction takes place when
electrons move synchronously with the mth spatial harmonic to the velocity
/e m mv v hω= = .
Introducing the field-phase shift 1q q qϕ ψ ψ+= − at the qth space and taking
into account that 1q q qL z z+= − , we can write the equivalent conditions of
synchronism for every spacing:
2 ,m q qh L mϕ π= + 1,2...q Q= (6)
The synchronism of electrons and field in nonuniform slowing systems is also
possible under more general conditions:
2 ,m q q qh L mϕ π= + 1,2...q Q= (7)
where 0, 1, 2...qm = ± ± varies from spacing to spacing, i.e., as if a particular qm th
synchronous spatial harmonic is taken at each spacing.
Taking into account the conditions of synchronism (5) and (6), one can rewrite
expression (3) for the ampli tudes of spatial harmonics:
5. ( ) ( ) ( )( )
1
1
exp
Q
q q m q
q
E h U M h i h h z
l =
= −∑ (8)
The amplitude of the selected mth harmonic that meets conditions (5) or (6) will
be maximal:
( ) ( )
1
1 Q
m q q m
q
E h U M h
l =
= ∑ (9)
In a periodic waveguide, ,q aL L ϕ ϕ≡ ≡ , and q qψ ϕ= ; therefore, conditions
(5) and (6) are met for an infinite series of spatial harmonics 'm m= when
( )' 2 ' /m mh h m m Lπ= + − , the difference in their amplitudes being determined
only by ( )q mM h .
In a nonuniform waveguide with different spacings qL , condition (2) can be
satisfied for one harmonic by choosing the appropriate phases qψ . For mh h≠ ,
this condition is either not satisfied or holds for the wave-number spectrum, which
is less dense than in a periodic waveguide. Thus, selection of spatial harmonics
takes place.
Such a mechanism can also be used for mode selection. Separating one spatial
harmonic of the operating mode, one can suppress other spatial harmonics of, not
only this mode, but of other modes as well.
2. THE COUPLING IMPEDANCE
AND INTERACTION COEFFICIENT
FOR PSEUDOPERIODIC SLOWING SYSTEMS
The relations derived above enable us to calculate the amplitudes of spatial
harmonics of a pseudoperi-odic slowing system. To analyze interaction of the elec-
tron beam with the field, it is also necessary to know the value of the parameter
characterizing the interaction efficiency. For a TWT, the coupling impedance of
the slowing system is usually chosen as such a parameter; however, in the case of
structures with pronounced non-uniformity and a small number of gaps (for
example, pseudoperiodic systems), it is expedient to apply also the interaction
coefficient which is similar to the quantity used in the theory of klystrons. Let us
determine these values according to the rules that are applied to the definition of
the known quantities.
According to (8), for a lossless structure ( qU U≡ ), we have
( ) ( )
UQ
E h M h
l
=
where
6. ( ) ( )( )
1
1
( ) exp
Q
q m q
q
M h M h i h h z
Q =
= −∑ (10)
Fig. 1. Section of the pseudoperiodic waveguide comprising Q spaces; q denotes the spacing
number.
is the electron-field interaction coefficient averaged over the total length of the
system that depends on the wavenumber h.
To determine the average coupling impedance ( )K h for a bilaterally matched
pseudoperiodic system with a limited length, one can use the relationship
( ) ( )
2 2
2 2
( )
2
E h M h
K h Z
h P ϕ
= = (11)
where 2
/2Z U P= is the gap characteristic impedance, and /hl Qϕ = is the
average phase shift per spacing.
The interaction coefficient considered here is generally a complex quantity;
however, when calculating the coupling impedance and investigating suppression
of spatial harmonics, only its modulus is of importance.
The obtained relationships allow us to calculate the efficiency of interaction of the
electrons with the field of spatial harmonics corresponding to different modes for
different wavenumbers and arbitrary number Q of the interaction gaps that have
different interaction coefficients qM , voltages qU , and arbitrary phase distribution
qΨ over the gaps. This method makes it possible to optimize pseudoperiodic
structures from the viewpoint of suppressing spurious modes and spatial
harmonics.
3. ANALYSIS OF THE SPATIAL HARMONIC SELECTION
Assuming, for the sake of simplicity, that all the gaps are equal, so that
( ) ( ), 1,2...q lM h M h q Q= = we obtain ( ) ( )q m l mM h M h= . We shall
7. characterize suppression of spatial harmonics with respect to the mth harmonic,
which satisfies conditions (5) and (6), by the quantity
1
( ) 1
exp( ( ) )
( )
Q
m q
qm
E h
i h h z
E h Q =
= −∑ (12)
Let us consider various cases.
Fig. 2. Distribution of spatial harmonics with respect to wavenumbers for a section of the
periodic system; / 0, 10L L QΔ = = .
Fig. 3. Suppression of spatial harmonics in a section of the pseudoperiodic system with linear
variation of the spacing for (a) / 0.1, 10L L QΔ = = and (b) / 0.05, 20L L QΔ = = .
8. Linear variation of the spacing, ( 1)qL L q L= + − Δ , where LΔ is the spacing
increment. In this case, we have
1
( 1)
2
q
q j
j
q q
z L qL L
=
−
= = + Δ∑
and expression (12) takes the form
( ) ( )
1
( ) 1
exp 1 1
( ) 2
Q
m
qm
E h L
i h h L q
E h Q L=
⎛ Δ ⎞⎡ ⎤
= − − + −⎜ ⎟⎢ ⎥⎣ ⎦⎝ ⎠
∑ (13)
which determines the ratio of this field to the synchronous field depending on the
difference of wavenumbers and the nonuniformity parameter /L LΔ .
Figure 2 shows this ratio for a section of the periodic waveguide with 10Q = and
LΔ = 0. In the periodic waveguide, the main maxima correspond to the spatial
harmonics, and their values are equal, because the interaction coefficients for all
gaps were assumed to be the same when formula (13) was derived. A finite width of
the lobes close to the main maxima and the presence of sidelobes are caused by the
finite length of the waveguide section under consideration.
In the pseudoperiodic waveguide, certain main maxima, i.e., spatial harmonics,
are suppressed, and the degree of suppression depends on the rate of the spacing
variation and number of gaps. As seen from Figs. 3a and 3b, the amplitudes of
spurious spatial harmonics can be reduced up to 0.4-0.5 of their value in the peri-
odic structure. As the number of spacings increases from 10 to 20, the efficiency of
suppression becomes more pronounced.
Abrupt variation of the spacing. A two-section system with one abrupt
variation of the spacing is the simplest version of a pseudoperiodic structure. In
this case, the section parameters are chosen so that the selected spatial harmonic
retains its value, and other harmonics are to a certain extent suppressed. Let the
first and second sections comprise, respectively, 1Q gaps with the spacing 1L and
2Q gaps with the spacing 2L . In this case, considering one mode in both sections,
we obtain from (12)
( )( )
( ) ( )
1
1
1
2
1 1 1
1 1
( ) 1
exp
( )
1
exp
Q
m
qm
Q
m
q Q
E h
i h h qL
E h Q
L
i h h Q q Q L
Q L
=
= +
= − − +
⎛ ⎞⎡ ⎤
+ − + −⎜ ⎟⎢ ⎥
⎣ ⎦⎝ ⎠
∑
∑
(14)
The diagrams in Figs. 4a and 4b show that even a two-section system enables one
to suppress some spatial harmonics.
9. 4. EXAMPLES OF PSEUDOPERIODIC SYSTEMS
In spiral slowing systems, the wave slowing factor essentially depends on the
pitch, radius of winding, and velocity of the wave propagation along the coiled line.
In [2], a family of planar pseudoperiodic spirals was considered; depending on the
law of winding, these spirals selected either the fundamental spatial harmonic m = 0
(logarithmic spiral) or higher harmonics m = ±1, ±2... (synchronous spirals). The
wave can travel along these systems without reflections due to continuous variation
of the pitch.
In other systems, an abrupt variation of the spacing (or of the pitch) can be
implemented in the simplest manner. In this case, the problem of matching separate
sections of the system arises, so that one has to choose their parameters not only in
order to obtain equal phase velocities of the operating spatial harmonic in the sec-
tions, but also to provide minimal reflections. Let us consider how this is done in
helical H- or П-waveguides, which were proposed in [6,7] for application in high-
power wide-band TWTs. In particular, it is demonstrated in these papers that there
exists a dense spectrum of spatial harmonics propagating in such waveguides, which
requires their selection. A cross-sectional view of a helical П-waveguide is shown
in Fig. 5. Consider the possibility of separating the fundamental harmonic using a
two-section waveguide. Electron beams interact with the waveguide field in the gaps
of a width d at a distance R from the axis. Therefore, radius R is the same in both
waveguide sections, and the pitch L, ridge width A, height B, and gap width d may
be varied. As a result of variation of the waveguide cross section, the phase velocity
( )v v xΦ Φ= of the wave traveling along the curvilinear waveguide axis x changes,
and the phase at the qth spacing is determined by the integral
0
( )
qx
q dx
v x
ω
Φ
Ψ = ∫
which is easily calculated for a sectional waveguide.
Choosing 2 1(0.7 0.8) ,L L= − , we obtain the coefficient of the harmonic
suppression for these values, which is presented in Figs. 4a and 4b.
In this case, the slowing factor of the fundamental wave in both sections must be
the same, i.e.,
2
01 02
0
2
, 1
кр
c R
v v
v L
π λ
λ
⎛ ⎞
= ≈ −⎜ ⎟⎜ ⎟
⎝ ⎠
where, for the cutoff wavelength, we have an approximate relationship
'/avB Al dλ π≈ .
Another condition consists in matching the charac teristic impedances of the
waveguide sections:
10. 1 2,Z Z=
( )
lim1,2
1,2 1,2
1,21 / c
Z
Z ξ
λ λ
=
−
where limZ is determined mainly by the ridge parameters (capacitance), and ξ
characterizes the effect of the bend and the transit channel.
Fig. 4. Suppression of spatial harmonics in a two-section pseudoperiodic system with an abrupt
variation of the spacing; 1 210, 5.Q Q Q= = = , 2 1/ 0.8L L = (a) and 2 1/ 0.7L L = (b).
Fig. 5. Helical П-waveguide.
The two conditions written above can be satisfied by changing the ridge width A
and height В together with pitch L and gap width d. Thus, one can match the char-
acteristic impedances of separate waveguide sections and, at the same time,
11. suppress spurious harmonics and preserve the amplitude of the fundamental
harmonic.
CONCLUSION
The possibility of selecting spatial harmonics and modes in pseudoperiodic
systems has been studied. The method of selection is based on the coordinated
variation of the spacing (pitch) and phase distribution along the system, which
provides the constant phase velocity of one spatial harmonic and destroys other
spatial harmonics. The efficiency of suppressing spurious spatial harmonics and
modes is evaluated. Using a sectional helical П-waveguide as an example, we have
shown that it is possible to match simultaneously the phase velocity of the
operating spatial harmonic and characteristic impedances of the sections.
In order to apply the developed principle of selection of spatial harmonics and
modes in slowing systems of various types (helical and resonator systems) in the
general case, it is necessary to study and select discontinuities and their distribution
in the system that would provide simultaneously the efficient electron-beam
interaction and mode selection, as well as obtaining the filtering properties which
govern the matching with external circuits.
ACKNOWLEDGMENTS
The work was supported by the Russian Foundation for Basic Research, project no.
97-02-16577.
REFERENCES
1. Solntsev, V. A., Proc. SPIE Int. Soc. Opt. Eng., 1994, vol. 2250, p. 399.
2. Solntsev, V. A., Radiotekh. Elektron. (Moscow), 1994, vol. 39, no. 4, p. 552.
3. Solntsev, V. A., Abstracts of Papers, 50 nauchnaya sessiya, posvyashchennaya
dnyu radio (50th Scientific Session Devoted to the Day of Radio), Moscow,
1995, part II, p. 136.
4. Solntsev, V. A. and Solntseva, K. P., Abstracts of Papers, Black Sea Region
Symposium on Applied Electromagne-tism, Athens, 1996, p. 13.
5. Silin, R. A., Elektron. Tekh., Sen 1: Elektronika SVCh, 1976,no. 11, p. 3.
6. Mukhin, S. V. and Solntsev, V. A., Izv. Vyssh. Uchebn. Zaved., Radioelektron.,
1990, vol. 33, no. 10, p. 35.
7. Amirov, V. A., Kalinin, Yu. A., Kolobaeva, Т.Е., et al., in Lektsii po SVCh-
elektronike i radiofizike (Lectures on Microwave Electronics and Radio
Physics), Saratov, 1996, Book 1, part II, p. 157.