Beam-wave Interaction Research Articles

Starting Currents for Eigenmodes of a Gyrotron Cavity With Mode Conversion

In the fixed-field (cold) approximation, a generalized formula is derived for the starting currents of eigenmodes excited by an electron beam in a gyrotron cavity with the mode conversion. Tapered gyrotron cavities with gradual and abrupt transitions are considered as examples. It is shown that the effect of the mode conversion on the starting current consists mainly in the change of the diffractive quality factor and, therefore, is small for cavities with low diffractive losses. For such cavities, our formula is in good agreement with single-mode, self-consistent (hot) calculations of the electron beam–wave interaction. The agreement degrades for high-order axial modes having clear-cut distinctions of cold and hot fields. The derived formula is used to test the validity of the single-mode approximation for a complex gyrotron cavity with the abrupt change in radius.

Regenerated amplification of terahertz spoof surface plasmon radiation

Regenerated amplification induced by a Fabry–Perot (F–P) cavity is introduced to enhance the interaction efficiency of the free-electron-driven spoof surface plasmon. A direct-current electron beam flies above the meta-grating surface and seeds noise-level plasmonic waves. This weak signal experiences multiple back-and-forth regenerated amplifications in the F–P cavity loaded grating system, and the system outputs a pulsed radiation when the signal leaves the cavity. When compared with the condition without the F–P cavity, the equivalent beam-wave interaction length is effectively extended, and the interaction efficiency is improved by orders of magnitude. The proof-of-principle scheme is verified in both backward-wave and forward-wave modes using the particle-in-cell simulation. This scheme is promising for developing high-efficient on-chip terahertz free-electron radiation sources.

Investigation of a cross-band relativistic Cherenkov oscillator based on the cathode adjustment

The mechanism and realization of a cross-band relativistic Cherenkov oscillator based on the cathode adjustment are presented. The device adopts coaxial dual-annular cathode to emit the inner and the outer electron beams, independently. When the inner annular cathode is extended and the outer annular cathode is retracted, the electron beams are emitted from the inner cathode and interact with the internal electromagnetic structure to generate Ka-band microwaves. On the contrary, the outer electron beams interact with the external electromagnetic structure to generate X-band microwaves. Thus, the cross-band microwave generation can be achieved only by adjusting the protrusion and retraction of dual-annular cathode. By the particle-in-cell (PIC) method, the physical process of beam-wave interaction in the device is studied, and the high efficiency internal-external double electromagnetic structures are designed. Simulation results show that the X-band microwave with a power of 1.50 GW and a frequency of 8.55 GHz is generated, corresponding to an efficiency of 32%. Meanwhile, the Ka-band microwave with power of 650 MW and frequency of 31.80 GHz is generated, corresponding to efficiency of 28%.

Design and preliminary experiment of radial sheet beam terahertz source based on radial pseudospark discharge

To satisfy the demands for compact, inexpensive terahertz (THz) sources with power of hundreds of watts, a radial sheet beam THz source which does not require an external magnetic field and is driven by a radial pseudospark discharge plasma electron gun (PSDP-EGUN) is proposed. Radial design has been used in pseudospark switches, but in this paper the design of a PSDP-EGUN to drive a radial THz source is presented for the first time. Being different from the latest reported axial quasi-rectangular sheet beam THz sources driven by an axial PSDP-EGUN, a new design consisting of a circular plate-shaped sheet beam that is directly generated by the radial PSDP-EGUN is reported. As compared to an axial system, the radial configuration may result in a larger beam current and a larger beam-wave interaction area together with a higher potential of THz output power. Theoretical analysis and particle-in-cell simulation have been employed in the design of the radial sheet beam THz source. Output powers in the kilowatt range have been observed in the simulation of this 0.22 THz source. Preliminary experimental results of the radial PSDP-EGUN are also presented.

Nonlinear Analytic Solution of Eulerian Beam-Wave Interaction Theory Considering Harmonic Interaction of Traveling-Wave Tube Amplifiers

In this paper, a novel Eulerian nonlinear beam-wave interaction (BWI) theory considering harmonic interaction of a helix traveling-wave tube (TWT) is developed. Derived from this Eulerian model, the novel Eulerian nonlinear analytic solutions (the fourth-order analytic solution of fundamental and the second-order analytic solution of harmonic) are first obtained by the method of successive approximation. The analytic relationships between electric fields of fundamental/harmonic frequencies and electron phases are also found. Then, the Eulerian nonlinear analytic solutions and Eulerian nonlinear BWI theory are compared to a Lagrangian theory. C-band and Ku-band helix TWTs based on a single pitch section are included in the simulation. It is found that the Eulerian nonlinear analytic solutions and Eulerian nonlinear BWI theory agree well with the Lagrangian theory at 1-dB gain compression point. Interestingly, the saturation effects caused by electron overtaking cannot be found by the traditional Eulerian analysis but can be described by the Eulerian nonlinear analytic solutions and Eulerian nonlinear BWI theory. Moreover, Eulerian nonlinear analytic solutions are simpler and more accurately than existing approaches and, thus, allow analytical progress. This paper confirms that the Eulerian nonlinear analytic solutions can outperform the previous proposals.

Numerical research on a 4 MW 170 GHz coaxial gyrotron with a double electron beam

In this paper, a coaxial gyrotron with a double electron beam is investigated on the ohmic loss, starting current, mode competition, and beam wave interaction. Its beam-wave interaction equation and dependence of the starting current on the static magnetic field and parameter K (the ratio of the current of an electron beam to the total current of a double electron beam) are given. On this basis, a 4 MW 170 GHz coaxial gyrotron with a double electron beam is studied. By the numerical calculation, the influence of K on the starting current is analyzed under a given static magnetic field and at different guiding center radii of the double electron beam. Studies show that the ability of the gyrotron to suppress the mode competition has a relation with the selection of the guiding center radii of the two electron beams. Then, the investigation of a time-dependent multi-mode competition of the gyrotron is performed, which shows that the gyrotron can stably operate in the TE38,18− mode. The results show that by considering the ohmic loss, the gyrotron can operate at 170.4 GHz with the output power of 4.04 MW and the beam-wave interaction efficiency of 35.47% when B = 6.82 T, U = 88 KV, I = 129 A, and K = 0.4. Each of the two electron beams in the gyrotron has different beam-wave interaction efficiencies. Compared to the coaxial gyrotron with one electron beam, the beam-wave interaction efficiency of each electron beam in the coaxial gyrotron with a double electron beam has a different increase.

Particle-in-cell simulation on effect of collector outgassing on relativistic backward oscillator

The relativistic backward-wave oscillator has been considered to be one of the most promising high-power microwave devices. As the output microwave power is further increased, the breakdown phenomenon inside the relativistic backward-wave oscillator, including the collector pole, becomes more and more serious, which eventually leads to the pulse shortening, becoming a biggest obstacle to the development of the device with high power and high energy. Such a problem has also been one of the important issues which constrain its development. Based on the 2.5D particle-in-cell simulation software, i.e. UNIPIC-2D developed by our research group, in this paper the dynamic gassing model is used to study the effects of the relativistic backward-wave oscillator collector breakdown process and the guiding magnetic field under different outgassing coefficients. The result of particle simulation demonstrates that as the electrons continue to bombard the collector, the surface pressure of the collector is increased, and gas ionization occurs. The generated plasma enters into the slow-wave structure along the guiding magnetic field, thus affecting the beam-wave interaction process and causing the output power to drop. With the increase of the gas release coefficient, the pulse shortening phenomenon becomes more and more obvious. In the case of low guiding magnetic field, the breakdown and pulse shortening are alleviated.

Theoretical analysis and design of G-band extended interaction klystron amplifier

Extended interaction klystron is a very important millimeter-wave and sub-millimeter-wave vacuum electron device with many actual and potential applications, such as space-borne cloud profiling radar, communication, imaging system, precision guided missiles, etc. Kinematical theory and space charge wave theory are extensively used to analyze the bunching process of electrons. Kinematical theory is precise when electron beam is especially small because the influence of space charge effect is ignored, while space charge wave theory is accurate when the modulation of electron beam is small since it is based on the premise of small amplitude. Based on kinematical theory, law of induce current, principle of charge conservation in a one-dimensioanl mode and small signal condition, the influence of electron beam on standing wave electric field in multiple-gap cavity is analyzed, and the expression of beam-loading conductance and beam-loading susceptance in multiple-gap cavity are derived. The influence of the direct current transmit angle of single gap, the number of multiple gaps and the direct current transmit angle of between center of adjacent gaps on beam-loading conductance and beam-loading susceptance are analyzed. The results show that the beam-loading conductance and beam-loading susceptance of multiple-gap cavity can change to a bigger extent when the number of cavity gaps is bigger, which means that the maximum beam-wave conversion efficiency and the range of loaded frequency increase with the number of cavity gaps increasing. The results also show that the direct current transmit angle between centers of adjacent gaps is the most important parameter for the beam-wave interaction effect. Based on the above analysis, a G-band extended interaction klystron amplifier consisting of three five-gap cavities is designed by an three-dimensional PIC code. An output power of 225.5 W at 217.94 GHz with an efficiency of 6.26%, whose gain and 3 dB bandwidth are 30.5 dB and 470 MHz respectively, is obtained by simulation. This study is of great significance for the physical design and process in engineering the G-band extended interaction klystron amplifier.

Theoretical Research on Properties of Spatial Harmonics in Corrugated Waveguide

This paper investigates the dependence of the properties of the spatial harmonics on the overmoded ratio of the corrugated waveguide operating in TM01 at 30 GHz with the consideration of the effects of the ripple shape. It is found that as the overmoded ratio grows, the electric fields concentrate towards the ripple surface, which weakens the enhancement of the power handling capacity caused by augmentation of the overmoded ratio. As the overmoded ratio grows, the ratio between the field amplitudes of the -1st spatial harmonic and the fundamental harmonic increases monotonically. Therefore, the total electric fields composed of the spatial harmonics become the spatial beating-wave with the single frequency, whose amplitudes vary along z-axis with the spatial period determined mainly by the -1st spatial harmonic and the fundamental harmonic. Researches on coupling impedances show that with the same overmoded ratio, the corrugated waveguide consisting of the improved rectangular ripples provides better synchronous coupling for the wave-beam interaction than that of the sinusoidal ripples does. Moreover, it is better to choose the fundamental harmonic close to the light line as the synchronous wave for the wave-beam interaction in the low magnetic field. In that case, even if the electron beam keeps far away from the ripple surface, the synchronous wave still provides strong enough coupling for the electron beam.

Nonlinear theory for beam-wave interactions of two electron beams with higher order TE20 mode in serpentine waveguide traveling wave amplifier

In this study, a nonlinear model is presented, which is used to analyze the beam-wave interaction of two electron beams with a higher TE20 mode in a serpentine waveguide (SW) traveling wave tube (TWT). Taking advantage of the novel model, the dimensions of SW are enlarged and the difficulties of fabrications of SW are reduced. To investigate the characteristics of two electron beams interacting with a high order mode in SW, the disk theory is used, in which the RF field in gap, space charge field, and the electron motion equations are combined, and the reactions of two electron beams to wave are considered. The nonlinear characteristics of power saturations, the distributions of electron velocity, and phase space are studied. To verify the validity of the nonlinear model, the theoretical results are compared with those of particle-in-cell simulations, and the output powers versus beam voltage and exciting frequency are studied. The results show that the relative errors are less than 10%, which are suitable for solving the SW-TWT operation characteristics.

Efficient dual space source interpolation method for the numerical solution of self-consistent static beam-wave interactions

Efficient dual space source interpolation method for the numerical solution of self-consistent static beam-wave interactions

Improvement of the Beam-Wave Interaction Efficiency Based on the Coupling-Slot Configuration in an Extended Interaction Oscillator

A method aimed at improving the beam-wave interaction efficiency by changing the coupling slot configuration has been proposed in the study of extended interaction oscillators (EIOs). The dispersion characteristics, coupling coefficient and interaction impedance of the high-frequency structure based on different types of coupling slots have been investigated. Four types of coupled cavity structures with different layouts of the coupling slots have been compared to improve the beamwave interaction efficiency, so as to analyze the beam-wave interaction and practical applications. In order to determine the improvement of the coupling slot to a coupled cavity circuit in an EIO, we designed four nine-gap EIOs based on the coupled cavity structure with different coupling slot configurations. With different operating frequencies and voltages takes into consideration, beam voltages from 27 to 33 kV have been simulated to achieve the best beam-wave interaction efficiency so that the EIOs are able to work in the 2π mode. The influence of the Rb and the ds on the output power is also taken into consideration. The Rb is the radius of the electron beam, and the ds is the width of the coupling slot. The simulation results indicate that a single-slot-type EIO has the best beam-wave interaction efficiency. Its maximum output power is 2.8 kW and the efficiency is 18% when the operating voltage is 31 kV and electric current is 0.5 A. The output powers of these four EIOs that were designed for comparison are not less than 1.7 kW. The improved coupling-slot configurations enables the extended interaction oscillator to meet the different engineering requirements better.

Study the Mechanism and Suppression of AM/PM Conversion of Traveling-Wave Tubes Using Eulerian Hydrodynamic Analysis

In this paper, the fourth-order analytic solution of amplitude modulation to phase modulation (AM/PM) conversion is first derived from an Eulerian nonlinear analytic model. The analytic relationships between electron phases, detuning parameter b, and AM/PM conversion are also found. Then, the mechanism of AM/PM conversion is studied. It is found that the generation of the harmonics in the dc component of the electron phase in the nonlinear beam–wave interaction region is the main mechanism of AM/PM conversion. Next, a series of AM/PM conversion suppression schemes is discussed by using the mechanism. The Eulerian formations are validated by an in-house code based on the Lagrangian theory. Results show that the fourth-order analytic solution of normalized axial electric field and AM/PM conversion agree well with the Lagrangian theory in the nonlinear region. In addition, the suppression schemes are applied to a high-efficiency Ku-band space traveling-wave tube (TWT). The AM/PM conversion distortion is greatly reduced by approximately 50% with a slight drop of output power. We hope that our efforts will help the nonlinear design of TWT in the future.

3-D Nonlinear Theory for Sheet-Beam Folded-Waveguide Traveling-Wave Tubes

A 3-D frequency-domain nonlinear model for sheet beam (SB) traveling-wave tubes (TWTs) based on folded waveguides (FWs) is presented in this paper. The SB with finite thickness is a 3-D asymmetric system. To characterize such a system, an accurate description of the radio frequency (RF) fields and the space charge (SC) fields in the interaction gap in all three dimensions is required. An analytical expression for the interaction electric fields is derived. Beside of the interaction electric fields, a modified analytical model for the dispersion and interaction impedance is also imbedded in our code predicting the cold characteristics of the waveguide, which agrees with the results of the 3-D simulation code CST. As a result, the model provides a through predictive capability from the geometrical parameters to the device performance, such as saturation power and gain. Due to the short computing time, our code is very useful for the large-scale optimizations of TWTs. For the calculation of the SC field, a particle-in-cell method is used by solving the 3-D Helmholtz equation and the motion equation. Such analytical technology is much more preferable to interpret the complicated beam–wave interaction than the conventional electron beam models, which attributes to the ever-increasing computing capacity of the computers. These features have been incorporated in the development of our large-signal code SB-FWTWT-3-D. The validation of the model is performed and comprehensive results are presented.

RF Coupling and Beam-Wave Interaction Study in a Periodically Loaded <inline-formula> <tex-math notation="LaTeX">${X}$ </tex-math> </inline-formula>-band 25-MW Gyro-Twystron

A megawatt class X-band gyro-twystron using periodically loaded alternate lossy dielectric and metal output waveguide section is studied for its beam-wave interaction behavior using a fully nonlinear, self-consistent, and multimode theory. Nonlinear amplification of the desired TE01 mode and its competing parasites including TE11, TE21, and second harmonic TE02 modes are investigated using multimode code to ensure the device stability. The present amplifier developed a peak RF output of ~25 MW in the desired TE01 mode that is validated with a 3-D commercial particle-in-cell code. Furthermore, an input coupler and an output RF window are simulated for their transmission and reflection characteristics. The return and transmission losses of input coupler are calculated as ~28 and ~0.13 dB, respectively. Similarly, the RF window is designed to be transparent for the output with a transmission loss of ~0.075 dB and a return loss of ~63 dB.

Analysis of the effect of field non-uniformity on energy conversion efficiency in a cyclotron-wave rectifier

The cyclotron-wave rectifier can efficiently convert microwaves into direct current in wireless power transmission. Its resonator operates in the quasi-H111 mode, where there is field non-uniformity; how this field non-uniformity will affect the energy conversion is determined. In this paper, through Computer Simulation Technology simulation, combining experiential analysis with numerical fitting obtains the field expression of the operating mode, approximately calculates the Coulomb field by using the model of a filamentary electron beam, and then through the numerical solution, analyzes the effect of the field non-uniformity on the energy conversion efficiency in both the resonator and the conversion region. The results demonstrate that when the relationship between the beam current I0 and the beam radius robr satisfies the Brillouin relationship, a lesser current density can maintain the beam shape very well and ensure a high beam-wave interaction efficiency; furthermore, in a reverse magnetic field region, when I0 ≤ 0.75Iobr, a higher energy conversion efficiency can be predicted. What is more, the conclusion is in agreement with particle-in-cell simulation. Finally, numerical computation also indicates that high beam-wave interaction efficiency requires a smaller radius of the electron beam.

Coherent Cherenkov-cyclotron radiation excited by an electron beam in a two-spiral metamaterial waveguide

We present the analysis of a microwave generator that uses two-spiral metamaterial (MTM) plates in a below cutoff WR340 waveguide that interacts with a high-power electron beam, motivated by recent results obtained by researchers at MIT. Particle-in-cell simulations using the MAGIC code demonstrated that power levels of 12 MW are achieved in a backward wave mode at a frequency of 2.47 GHz from an anomalous Doppler instability using a 1 μs pulsed electron beam of energy 400 keV, current 82 A in a 415 G magnetic field. In addition, a backward wave with 9 MW output power is achieved at a frequency of 2.54 GHz attributed to a Cherenkov instability using a 1 μs pulsed electron beam of energy 400 keV, current 82 A in a 1200 G magnetic field. MAGIC simulations demonstrate that the beam-wave interaction electronic efficiency can be as high as 27.4%. Nonlinear simulations indicate that beam interception leads to secondary electron emission from surfaces, which makes the anomalous Doppler instability and Cherenkov instability more complicated by a shift in frequency. This work seeks to clarify some discrepancy between particle-in-cell simulations and experiments at MIT over a range of guide magnetic field.

Optimization and Improvement of Output Performance in G-Band Extended Interaction Klystron

To improve the output performance of G-band extended interaction klystron (EIK), several practicable methods have been discussed. Firstly, the synchronization characteristics of the electron beam with the operating mode are analyzed in order to obtain large output power for optimized period. The influence of input gap voltage on the beam-wave interaction is studied, and the well-matched condition is established by optimizing the structure of input cavity. The gap length of output cavity is optimized to improve the electric field distribution. By adopting the optimized gap length and non-uniform gap lengths, the output power significantly increases from 360 to 570 W and 660 W, respectively; the corresponding bandwidth reaches to 650 MHz and 470 MHz. Moreover, AJDISK calculation is adopted to compare the results with CST simulation, and the similar gains and tendencies validate the relative reliability of our designed beam-wave interaction circuit. Therefore, our proposed methods for improving the output performance of G-band EIK are feasible and utilizable.

Time growth rate optimisation of terahertz electromagnetic wave generation by converting occupied plasma region from annular plasma to filled plasma in the core, in an elliptical Cherenkov maser with two energy sources

In this work, a comparison between two different cases of an elliptical Cherenkov maser with two electron beams for the generation and amplification of terahertz electromagnetic waves has been presented. The waveguide is made of a hollow dielectric layer filled with a cold collisionless unmagnetised plasma. In the above-mentioned configuration, there are two electron beams with opposite velocities. The dispersion relation graph and its characteristics, such as its dependence on geometrical dimensions and characteristics of the electron beam, are presented. The growth rates of the hybrid modes are numerically calculated and their diagrams in some operating frequencies are studied. The effective factors on the time growth rate of hybrid electromagnetic waves, such as geometrical dimensions, dielectric constant of the dielectric layer, accelerating voltage, plasma frequency and applied current intensity, are analysed. It is shown that the injection of background plasma into the core region of the waveguide can enhance the output frequency and the wave growth rate of the beam–wave interaction.

Linear analysis of traveling sheet electron beam in sine waveguide tubes

A theoretical model is proposed for linear analysis of the beam–wave interaction in a sine waveguide (SWG) with slow-wave structure. The field expressions and “hot” dispersion equation are obtained by means of field matching. The ohmic loss and attenuation constant due to imperfect conductors are also derived using the theoretical model. Moreover, the effects of voltage, current, beam thickness, period, and oscillation amplitude on the linear gain and bandwidth are calculated. The results indicate a peak gain and 3-dB bandwidth of 6.82 dB/cm and 19.5%, respectively, for a 0.22-THz SWG traveling-wave tube upon selecting reasonable structural parameters and electron-beam dimensions. Furthermore, by considering the ohmic losses for the finite conductivities of 5.8 × 107 S/m and 2.2 × 107 S/m, the theoretical results are compared with those of particle-in-cell simulations performed using Computer Simulation Technology Particle Studio.