Nonlinear Dynamics of Radiation in Multiple-Beam Vacuum Electronic Devices

Provided a review of physical processes underlying the functioning of vacuum electronic devices, namely, nonlinear processes of radiation of high-current beams of charged particles during their passage through spatially periodic structures (resonators) and their interaction with an electromagnetic field. Principles of functioning of travelling wave tubes, backward wave tubes, multi-wave Cherenkov generators, free electron lasers and free electron masers, volume free electron lasers are considered. These devices operate in a wide spectrum range from microwave to X-ray, have high efficiency, and allow obtaining high radiation powers in narrow spectral ranges. Increase the performance and reliability of electronic vacuum devices is based on improving the complex electromagnetic structures in resonators. The article demonstrates a variety of such devices with an obvious generality of physical principles used in them. Nonlinear chaotic dynamics of their functioning is considered. Particular attention is paid to consideration of principles of operation of volume free electron lasers as well as their difference from other devices.

Nonlinear phenomena originating in volume free electron laser (VFEL) are investigated by methods of mathematical modelling using computer code VOLC. It was demonstrated the possibility of excitation of quasiperiodic oscillations not far from threshold values of electron beam current density and VFEL resonator length. It was investigated sensibility of numerical solution to initial conditions for different VFEL regimes of operation. Parametric maps with respect to electron beam current and detuning from synchronism condition present complicated root to chaos with windows of periodicity in VFEL. Investigation of chaotic lasing dynamics in VFEL is important in the light of experimental development of VFEL in Research Institute for Nuclear Problems.

This contribution is devoted to investigation of multiwave Volume Free Electron Laser (VFEL) by methods of mathematical modelling. Special emphasis is placed on consideration of three‐wave VFEL. Mathematical modelling carried out confirmed some preliminary physical estimates. Computer code VOLC for simulation of different schemes of two‐ and three‐wave VFEL is described. Key words: free electron laser, quasi‐Cherenkov instability, simulation, nonlinear integro‐differential system.

Compact, coherent, high power, THz sources of frequency varying from 0.1THz to 5THz are required for their numerous applications in Spectroscopy, Imaging, Radar, etc. There are need for both CW and pulsed THz sources of broad bandwidth and wide tuning range. Different types of THz sources based on optical device, solid state device and vacuum electronic device (VED) are compared. VED is selected for further investigation because of its high power, high efficiency and low cost. Among VEDs, backward wave oscillator (BWO) is the most preferred THz source because of its compact size, simplicity and wide tuning range. Simplified analytical approach is presented for designing slow-wave-structure (SWS) for a THz BWO. Designs for two BWOs of 0.22THz, 100W output power, and of 1.2THz, 1W output power are presented. Planar RF structure is selected for BWO because it is easier to fabricate by MEMS technology with high precision and surface finish.

When the working frequency of vacuum electronic device reaches the terahertz frequency, the ohmic loss has a significant impact on the vacuum electronic device. To study the effect of the ohmic loss on the working characteristic of the vacuum electronic terahertz devices, this paper implements the frequency-dependent surface impedance boundary condition (SIBC) in the 3 dimensional particle in cell code UNIPIC-3D. Conformal mesh is adopted in the code to overcome the staircase error in traditional particle in cell method. By using the surface impedance boundary, we eliminate the need to study the field inside the lossy dielectric objects which require extremely small grid cells for numerical stability. In comparison with constant parameter SIBC, the dispersive SIBC is applicable over a very large frequency bandwidth and over a large range of conductivities. The correctness of the implementation is verified by simulating the lossy resonant cavity and circular waveguide, the simulated power loss is comparable with the theoretical predication. High power vacuum electronic devices of terahertz regime are attracting extensive interests due to their potential applications in science and technologies. The impulse-wave relativistic surface wave oscillator (SWO) and low-voltage continuous-wave planar grating backward wave oscillator (BWO) both made of copper are numerically studied by using UNIPIC-3D and dispersive surface impedance boundary condition. Numerical results show that the strongest field is very close to the slow wave structure where the beam-wave interaction occurs and that terahertz wave generates both in these two devices. The distributed wall loss has a considerable effect on the devices: the output power has a significant decrease and the startup time becomes longer, but the working frequencies of the two devices keep unchanged. To improve the efficiency of relativistic SWO, a resonant reflector is proposed between the diode and the slow wave structure. Numerical results show that the working frequency of the device with a resonant reflector keeps unchanged as the original one, but the output power increases to 60 MW from 41 MW of the original one when the ohmic loss is considered.

The primary energy exchange in a relativistic backward wave oscillator (BWO) occurs between the electron beam and the backward travelling wave within the slow wave structure (SWS). In most high power BWOs the backward travelling wave is reflected by a cutoff neck at the entrance of the SWS and radiation is extracted in the direction of the electron beam. Recently, researchers have investigated the effect of the forward travelling wave on the energy exchange between the electron bunches and the backward wave and the effect of multiple end reflections and cavity effects on the efficiency of microwave generation. This poster paper presents detailed measurements of the interaction of the electron beam with the forward travelling wave, and the effect of end reflections on the radiation frequency and efficiency. Numerical simulation results are found to be in agreement with the experimental measurements. A Sinus 6 relativistic electron beam accelerator is used for a detailed mapping of BWO performance as a function of input parameters. For uniform amplitude SWSs of various lengths the BWO output power, rf frequency and conversion efficiency were measured as a function of beam current and cathode voltage In addition, BWO performance was characterized as a function of phase of reflections at both ends of the SWS.

I. Plasma Oscillations and Radio Noise from the Disturbed Sun. Many investigators have suggested that plasma oscillations in the solar corona may be the source of large bursts of radio noise in the meter wavelength region. Two aspects of this problem are considered in this report: (a) the excitation of plasma oscillations by directed beams of charged particles, and (b) the conversion of energy in the longitudinal plasma oscillations to transverse electromagnetic waves by means of random inhomogeneities in electron density. It appears unlikely that charged particles whose velocity is much less than the r.m.s. thermal velocity of the coronal electrons will excite plasma oscillations. Charged particles whose velocity is much greater than the r.m.s. thermal velocity excite oscillations in a band of frequencies, including frequencies above the local plasma frequency. However, qualitative arguments indicate that the noise should be concentrated in a narrow band of frequencies slightly below the local plasma frequency. Thus it is impossible to explain the Type II (slow) bursts in the manner assumed and unlikely that the Type III (fast) bursts are explainable in this manner. The transfer of energy is studied in detail and it is shown that only waves whose phase velocity is less than the directed beam of charged particles receive energy from the beam. It is shown that plasma oscillations radiate a small fraction of their energy if the electron density is not uniform. In particular, random fluctuations in density, of the amount expected in thermal equilibrium, cause about 10[superscript -5] of the plasma-oscillation energy to be radiated; the remainder is dissipated by short-range collisions. Larger fluctuations than this are likely, and hence more energy should be radiated. II. A Field Analysis of the M Type Backward Wave Oscillator. A field theory of electron beams focused by crossed electric and magnetic fields is given. The theory is basic to the understanding of the small signal behavior of crossed field electron devices. It is applied to explain the slipping stream, or diocotron, effect as a coupling of two surface waves of the electron beam, and to derive the start oscillation conditions of the M-type backward wave oscillator. It is found that the slipping stream effect can reduce the starting current by an appreciable factor. The results are compared with the thin beam theory which neglects space charge effects. An analysis of a loaded strip transmission line is given, from which a method of representing space harmonic slow wave circuits by a surface admittance boundary condition is obtained. Forward and backward space harmonic interaction may be treated equally well.

Electron Beams and Microwave Vacuum Electronics

The feasibility of generation of powerful x-ray radiation by a cascade free-electron laser (FEL) with amplification of higher harmonics using a two-frequency undulator is studied. To analyze the FEL operation, a complex phenomenological single-pass FEL model is developed and used. It describes linear and nonlinear generation of harmonics in the FEL with seed laser that takes into account initial electron beam noise and describes all main losses of each harmonic in each FEL cascade. The model is also calibrated against and approved by the experimental FEL data and available results of three-dimensional numerical simulation. The electron beam in the undulator is assumed to be matched and focused, and the dynamics of power in the singlepass FEL with cascade harmonic multipliers is investigated to obtain x-ray laser radiation in the FEL having the shortest length, beam energy, and frequency of the seed laser as low as possible. In this context, the advantages of the two-frequency undulator used for generation of harmonics are demonstrated. The evolution of harmonics in a multicascade FEL with multiplication of harmonics is investigated. The operation of the cascade FEL at the wavelength λ = 1.14 nm, generating ~30 MW already on 38 m with the seed laser operating at a wavelength of 11.43 nm corresponding to the maximal reflectivity of the multilayered mirror MoRu/Be coating is investigated. In addition, the operation of the multicascade FEL with accessible seed UVlaser operating at a wavelength of 157 nm (F2 excimer UV-laser) and electron beam with energy of ~0.5 GeV is investigated. X-ray radiation simulated in it at the wavelength λ ~ 3.9 nm reaches power of ~50 MW already at ~27 m, which is by two orders of magnitude shorter than 3.4 km of the x-ray FEL recently put into operation in Europe.

In this work, we propose a simple method for generating Bessel vortex beams in the subterahertz (subTHz) range with the orbital angular momentum with l = 1 based on reflecting metal diffractive optical elements with a continuous helical microrelief. The elements are fabricated by micromilling in a polished duralumin substrate and by tin casting, and tested using a backward wave oscillator (wavelength λ = 855 µm). When using the micromilled element, Bessel vortex beams are shown to be generated and retain a Bessel intensity profile at a distance of 20–50 mm from the reflecting element, which is in good agreement with the results of numerical simulation. An experimental estimate of the energy efficiency of this element is 63%. When using elements made by tin casting, the vortex beams are generated with a distorted profile due to the presence of residual deformations of tin, which has plasticity. Due to their high conductivity, metallic reflecting elements can be used with high power density sub-THz radiation sources such as free electron lasers and gyrotrons.

In this paper, we first introduce the high power vacuum electron devices (VEDs) such as magnetron, klystron, backward wave oscillator, traveling-wave tube, and gyrotron which can be used in the biomedical areas. And then we present the significant progress in the emerging metamaterial-inspired VEDs in our group in details and briefly address the future applications to the biomedical fields. Finally, in order to further improve the armarium's performance, we report the recent advances in the high power terahertz sources developed from the conventional VEDs and novel metamaterial VEDs.

Volume free electron lasers

To increase the output power of compact low-voltage subterahertz-range vacuum electron devices (VEDs) to hundreds of watts and overcome the difficulties of the fabrication and assembly, a novel low-voltage subterahertz-range radial backward wave oscillator (BWO), in which the electron beam emits radially inward and interacts with the slow wave structures (SWSs) machined on a planar plate, is presented in this paper. Compared to the VEDs where the axial electron beam or planar sheet electron beam is adopted, the dispersion curve of the proposed radial BWO is independent of the radius and azimuthal coordinate. Hence, the power capacity is increased by using the overmoded SWSs, and the azimuthal asymmetrical modes cannot be excited.

An electron beam is commonly used for generating and amplifying coherent electromagnetic waves over the wide-frequency spectrum of microwaves through to ultraviolet rays. Many kinds of electron beam devices, including the klystron, traveling wave tube (TWT), and backward wave oscillator (BWO), have been developed [1]. These beam devices have several advantages over semiconductor devices, such as a wide frequency tuning range and higher output power. These beam devices are mostly microwave or millimeter wave amplifiers or oscillators. Only free electron lasers (FEL) can oscillate in the visible region [2]. However, FELs use an electron accelerator as a beam source, so their applications are strongly limited. For general use, a new compact beam device similar to the semiconductor laser, is required.

Electromagnetic response properties of carbon nanotubes (CNTs) are discussed. A basic approach to the problem is proposed synthesizing present‐day solid‐state physics and classical electrodynamics of nonhomogeneous mediums.[1] The developed theoretical model predicts the property of CNTs to be a strong slowing‐down system for surface waves[1,2] and allows proposing the physical schemes of the carbon nanotube use as monomolecular optoelectronic devices, such as a surface wave waveguide in IR frequency range, a monomolecular optical nanoantenna, a nanoantenna excitation device based on the Purcell effect, etc. A particular emphasis is given to the stimulated emission of electromagnetic waves by electron beam in nanotube. The significant retardation of the surface wave along with the ballistic character of the electron motion in nanotubes are shown[3] to be underlying the idea of the monomolecular light emitter with the Cherenkov lasing mechanism: the electrons in nanotube imposed to a realistic voltage can be accelerated to the velocities synchronous with the phase velocity of the surface wave. Since the achievable current density in nanotubes exceeds drastically corresponding characteristic values in vacuum electronic devices, the stimulated emission in CNTs is started at a very small, of the order of several microns, length of electron‐photon interaction. A dispersion equation for the electron beam instability in a nanotube is presented and analyzed. The potential of carbon nanotube as traveling wave tube (TWT) and backward wave oscillator (BWO) is demonstrated.