Effect Of 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.

Investigation of the Effect of Electron Beam Quality on a 0.68-THz Second Harmonic Gyrotron

The lack of high-power terahertz sources is a major impediment to the development of terahertz science and technology. The gyrotron has great potential to generate high-power terahertz radiation, and so attracts extensive attention. In order to alleviate the problems of limited power capacity and wall loading, the high-order modes are often chosen to be the operating modes. Due to the dense spectrum of the modes, it will cause intense mode competition, which is harmful for the stable operation of a gyrotron. Currently, a 0.68-THz second harmonic gyrotron is under development in the Terahertz Research Center of University of Electronic Science and Technology (UESTC). The experiment shows that the measured output power is 2.75 kW with the efficiency of 9.05%. In order to determine whether the operating mode is the desired mode TE−15,2, the calculation of the starting current should be more accurate. In this article, we generalize the existing linear theory for the starting current, considering the effects of beam thickness and velocity spread. The starting currents of the operating mode and its competing modes are calculated using our designed gyrotron. We find out that the velocity spread and the beam thickness have significant influence on the starting current. The calculations also show that the desired mode TE−15,2 can be triggered first at the operating point. Besides, the measured output power from the experiment is much lower than that of the simulation result. Therefore, the effects of the velocity spread and beam thickness on beam–wave interactions are also analyzed; our results show that the efficiency is sensitive to the beam quality.

Effect of Electron Beam Velocity Spread in a Clinotron

We have studied the effect of velocity spread in the electron beam cross section on the output power, frequency, and starting current in a clinotron. It was shown that in the case when the lower electron layers move faster than upper ones there is an increase in the output power compared to the single velocity beam case. In the opposite case of faster upper layers, the output power decreases drastically and both the starting current and probability of multifrequency oscillations increase.

Molecular dynamics simulations of wake structures behind a microparticle in a magnetized ion flow. II. Effects of velocity spread and ion collisions

The influence of velocity spread and ion-neutral collisions on the wake of a microparticle in a collisional magnetized ion flow is explored by means of molecular dynamics simulations. The ion flow is described in the constant-mean-free-path limit. A constant electric field is superimposed that maintains the ion drift at the Bohm speed and approximates conditions in the plasma sheath. The contribution of ion Landau damping to the wake structure is separated by simulations with a collisionless drift distribution. It is found that ion Landau damping and collisions have a counteracting effect on the ion density in the focus region. The dynamic shadows that are a typical feature of collisionless magnetized wakes with cold ion beams are damped by the velocity spread and vanish by a collision-enhanced ion density in the wake. Dynamic shadows reappear only at very high magnetic fields, B ≈ 10 T. In two-particle arrangements, the full collisional model shows that horizontal attractive forces persist up to B = 4 T but become repulsive for higher magnetization.

Theory of Linear and Nonlinear Gain in a Gyroamplifier using a Confocal Waveguide.

The linear and nonlinear theory of a gyroamplifier using a confocal waveguide is presented. A quasi-optical approach to describing the modes of a confocal waveguide is derived. Both the equations of motion and the mode excitation equation are derived in detail. The confocal waveguide circuit has the advantage of reducing mode competition but the lack of azimuthal symmetry presents challenges in calculating the gain. In the linear regime, the gain calculated using the exact form factor for the confocal waveguide agrees with an azimuthally averaged form factor. A beamlet code including velocity spread effects has been written to calculate the linear and nonlinear (saturated) gain. It has been successfully benchmarked against the MAGY code for azimuthally symmetric cases. For the confocal waveguide, the beamlet code shows that the saturated gain is reduced when compared with results obtained using an azimuthally averaged form factor. The beamlet code derived here extends the capabilities of nonlinear gyroamplifier theory to configurations that lack azimuthal symmetry.

The effect of velocity spread of pseudospark-sourced electron beam to Y-band extended interaction oscillator

Extended interaction oscillator (EIO) operation in the terahertz range puts greater demand on the current density and brightness of an electron beam. The pseudospark (PS)-sourced electron beam is a good candidate for driving such high frequency EIOs as it has a very high combined beam current density and brightness. However, the PS-sourced electron beam can have an inherent velocity spread unless some form of post acceleration is used. Before a new EIO device in the Y-band (220 GHz–325 GHz) based on a PS-sourced electron beam can be realized, it is first necessary to analyze the influence of the beam velocity spread on performance. This paper presents the numerical studies of the EIO performance with the inclusion of the beam velocity spread. It was found that the Y-band EIO circuit can operate in a relatively wide velocity spread range when a high beam current density is used. For an electron beam current density of 1 kA/cm2, the output power is not less than 0.9 times of the power obtained with an electron beam with no velocity spread when the velocity spread is within the range of 0%–15%. We also present our latest results that demonstrate the successful design and optimization of a Y-band EIO driven by a 36 kV, 255 mA (800 A/cm2) PS-sourced electron beam. A peak power over 1.67 kW at 283.7 GHz was achieved using an electron beam, which can be generated by PS discharge, with a velocity spread of 12.5%.

Dispersion relation and growth rate in a Cherenkov free electron laser: Finite axial magnetic field

A theoretical analysis is presented for dispersion relation and growth rate in a Cherenkov free electron laser with finite axial magnetic field. It is shown that the growth rate and the resonance frequency of Cherenkov free electron laser increase with increasing axial magnetic field for low axial magnetic fields, while for high axial magnetic fields, they go to a saturation value. The growth rate and resonance frequency saturation values are exactly the same as those for infinite axial magnetic field approximation. The effects of electron beam self-fields on growth rate are investigated, and it is shown that the growth rate decreases in the presence of self-fields. It is found that there is an optimum value for electron beam density and Lorentz relativistic factor at which the maximum growth rate can take place. Also, the effects of velocity spread of electron beam are studied and it is found that the growth rate decreases due to the electron velocity spread.

High resolution electron imaging system for sub-micron sized metastable atom beams produced by Stern–Gerlach interferometry

The method of modulating an atom beam profile by an immaterial magnetic mask generated in a Stern–Gerlach interferometer is recalled. A special magnetic configuration aimed at producing a single central bright interference fringe (atomic spot) was used. The effects of velocity spread, source coherence and source size on the limiting spot size at large values of the magnetic gradient are discussed. The observation of such small sizes requires a high spatial resolution of the position-sensitive detector. A new electron optical device is described, which images the secondary electron source generated by the impact of the atomic beam on a metallic electrode (detection in real time). Magnifications as high as 65 are accessible, leading to a better than 100 nm resolution of the atomic beam profile when a position-sensitive detector of a few µm resolution is used. Geometric and chromatic aberrations are discussed and, according to simulations, they do not significantly deteriorate the resolution.

Mode Competition and Self-Consistent Simulation of a Second Harmonic Gyrotron Oscillator

A nonlinear numerical simulation of a second harmonic gyrotron oscillator is presented in this paper. Mode competition from a competing fundamental mode is investigated. In addition, a self-consistent nonlinear theoretical model, including the effect of velocity spread, is applied to analyze the second harmonic gyrotron. A series of numerical calculations is carried out for different electron beam parameters. The results are compared with that of calculations using the cold-cavity, fixed field approximation and with experiments. Good agreement is found between our calculations and an experiment at Fukui University. The azimuthal polarization of the field and the choice of the electron beam radius are also discussed.

Stabilization of spatio-temporal dynamics of free-electron laser operation under effect of spread in electron velocity

The effect of velocity spread on the dynamics of the interaction of longitudinal modes is studied for a FEL-oscillator with broadband feedback. It is shown that the spread shortens the process of mode competition and increases the electron-current threshold of stable single-mode operation. In addition, the spread leads to a shift in the frequency of the excited mode to the range of the most efficient electron-wave interaction. This results in a very weak sensitivity of the efficiency to the spread.

An investigation of X-band gyrotwystron amplifiers

Experimental and theoretical studies of the cyclotron maser instability in the gyrotwystron configuration have been made. Several configurations of a three-stage TE/sub 01/ mode X-band gyrotwystron with variable buncher cavity lengths, drift lengths, and output sections, have been tested. An efficiency in excess of 27.5% and a full-width half-maximum (FWHM) bandwidth of 1.6% have been demonstrated for a 16-kV, 1-A electron beam. This bandwidth represents a substantial improvement of over the 1% bandwidth measured for a three-cavity gyroklystron cavity employing the same input and buncher cavities. Experimental results from three gyrotwystron configurations have been compared with predictions of theory and good agreement was obtained. The effect of velocity spread on efficiency and bandwidth was also studied. The favorable comparison of experimental and theoretical data indicates that the model is a useful tool in the design and analysis of gyrotwystron amplifiers.

Theory and simulation of an 85 GHz quasioptical gyroklystron experiment

The linear theory used to design a two-resonator 85 GHz quasioptical gyroklystron with a nonuniform magnetic field is presented. It is shown that a tapered magnetic field in the prebunching resonator has a relatively small effect on the electron bunching parameter. The effect of velocity spread of the electron beam can be minimized by adjusting the magnetic field strength in the two resonators. Measured amplifier performance is in good agreement with calculations from the nonlinear multimode simulation code. Gyrophase bunching of the electrons is preserved over the long drift region (30 radiation wavelengths) even though no attempt has been made to minimize the velocity spread of the beam.

Theory of relativistic gyro-traveling wave devices

Using a Hamiltonian formalism, nonlinear, fully relativistic, multimode, multifrequency equations are derived which describe gyro-traveling wave devices. Nonuniform waveguides and nonlinearly tapered magnetic fields are incorporated into the analysis. The formalism is used to analyze the effect of velocity spread on Doppler upshifted operation. It is shown that with present technology, gyro-traveling wave devices cannot operate far from cutoff if high efficiency is desired. As an example, the analysis is applied to a 10 GHz, 430 kV, 240 A gyrotwistron operating at the fundamental cyclotron harmonic with a tapered wall radius and magnetic field. A realistic design that achieves over 30% efficiency is produced. The issue of stability of this device with respect to competition from parasitic modes is taken up in a companion paper [Phys. Plasmas 2, 3511 (1995)].

Theory and design of a high-harmonic gyrofrequency multiplier

In a gyrofrequency multiplier, the entire electron beam enters the output cavity optimally phased to lose energy in a first-order interaction (in contrast to the second-order standard gyrotron process) resulting in a high conversion efficiency. Because the electrons radiate at a high harmonic of the cyclotron frequency, a gyrofrequency multiplier is capable of efficiently generating power in the millimeter to submillimeter wave region. The operational principles of the gyrofrequency multiplier are described in this paper. Results from nonlinear simulation show that radial guiding-center spread of the beam can dramatically affect the device's efficiency while velocity spread effects are negligible. The design is presented for a 150 kW, 17.4 GHz, sixth-harmonic gyrofrequency multiplier which is under construction and is predicted to yield 31% conversion efficiency of the electron beam into the output wave. The 300 keV, 1.67 A axis-encircling beam is produced by a 1 MW, 2.9 GHz gyroresonant RF accelerator. >

Numerical analysis on laser blow-off lithium beam probing.

A new reconstruction method from the data obtained by laser blow-off Li-beam probing and the best observation condition are given through numerical analysis for the measurement of electron density profile at tokamak edge. It includes the effect of velocity spread of beam particles, and can be applied to the electron density above 1012cm-3, in which the contribution from the excited state of Li atoms is important for their ionizations. Both the velocity sperad and the high electron density cause inaccuracy when a simple reconstruction procedure is employed as has been done in the case of thermal Li-beam.

A linear three-dimensional model for free electron laser amplifiers

This paper introduces a generalized, linear, three-dimensional model of the FEL amplifier. This 3-D model that is represented by a matrix gain-dispersion equation is valid in the various FEL gain regimes; the low and high gain regimes and the space-charge dominated regimes. It includes electron-beam longitudinal velocity spread effects that are caused by energy spread, transverse emittance and betatron motion. The model provides solutions for the EM-wave amplitude and phase profiles for any initial transverse profiles of the electron beam and of the EM wave, given at the entrance to the interaction region. The matrix gain-dispersion equation consists of angular spectrum components and therefore it is applicable for free-space FEL schemes and for rectangular waveguide schemes as well. Different linear three-dimensional effects, such as optical guiding, gain focusing, reduction of space-charge effects, bending of the radiation beam, off axis-gain, etc., are all inherently included in the presented model. Figurative results, derived according to the parameter sets of two representative high-gain FELs, are demonstrated.

Feasibility of high gain X-ray free electron lasers

We investigate the feasibility of a tunable VUV/soft X-ray FEL operating in a dedicated storage ring. Because of poor mirror reflectivity available at these wavelengths, the FEL must operate in the intermediate high gain regime (gain = 3−5). In order to obtain this high gain, a long interaction length (27 m), a high current (270 A) and strong magnetic fields ( a w > 1 ) are necessary. Consequently some velocity spread effects and possibly even some space charge effects must be considered. We use a one-dimensional, comprehensive small signal gain analytical model to conduct a parametric study of the FEL operating parameters and their scaling laws. The results of the analytic model are compared with results obtained with the 2-D FEL simulation code FRED, and the effect of optical guiding on the gain is estimated using an enhanced filling factor based on the observed guided mode size. We conclude that oscillation below 300 Å is feasible with existing mirror technology.

Investigation of the gain regimes and gain parameters of the free electron laser dispersion equation

We compute the small signal gain curve and various gain parameters by solving numerically the generalized gain-dispersion equation of free electron lasers (FEL), which characterizes the conventional magnetic bremsstrahlung FEL, as well as a large number of other FEL devices. The model includes high gain, collective, and axial velocity spread effects, and some waveguide effects. The FEL gain regimes are investigated and presented in terms of only three universal FEL characteristic parameters. The approximative analytic gain expressions are compared to the numerical computation results, and the approximation error is computed and displayed. In the intermediate regimes (high-low gain, tenuous-collective beam, cold-warm beam), the gain parameters are given in terms of useful curves, and a heuristic approximative formula is suggested for estimating the axial velocity spread gain reduction factor in all gain regimes. We also define and compute gain bandwidth and beam quality acceptance parameters in all gain regimes.

A linear theory and design study for a gyrotron backward-wave oscillator†

Abstract A linear theory for a gyrotron backward-wave oscillator (gyro-BWO) is developed. The theory solves a reduced one-dimensional Maxwell-Vlasov equation in the form of a linear integro-differential equation using the Laplace transformation. The relative amplitudes among the waveguide modes and beam modes are completely determined and enable one to calculate gyro-BWO start-oscillation conditions. Using this analysis and including velocity spread effects, a design of a millimetre-wave gyro-BWO has been carried out based on the operating parameters of an existing electron gun. Tunability over a range of 86 GHz to 103 GHz is predicted with output power estimated to be ∼ 1 kW.

Theory and Numerical Simulation of a TE/sub 111/ Gyroresonant Accelerator

The production of spiral relativistic electron beams in a TE/sub 111/ gyroresonant accelerator cavity for injection into a compact high-harmonic gyrotron is studied. Parametric studies are performed to determine the effects of variations in the background magnetic field amplitude, the RF amplitude in the cavity, and the initial beam voltage on the output beam.The effects of velocity spread and a finite radial extent of the input beam are also discussed. Power curves for obtaining optimum operating regimes for the TE /sub111/ accelerator are provided.