Three-wave Theory Research Articles

Modification of Pierce’s Classical Theory of Traveling-Wave Tubes

For a realistic case of an electron beam interacting with the electromagnetic fields supported by a thin perfectly conducting tape helix, we derive the exact dispersion relation, from which an unambiguous determination of Pierce's space-charge parameter Q is made. In the process of doing so, we discover that the circuit mode in the equivalent three-wave theory of Pierce must be modified at high beam current, an aspect not included in Pierce's original analysis. We quantify this circuit mode modification by a new parameter that we call q, introduced here for the first time in traveling-wave tube theory. In a realistic example, we find that the effect of q is equivalent to a modification of the circuit phase velocity by as much as two percent, which is a significant effect equivalent-to a detune of two percent.

ЦИФРОВІ ТЕХНОЛОГІЇ В НАВЧАННІ СТУДЕНТІВ МЕДИКІВ

There is bountiful evidence of the urgency of introducing modern approaches to higher medical education, especially digitalization and Web 2.0. This review presents the possibilities of using educational techniques such as information technology and the integration of Internet resources in medical education, in particular teaching the pre-clinical subject of “Physiology”. The Taekke and Paulsen (2017) “three-wave theory” of using digital technology and media in medical education which initially contributed to the reduction of students’ attention, was but, once accepted, became a source of motivation and information for creating a local learning environment which is connected to the world educational room. The advantages of using digital training platforms and resources for the qualification of a doctor (master degree) and for future medical career development are described. The experience of the Physiology Department of the Lviv National Medical University in introducing digital technology and media to encourage medical students to study the “Physiology” course (“Student Mediateka” via iCloud) both in Ukrainian and English are presented here. The teaching material is in line with international subject benchmarks in physiology. The experience of the education of the faculty in utilizing social media, the collaboration with other education institutions and utilization of online resources (such as edX, MedEdPORTAL, and the Physiology Education Community of Practice [PECOP]) are discussed.

Analytic Exploration of the Accuracy of Pierce’s Three-Wave Beam-Wave Interaction Theory of Traveling-Wave Tubes

As it is well known that the simplified classical Pierce's three-wave theory can provide scaling insights into traveling-wave tube (TWT) operation for its close-form solutions, and thus becomes a useful guide for TWT design. However, the classical Pierce's three-wave theory shows poor agreement with Lagrangian theory, so determining how to achieve a more accurately Pierce's three-wave theory from Pierce's four-wave theory becomes an open problem. In this paper, a more accurately revised Pierce's three-wave dispersion relation is deduced by using an approximate treatment on the nonlinear term of the dispersion relation of Pierce's four-wave beam-wave interaction theory. Meanwhile, the boundary conditions of classical Pierce's three-wave theory are revised by theoretical analysis. Thus, the revised Pierce's three-wave theory is established. The Pierce small-signal theories are compared to each other and Lagrangian theory on a set of TWT parameters which are based on a single pitch section of C- and Ku- bands TWTs. It is found that the revised Pierce's three-wave theory agrees extremely well with Lagrangian theory and gains more accuracy than the classical Pierce's three-wave theory in the small-signal beam-wave interaction region. Finally, the phase difference between Pierce's four-wave theory and revised Pierce's three-wave theory is discussed.

Theoretical and numerical study on detonation wave Mach reflection in high explosive charge with waveshaper

On the basis of the three-wave theory and Whitham's method, the flow fields associated with regular reflection and Mach reflection in high explosives with waveshapers were investigated, and the relevant theoretical model for deriving the detonation configuration was proposed. The calculated results of pressure, flow velocity and triple point growth angle of Mach stem were presented and the Mach stem height was also determined based on the modified Whitham's method. The finite element code was used to numerically simulate the detonation processes of the high explosives with waveshapers. The shock initiation of the cylindrical charge was described by the Jones-Wilkins-Lee(JWL) and Lee-Travel models. The calculated results show that the Mach stem height increases with the propagation of detonation wave. The numerical results are consistent with the predictions based on the presented model, which shows that the analytical model provides reasonably accurate predictions of the Mach reflection process.

Nonlinear Trivelpiece-Gould waves: Frequency, functional form, and stability

This paper considers the frequency, spatial form, and stability of nonlinear Trivelpiece-Gould (TG) waves on a cylindrical plasma column of length L and radius rp, treating both traveling waves and standing waves, and focussing on the regime of experimental interest in which L/rp≫1. In this regime, TG waves are weakly dispersive, allowing strong mode-coupling between Fourier harmonics. The mode coupling implies that linear theory for such waves is a poor approximation even at fairly small amplitude, and nonlinear theories that include a small number of harmonics, such as three-wave parametric resonance theory, also fail to fully capture the stability properties of the system. It is found that nonlinear standing waves suffer jumps in their functional form as their amplitude is varied continuously. The jumps are caused by nonlinear resonances between the standing wave and nearly linear waves whose frequencies and wave numbers are harmonics of the standing wave. Also, the standing waves are found to be unstable to a multi-wave version of three-wave parametric resonance, with an amplitude required for instability onset that is much larger than expected from three wave theory. It is found that traveling waves are linearly stable for all amplitudes that could be studied, in contradiction to three-wave theory.

Simulation analysis of rectangular dielectric-loaded traveling wave amplifiers for THz sources

Nonlinear simulation results for a 220-GHz rectangular dielectric-loaded traveling-wave amplifier are presented. Simulations are used to check a linear theory that is developed by phenomenological introduction of an effective dielectric parameter for electron beam channel, and it is found that the rf power gains from Pierce three-wave theory and particle simulations are in reasonable agreement. It is shown that the rf power gain during initial beam-wave interaction is positive; the falling on the initial rf power profile, which has been thought to be the rf power transferred to the beam for bunching buildup (negative gain effect), is probably resulting from numerical errors. Beam-wave interaction mechanism is analyzed by examining the evolution of beam bunching centers. Influences of various parameters on amplifier performance are examined, and transverse space-charge effect is analyzed. A symmetric excitation scheme for rf couplers is proposed, and rf field jumps on the common intersection line of vacuum, dielectric, and metal wall, which were found in rf simulations, are explained theoretically.

Generation of circularly polarized radio waves within magnetic holes of the solar wind

The possibility of nonlinear interaction between Langmuir waves and ion–acoustic waves in the solar wind has received considerable interest in the last years. However, little attention has been paid to the possibility of nonlinear coupling between Langmuir waves and whistler waves in the interplanetary medium. Close temporal correlation between high-frequency Langmuir waves and low-frequency electromagnetic whistler waves has been observed recently within magnetic holes of the solar wind. In order to account for these observations within magnetic holes of the solar wind, we develop a nonlinear three-wave theory describing the parametric interaction of Langmuir waves, electromagnetic whistler waves with either right- or left-hand circularly polarized electromagnetic waves. We suggest that the nonlinear coupling of Langmuir waves and whistler waves may lead to the formation of modulated Langmuir wave packets as well as the generation of circularly polarized radio waves at the plasma frequency in the solar wind.

Behavior of traveling-wave tubes near circuit cutoff

A theory is developed which explains the operation of a traveling-wave tube when operated near the cutoff frequency of the slow-wave circuit, including the effect of two circuit waves instead of the usual one. The theory is normalized in a manner analogous to that used in more conventional analyses and a first-order expansion about the cutoff frequency is used, making a relatively small number of curves applicable to a large number of cases. The relationship between this theory and the three-wave theory usually used in traveling-wave-tube analysis is shown, and they are in agreement when the system is operated far from the cutoff frequency. Numerical results are given for a range of parameters which might be useful in traveling-wave-tube design, and an excellent agreement with published experimental results is shown.