Electron Velocity Spread Research Articles

Effect of Electron Beam Properties on a Second Harmonic Gyrotron

In harmonic gyrotrons, the narrow operating region of the harmonic mode is significantly restricted by the severe mode competition from the fundamental parasitic modes, which makes it important to study the nonlinear effects of beam-wave interaction in the case of a nonideal electron beam. In this article, the effect of the electron velocity spread and the beam radius spread on the mode excitation, interaction efficiency as well as mode competition are analyzed for the desired harmonic mode and the parasitic fundamental mode operating far from the cut-off frequency. The effect of velocity spread is interpreted via the electron cyclotron resonance condition as well as the electron beam susceptibility with respect to the resonator field. The results show that the velocity spread can greatly broaden the effective operating region of the harmonic mode and the efficiency degradation can be contained at a reasonable level by proper design consideration of the interaction circuit. Whereas, the beam radius spread is the main factor that accounts for the efficiency degradation and can aggregate the mode competition. The results are referential to the design and analysis of harmonic gyrotrons as well as continuously frequency tunable gyrotrons.

Formation of Sheet Helical Electron Beams for High-Power Planar Gyrotrons

Planar magnetron-injection gun forming a powerful (3 MW) sheet helical electron beam (HEB) for 140 GHz gyrotron was designed. Modified scheme of an electron beam analyzer based on the retarding electric field method was developed to measure the electron beam characteristics, including pitch-factor and velocity spread. Experimental results are in good agreement with theoretical predictions and demonstrate feasibility of formation of a wide (20 mm) sheet HEB with an energy of 100 keV, a current of 30 A and a pitch-factor of above 1.2 – 1.3.

Electron Gun for the Hollow Beam of a High Power W-Band Extended Interaction Klystron

Results are presented from a theoretical study on optimizing the parameters of an electron gun of a powerful multicavity extended interaction klystron at a frequency of 95 GHz, ensuring the formation of a dense annular electron beam and its transport through interaction region with a current transmission coefficient of 99%, with taking into account of the thermal spread of electron velocities at the cathode.

On the Influence of the Electron Velocity Spread on the Passband Properties of Gyroklystrons

We present the results of studying the passband properties of gyroklystrons theoretically and experimentally and analyze the main causes of limitations in the bandwidth of the frequencies that they amplify. It is shown that in the range of low beam currents, where the electron velocity spread is rather low, the amplification bandwidth of a two-cavity gyroklystron is close to the bandwidth of the output cavity loaded with an electron beam. In the range of high currents, the amplification bandwidth depends only weakly on the parameters of the output cavity and is determined mainly by the spread in the times of electron passing through the drift space, which is caused by the difference in their translational velocities. Good qualitative agreement of the calculated and experimental dependences indicates that the proposed method can be applied to the calculation and interpretation of frequency characteristics of gyroklystrons. The possibility to expand the passband of operating frequencies in the high-current region by decreasing the influence of the electron velocity spread on beam bunching in the three-cavity gyroklystron operating in the maximum acceleration regime is demonstrated experimentally. Theoretically, the developed method for calculation of frequency characteristics can be expanded to the case of a three-cavity gyroamplifier with slight modifications.

Development of Third-Harmonic 1.2-THz Gyrotron With Intentionally Increased Velocity Spread of Electrons

We develop the concept of a continuous wave (CW) 1.185 THz (wavelength about 250- $\mu \text{m}$ ) gyrotron with an output power of several watts, intended for dynamic nuclear polarization (DNP)/nuclear magnetic resonance (NMR) spectroscopy applications. For a 15-T magnetic field provided by a commercially available cryomagnet, the required frequency can be achieved by operating at the third cyclotron harmonic. Under conditions of extreme density of the mode spectrum, we propose using interaction with an electron beam intentionally formed with a high (up to 40%) velocity spread as a selection mechanism. This ensures suppression of the most dangerous parasitic traveling modes at the first and the second cyclotron harmonics, which are very sensitive to the spread. The main parameters of the gyrotron are determined both using the start currents analysis and within the framework of a nonstationary self-consistent model. Experimental feasibility of the single-mode third-harmonic generation under conditions of mode competition is verified based on 3-D particle-in-cell (PIC) simulations.

Zones of soft and hard self-excitation in gyrotrons: Generalized approach

It is known that the gyrotron theory is developed in a general form that allows one to draw many important conclusions about gyrotron operation, which are valid for gyrotrons operating in arbitrary modes, at arbitrary frequencies, and driven by electron beams with different voltages and currents. One of important issues in this theory is the analysis of possible start-up scenarios, i.e., the methods allowing, first, to excite the desired mode prior to competitors in the region of soft self-excitation of this mode and, then, drive it into the zone of hard self-excitation where, as a rule, the operation with high efficiency is possible. So far, in all studies, these zones of soft and hard self-excitation were defined for specific voltages. In the present paper, it is shown how one can determine these zones in a more general manner that makes the results applicable to gyrotrons operating at arbitrary voltages. The study also includes consideration of the no-start-current zones and the role of electron velocity spread.

Analysis and Optimization of the Characteristics of Superpower Virtode Generation

We report on the results of the 3D numerical simulation of perspective design of an oscillator based on an external-feedback virtual cathode (virtode), as well as optimization of characteristics of its generation. We have analyzed the effect of beam parameters on the virtode output characteristics. In particular, we have obtained the dependence of the efficiency on the feeding voltage and on the current being injected. We have studied the effect of beam velocity premodulation and electron velocity spread on virtode generation characteristics. It has been established that the introduction of premodulation sharply increases the generation efficiency up to 13% for optimal parameters. The possibility of stable generation in the virtode at relatively large spread in electron velocities has been demonstrated.

Исследование и оптимизация характеристик генерации сверхмощного виртода

AbstractWe report on the results of the 3D numerical simulation of perspective design of an oscillator based on an external-feedback virtual cathode (virtode), as well as optimization of characteristics of its generation. We have analyzed the effect of beam parameters on the virtode output characteristics. In particular, we have obtained the dependence of the efficiency on the feeding voltage and on the current being injected. We have studied the effect of beam velocity premodulation and electron velocity spread on virtode generation characteristics. It has been established that the introduction of premodulation sharply increases the generation efficiency up to 13% for optimal parameters. The possibility of stable generation in the virtode at relatively large spread in electron velocities has been demonstrated.

Double Plasma Resonance at Ion Cyclotron Harmonics in the Jovian Magnetosphere

AbstractThe ion cyclotron waves instability near the frequencies of ionic cyclotron harmonics is studied under conditions typical for the Jovian kilometer radio emission source. This instability is caused by the presence of the ions with a nonequilibrium loss cone‐type distribution function in the source. Expressions for the growth rate of the ion cyclotron wave's instability are obtained, and it is shown that the amplification of these waves significantly increases when the frequency of the lower‐hybrid resonance coincides with one of the ion cyclotron harmonics. Possible mechanisms for conversion of the ion cyclotron waves excited in the Jovian kilometer radio emission source into electromagnetic radiation are discussed. It is shown that the conversion of ion cyclotron waves, due to their coalescence with high‐frequency plasma waves, is possible only into ordinary electromagnetic waves, while the process capable of providing conversion of ion cyclotron waves into fast extraordinary electromagnetic waves is scattering by suprathermal electron fluxes. In the latter, despite the thermal spread of electron velocities, the radiation that leaves the source region is concentrated in a narrow frequency range Δω ≪ ω near the local gyrofrequency ω≃ωBe, and the polarization of this radiation corresponds to the extraordinary wave. The estimates of the electron energy, which is necessary for such conversion, have shown the possibility of the process realizing under conditions characteristic for the Jovian kilometer radio emission source.

Investigation of tunable gyrotron on a cone-shaped waveguide

The results of calculations of a nonlinear model of a tunable frequency gyrotron on a cone-shaped waveguide and the main wave TE01 are presented. It is shown that the adjustment range can reach 2.8 %. To extend this band, it is necessary to lengthen the cone-shaped part of the waveguide without changing the angle of increase in the radius of the waveguide.The wave efficiency of a waveguide expanding along the axis is 21 % at a working frequency of 10 GHz. To achieve these parameters, it is necessary to divide the gyrotron electromagnet into two parts – the main electromagnet and auxiliary one, which has a limited length and can move along the waveguide. The second magnet can be made in the form of a set of individual electromagnets of limited length the set of electromagnets must fill the entire length of the cone-shaped waveguide. The fulfillment of this condition will allow to move the resonant magnetostatic field along the waveguide by switching the current in the coils of this set of electromagnets, which will exclude the mechanical movement of the auxiliary electromagnet. At a frequency of 200 GHz, the wave efficiency is reduced to 15 %, while the ohmic losses in the walls of the waveguide are 3 % of the power of the electron beam.The dependence of the gyrotron efficiency on the initial angular spread of electron velocities was investigated. It was concluded that the initial angular spread of the electron velocities has very little effect on the efficiency of the tunable gyrotron.The wave efficiency of a waveguide narrowing in length can reach 29 % at a frequency of 200 GHz, ohmic losses in the walls of a copper waveguide amount to 4 % of the power of the electron beam. Calculations have shown that a lamp backward wave gyrotron with a waveguide narrowing along the axis is more efficient than the version of the gyrotron traveling wave tube. However, in both cases, the synchronous value of the magnetostatic field must be displaced along the axis, depending on the required operating frequency, otherwise there occurs either a rearrangement of the electron beam or a return of the energy to the high-frequency field by the electron beam.

Excitation of Surface Plasma Waves in Microwave Radiation Sources by Electron Beam with Allowance for Thermal Velocity Spread

Based on the hydrodynamic model, in the linear approximation, the problem of excitation by an electron beam of surface waves in electrodynamic systems of plasma relativistic microwave electronics has been considered with consideration of electron velocity spread. Complex instability increments have been determined for complex parameters of the beam-plasma system. Two instability regimes differing in the dynamics of beam plasma oscillations during instability development have been observed: Compton (singleparticle) and Raman (collective) instabilities. The role of thermal effects in an electron beam and its density in the formation of a particular mode of beam instability has been analyzed.

Simulation of Non-Uniform Electron Beams in the Gyrotron Electron-Optical System

New calculated data on the effect of emission inhomogeneities on the quality of the electron beam, which is formed in an electron-optical system of a gyrotron, have been obtained. The calculations were based on emission current density distributions, which were measured for the different cathodes in the gyrotron of Peter the Great St. Petersburg Polytechnic University. A satisfactory agreement between the experimental and calculated data on the influence of emission nonuniformities on the velocity spread of electrons has been shown. The necessity of considering the real distribution of the emission current density over the cathode surface to determine the main parameters of the electron beam—the velocity and energy spreads of the electrons, spatial structure of the beam, and coefficient of reflection of electrons from the magnetic mirror—has been demonstrated. The maximum level of emission inhomogeneities, which are permissible for effective work of gyrotrons, has been discussed.

The influences of beam quality and Ohmic loss on the beam-wave interaction in a 420 GHz second-harmonic complex-cavity gyrotron

Recently, a 0.42 THz second-harmonic gyrotron with complex cavity has been investigated and measured in the Terahertz Research Center. The experimental results show that the designed gyrotron can operate stably at the candidate mode TE−17.4 with the pulsed power of 19.3 kW, corresponding to an efficiency of 8.6%. However, the measured output power and efficiency are much lower than the theoretical values. In this paper, the influences of beam quality and Ohmic loss on the beam-wave interaction in the designed complex-cavity gyrotron are analyzed explicitly by a nonlinear, time-dependent, multi-mode code. The numerical simulations show that in the low-beam-voltage region, the calculated powers perfectly fit with the experimental results when the electron beam width is 0.195 mm, the electron velocity spread is 6% and the Ohmic quality factor of TE−17.4 is about 75000. Meanwhile it is also found that competing modes are well suppressed although considering the beam quality and Ohmic loss, which reproduces the experimental observation of the high-power single-mode oscillation of the TE−17.4 mode as the design mode.

Efficiency enhancement of slow-wave electron-cyclotron maser by a second-order shaping of the magnetic field in the low-gain limit

Based on the anomalous Doppler effect, we put forward a proposal to enhance the conversion efficiency of the slow-wave electron cyclotron masers (ECM) under the resonance condition. Compared with previous studies, we add a second-order shaping term in the guild magnetic field. Theoretical analyses and numerical calculations show that it can enhance the conversion efficiency in the low-gain limit. The case of the initial velocity spread of electrons satisfying the Gaussian distribution is also analysed numerically.

On the influence of the electron-velocity spread in a beam on the mechanism of Cherenkov beam–plasma interaction

The instability of an electron beam in cold plasma is considered in the linear potential approximation with different velocity-distribution functions of beam electrons. It is demonstrated that the mechanism of beam instability in plasma changes as the electron-velocity spread is increased: the hydrodynamic single-particle instability mode evolves into the hydrodynamic collective mode or the single-particle kinetic one. Instability growth rates in different modes are determined analytically and numerically.

Influence of the electron velocity spread and the beam width on the efficiency and mode competition in the high-power pulsed gyrotron for 300 GHz band collective Thomson scattering diagnostics in the large helical device

We present results of a theoretical study of influence of the electron velocity spread and the radial width on the efficiency and mode competition in a 300-kW, 300-GHz gyrotron operating in the TE22,2 mode. This gyrotron was developed for application to collective Thomson scattering diagnostics in the large helical device and 300-kW level high power single TE22,2 mode oscillation has been demonstrated [Yamaguchi et al., J. Instrum. 10, c10002 (2015)]. Effects of a finite voltage rise time corresponding to the real power supply of this gyrotron are also considered. Simulations tracking eight competing modes show that the electron velocity spread and the finite beam width influence not only the efficiency of the gyrotron operation but also the mode competition scenario during the startup phase. A combination of the finite rise time with the electron velocity spread or the finite beam width affects the mode competition scenario. The simulation calculation reproduces the experimental observation of high power single mode oscillation of the TE22,2 mode as the design mode. This gives a theoretical basis of the experimentally obtained high power oscillation with the design mode in a real gyrotron and moreover shows a high power oscillation regime of the design mode.

Design and Modeling of a Slow-Wave 260 GHz Tripler

The extended-interaction klystron frequency multiplier with a hollow electron beam has been studied numerically as a source of subterahertz radiation with controlled phase. The designs of electrodynamic and electro-optical systems are discussed for the frequency tripler with an output frequency of 260 GHz. The simulations of electron-wave interaction take into account the electron velocity spread, beam interception by a slow-wave structure, and the space charge effects. According to simulations, a two-cavity frequency tripler fed by a 1 W input signal at 86.67 GHz can deliver a maximum output power of about 15 W at a frequency of 260 GHz with a 90 MHz bandwidth (FWHM). Such a device is aimed to pulsed methods of the dynamic nuclear polarization in nuclear magnetic resonance spectroscopy.

Effects of electron beam parameters and velocity spread on radio frequency output of a photonic band gap cavity gyrotron oscillator

In this paper, the effects of electron beam parameters and velocity spread on the RF behavior of a metallic photonic band gap (PBG) cavity gyrotron operating at 35 GHz with TE041–like mode have been theoretically demonstrated. PBG cavity is used here to achieve a single mode operation of the overmoded cavity. The nonlinear time-dependent multimode analysis has been used to observe the beam-wave interaction behavior of the PBG cavity gyrotron, and a commercially available PIC code “CST Particle Studio” has been reconfigured to obtain 3D simulation results in order to validate the analytical values. The output power for this typical PBG gyrotron has been obtained ∼108 kW with ∼15.5% efficiency in a well confined TE041–like mode, while all other competing modes have significantly low values of power output. The output power and efficiency of a gyrotron depend highly on the electron beam parameters and velocity spread. The influence of several electron beam parameters, e.g., beam voltage, beam current, beam velocity pitch factor, and DC magnetic field, on the PBG gyrotron operations has been investigated. This study would be helpful in optimising the electron beam parameters and estimating accurate RF output power of the high frequency PBG cavity based gyrotron oscillators.

Genetic Algorithm-Based Shape Optimization of Modulating Anode for Magnetron Injection Gun With Low Velocity Spread

The magnetron injection gun (MIG) is an important component in the gyro-traveling wave tube (gyro-TWT). The electron velocity spread induced to the mismatch of the electric and magnetic fields influences the performance of gyro-TWT. To improve electron beam quality, we designed a modulating anode with curved geometry. And the multi-objective genetic algorithm was employed to optimize the curved geometry. An electron beam with a velocity ratio of 1.05 and low transverse velocity spread of 0.31% in a MIG for a Q-band gyro-TWT is obtained. Compared with the previous design with a transverse velocity spread of 1.17%, the electron beam performance got improved. And the thermal analysis and parametric sensitivity were done. The curved MIG can stably provide an electron beam with a transverse spread lower than 0.8%.

Effect of ion compensation of the beam space charge on gyrotron operation

In gyrotrons, the coherent radiation of electromagnetic waves takes place when the cyclotron resonance condition between the wave frequency and the electron cyclotron frequency or its harmonic holds. The voltage depression caused by the beam space charge field changes the relativistic cyclotron frequency and, hence, can play an important role in the beam-wave interaction process. In long pulse and continuous-wave regimes, the beam space charge field can be partially compensated by the ions, which appear due to the beam impact ionization of neutral molecules of residual gases in the interaction space. In the present paper, the role of this ion compensation of the beam space charge on the interaction efficiency is analyzed. We also analyze the effect of the electron velocity spread on the limiting currents and discuss some effects restricting the ion-to-beam electron density ratio in the saturation stage. It is shown that the effect of the ion compensation on the voltage depression caused by the beam space charge field can cause significant changes in the efficiency of gyrotron operation and, in some cases, even result in the break of oscillations.