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Additional file 3: Table S1. Primer sequences for RT-qPCR.

This paper investigates the properties of traveling wave-beam interaction in a rectangular helix traveling-wave-tube (TWT) for a solid sheet electron beam. The ‘hot’ dispersion equation is obtained by means of the self-consistent fleld theory. The small signal analysis, which includes the efiects of the beam parameters and slow-wave structure (SWS) parameters, is carried out by theoretical computation. The numerical results show that the bandwidth and the smallsignal gain of the rectangular helix TWT increase as the beam current increases; and the beam voltage not obviously in∞uences the small signal gain. Among difierent rectangular helix structures, the small-signal gain increases as the width of the rectangular helix SWS increases, however, the bandwidth decreases whether structure parameters a and

In this paper, we present a design where a bunched relativistic electron beam traversing inside the rectangular dielectric-loaded (DL) waveguide is used as a high power microwave generation device. Two kinds of methods of calculating the electromagnetic (EM) field excited by a bunched beam are introduced, and in the second method the calculation of EM pulse length is discussed in detail. The desired operating mode is the LSMn due to its strong interaction with the electron beam. For the designed 7.8 GHz operating frequency, with a 100 nC/bunch drive train of electron bunches separated by 0.769 ns, we find that high gradient (> 30 MV/m) and high power (> 160 MW) can be generated. An output coupler is also designed which is able to extract the generated power to standard waveguides with a 94% coupling efficiency.

A period-varying folded waveguide is formed by varying the period of a folded waveguide. It has the advantages of the space harmonic selectivity and the wide bandwidth. However, the regularities of the variety of these period-varying folded waveguides are unavailable from the published papers. In order to solve this problem, the principle of the space harmonic selectivity of a period-varying folded waveguide is analysed, and the conditions to select the space harmonic for this slow wave system are obtained. In addition, the space harmonic selectivities for a linear period-varying folded waveguide and a hyperbolic sine-varying period folded waveguide are also analysed as examples.

The periodic nonuniform folded waveguides are special structures, the physical dimension of which is between the periodic folded waveguide and the tapering period folded waveguide. Therefore, the synchronization between the microwave and the electron beam can be maintained in the whole interaction process and the periods are not tapered. In comparison with the tapering period folded waveguide, the theoretical analysis and the technological requirements for this structure are more convenient. In order to study this structure, the space harmonics are analysed, the conditions to make the m-th space harmonic synchronizing with the electron beam in the whole interaction process are present, and the dispersion curve and the coupling impedance curve are obtained by the simulation software HFSS.

A new type of printed rectangular helix slow-wave structure (SWS) is investigated using the field-matching method and the electromagnetic integral equations at the boundaries. The radio-frequency characteristics including the dispersion equation and the coupling impedance for transverse antisymmetric (odd) modes of this structure are analysed. The numerical results agree well with the results obtained by the EM simulation software HFSS. It is shown that the dispersion of the rectangular helix circuit is weakened, the phase velocity is reduced after filling the dielectric materials in the rectangular helix SWS. As a planar slow-wave structure, this structure has potential applications in compact TWTs.

On the basis of a rigorous field theory, two different physical models of attenuator and sever have been proposed. One is named High attenuation (HATT) model in which both attenuator and sever are considered as a unified attenuator, but the sever is regarded as an area of very high loss; the other is called Sever and attenuator (SATT) model in which the sever is modelled as a drift area in which the electric and magnetic fields both vanish. A complex function is derived and potential sinking effect is also considered. Thus, a set of more practical self-consistent equations of nonlinear beam-wave interaction is formulated. Simulations are carried out under the conditions of the two different physical models, and the simulation results are compared with the experimental data. The results show that in the case of single signal drive, the unknown second harmonic should be included for predicting the saturated output power. It is also evident that the SATT model and the HATT model predict the same physical nature, whereas the results predicted by the HATT model are much closer to the experimental data than those obtained from the SATT model. Therefore, these results provide a strong theoretical basis for designing broadband and high gain helix travelling wave tubes.

The output section of a helix travelling wave tube usually contains a helix pitch taper for high rf electron efficiency. By keeping the rf field as synchronous as possible with the decelerating electron beam bunches, the rf field can extract much more energy from the beam, and thus the maximum electron efficiency can be realized. Recently, a global simulated annealing algorithm has been employed to design the helix pitch profile so as to improve the electron efficiency as much as possible. From the numerical results, it is concluded that the electron efficiency can be enhanced by about 4%–8%.

We present a novel helix slow wave structure with an elliptical cross section shielded by an elliptical waveguide. The rf characteristics including dispersion properties, interaction impedance of zero mode in this structure have been studied in detail. The theoretical results reveal that weaker dispersion even abnormal dispersion characteristics is obtained with the increasing eccentricity of the elliptical waveguide, while the interaction impedance is enhanced by enlarging the eccentricity of elliptical helix.

In this paper, five modified Tunneladder slow-wave structures (SWS), the ridge-loaded stub-supported meander line with circular electron tunnel (CET-RSML), ring-plane frame line (RPFL), the ridge-loaded thick ladder line (RLTLL), the ridge-loaded pole-piece folded-waveguide circuit (RLPFWL), and the double-period Tunneladder line (DPTL) were discussed. The dispersion characteristics and the interaction impedances of the five modified Tunneladder SWS were calculated by simulation and the corresponding analytic models. The calculation results explain that the CET-RSML and the RLTLL hold wider bandwidth in comparison with the Tunneladder, when the volume dimensional lengths are same. When the bandwidth is definite, the interaction impedance of RLTLL can be higher than Tunneladder, but that of CET-RSML can’t. The dispersion curves of the RLPFWL and the DPTL are more linear in comparison with Tunneladder, but the interaction impedances are very low.

A slow-wave structure (SWS) with two opposite gratings inside a rectangular waveguide is presented and analysed. As an all-metal slow-wave circuit, this structure is especially suited for use in millimetre-wave travelling wave tubes (TWTs) due to its advantages of large size, high manufacturing precision and good heat dissipation. The first part of this paper concerns the wave properties of this structure in vacuum. The influence of the geometrical dimensions on dispersion characteristics and coupling impedance is investigated. The theoretical results show that this structure has a very strong dispersion and the coupling impedance for the fundamental wave is several tens of ohms, but the coupling impedance for –1 space harmonic wave is much lower than that for the fundamental wave, so the risk of backward wave oscillation is reduced. Besides these, the CST microwave studio is also used to simulate the dispersion property of the SWS. The simulation results from CST and the theoretical results agree well with each other, which supports the theory. In the second part, a small-signal analysis of a double rectangular waveguide grating TWT is presented. The typical small-signal gain per period is about 0.45 dB, and the 3-dB small-signal gain bandwidth is only 4%.

The rectangular waveguide grating slow-wave structure (SWS) with arbitrary shaped grooves is presented and analyzed in this paper. As an all-metal slow-wave circuit, it has properties that can be used in high-power millimeter-wave or sub-millimeter wave traveling wave tube (TWT). The unified dispersion equation and the expression of coupling impedance are obtained in this paper by means of an approximate field-theory analysis, in which the profile of the groove is approximately replaced by a series of steps and the field continuity at the interface of two neighboring steps together with the field matching conditions at the interface between the groove region and the interaction region are employed. A rectangular groove SWS was manufactured and the cold measurement was made. The experimental data are in good agreement with the numerical calculation. The derived transcendental equations are resolved numerically for four classical structures such as rectangular, dovetail, ladder and cosine. Finally, taking the rectangular waveguide grating SWS with rectangular grooves for example, the influences of physical dimensions on dispersion relation and coupling impedance are discussed.

We present the formulation of elliptical corrugated waveguides with a concentric circular hole using the field-matching method and the addition theorem for Mathieu functions. The dispersion equation and the mean interaction impedance of this structure are derived separately. The numerical results, which are generally based on the current approach, agree well with the results obtained by the commercial software package CST. As a slow-wave structure, this structure has potential applications in high power microwave amplifiers and possibly filtering structures.

A model for studying the ionization effects in a microwave tube has been developed. This model is simulated by a two-dimensional particle-in-cell code with the Mont Carlo collision model for the electron-neutral ionization process. The transient-state process of ion noise and ion focusing effects are observed. A simple theory about ion motion is given for interpreting the phenomenon of the ion moving to the wall of the tube when the beam is not neutralized. The computed result agrees with the experiment and simulation result.

We present a new periodic all-metal slow wave structure, a coaxial step-disc-loaded system and the dispersion characteristics of the structure. By using the field-matching method, the dispersion equation and the coupling impedance of this structure are obtained. The coaxial structure makes the bandwidth broader than that of the non-coaxial one. Compared with the coaxial disc-loaded and ridged-disc-loaded structures, the pass-band of coaxial step-disc-loaded structure is the broadest. The calculation results show that increasing the step width and decreasing the step thickness can improve the bandwidth.

A rhombus-shaped microstrip meander-line slow-wave structure is proposed for use in a low voltage, wide bandwidth, moderate power and high efficiency millimeter-wave traveling-wave tube. The structure is evolved from the original V-shaped microstrip meander-line slow-wave structure. Compared with the conventional slow-wave structure, it is a kind of planar structure, whose fabrication can be easily realized by utilizing the technology of 2-D micro-fabrication. Whats more, the structure can realize beam-wave interaction with sheet electron beam, and no additional electron beam channel is needed. The electromagnetic characteristics and the interaction between the sheet electron beam and slow wave in the structure are obtained by utilizing the electromagnetic simulation software HFSS and the particle-in-cell code in CST Particle Studio, respectively. Our calculations indicate that, at a beam voltage of 7 kV and a beam current of 90 mA, the traveling wave tube based on the structure is capable of delivering several tens of watts output power with an interaction efficiency of 14.3％ and a transient 3 dB bandwidth of 18 GHz(ranging from 132 GHz to 150 GHz)

A new type of partial-dielectric-loaded helical groove slow-wave structure (SWS) for millimetre wave travelling wave tube (TWT) is presented in this paper. The radio-frequency characteristics including the dispersion properties, the longitudinal electric field distribution and the beam-wave coupling impedance of this structure are analysed. The results show that the dispersion of the helical groove circuit is weakened, the phase velocity is reduced and the position of the maximum Ez is moved from the mouth to the inside of the groove after partially filling the dielectric materials in the helical groove SWS. Therefore, the dielectric-loaded helical groove SWS is suitable for a multi-beam TWT with broad band and high gain.

The structure of cylindrical cavity coupling with rectangular waveguides through large apertures on the cavity’s sidewall is studied in detail. The fields in the cavity is properly expanded by derived mode functions. By making reasonable approximation of the boundary conditions, the process of derivation and the formation of the characteristic equation is greatly simplified. The characteristic equation and model coefficients are obtained. The reliability of the derived characteristic equation is tested. Numerical results of characteristic frequency and quality factor changing with dimensions of coupling holes are given.

A congestion evaluation strategy which contained multi-index real-time evaluation and non-real-time evaluation was proposed in order to tackle the problem that the convention strategy can not evaluate traffic congestion effectively, because of the single index, incomprehensive type. In the real-time evaluation of this scheme, if data was missing seriously, the traveling speed should be taken as the only index to evaluate the traffic congestion, else the traveling speed, saturation and delay should be taken as the index to evaluate the traffic congestion by using running state classification. In the non-real-time evaluation, the traveling speed throughout one day should be taken as the independent variable to establish Gaussian mixture distribution model and the evaluation result could be get by analyzing this model. Simulation results indicate that the real-time evaluation and the non-real-time evaluation can analyze the traffic flow objectively and evaluate the traffic congestion effectively.

A novel sine-shape ridge waveguide (SSRWG) is put forward to develop the ultra-broadband high power terahertz (THz) backward-wave oscillator (BWO). It is found that this kind of slow-wave structure (SWS) possesses very wide 'cold' bandwidth and quite low transmission losses from the analyses of the electromagnetic characteristics. Moreover, the beam-wave interaction results indicate that the BWO based upon the SSRWG SWS can produce the output power exceeding 0.625 W in the frequency range from 0.617 THz to 0.99 THz. In particular, the output power at the typical operating frequency of 0.853 THz can reach 1.186 W by using the sheet electron beam of 16 kV and 8 mA. Therefore, this device has great potential to be an ultra-broadband watt-level THz radiation source.

Based on the empirical electron theory of solids and molecules, analysis of valence electron structures is made on Fe&l intermetallic compounds. The bonding complex model of the DO3 cell is set up. Some preliminary attempts to discover the relationship between alloy composition, structure and properties and the Fe&l alloy phase valence electron structure are presented.

By use of XRD, we have found that cubic crystals Ca x Zr 1- x O 2- x (CaF 2 structure) exist in the fused iron catalyst containing ZrO 2 and a small amount of CaO. We also found that Fe 2+ could enter monoclinic ZrO 2 lattices to convert it into cubic ZrO 2 (Fe x Zr I- x O 2- x ), which in turn causes a small portion of Fe 3 O 4 to be broken down to form Fe 2 O 3 (10R). SEM observation of the catalyst surface indicates that Ca x Zr I- x O 2- x separates out of the α-Fe lattice and is concentrated in the cracks or channels of the reduced catalyst, while in the unreduced catalyst, Ca x Zr 1- x O 2- x has a relatively uniform dispersion. For the catalyst without CaO, however, ZrO 2 exhibits an even distribution on the surface of both reduced and unreduced catalysts. The result of the specific surface area measurement shows that the BET surface area of the catalyst decreases somewhat as the content of ZrO 2 increases. By the thermoanalytical technique (TG), we have further confirmed that ZrO 2 promotes the reduction of the fused iron catalyst. If ZrO 2 and CaO are added together to the catalyst the reduction behavior of the catalyst is greatly improved.

This paper introduces the quality characteristics of new peasants in China, and analyzes the current status of peasants’ quality in China from 5 aspects. Finally, this paper puts forward the related countermeasures for improving the peasants’ quality.

Two series of potassium ferrites, KFeO2 and K1+xFe11O17 (x = 0–1), were prepared by several methods and their leaching process was studied. Because of its structural characteristics, KFeO2 can be easily hydrolyzed and its structure can be completely destroyed during leaching in water, whereas for K1+xFe11O17 only a portion of the potassium ions shifts out of the system and its structure still remains after soaking in water. The kinetic parameters for potassium leaching from the K1+xFe11O17 system have also been determined. It is suggested that both types of potassium ferrites coexist in fused iron catalysts for ammonia synthesis: KFeO2 occurs at boundaries, while K1+xFe11O17 mainly remains in the crystal grains of the catalyst. The former belongs to the so-called soluble and the latter to the insoluble potash of the catalyst. The catalytic activity largely depends on the latter.

Based on the standardized precipitation index data of 89 meteorological stations in southwest China (Sichuan Province, Yunnan Province, Guizhou Province, Chongqing) during 1961-2010, probability model containing drought duration and drought severity is established by using the theory of run and the Copula function. The influences of the drought sample number on the distribution parameters, the probability and drought return period are discussed. The result shows that the stability of distribution parameters needs larger sample number. The sample number is greater than 50 in some regions and the requirements for sample number of each parameter is not consistent. The sample number of severity distribution parameters is largest. The probability and return period obtained in the case where the sample number is about 10 have no significant difference (the significant level is 0.05) from those in the case where the sample number is 40 in most of region. With the results used as the standard, statistical model can greatly reduce the requirements for the sample number. And then it demonstrates that the distribution function of drought duration and drought severity can still be established in the lack of measurement data and the inconsistency between starting and ending time. Climate warming has no influence on the minimum of sample number. The fluctuation is mostly between -5 to 5. Statistical model has a certain stability. Meanwhile, the division of climate state reduces the need for distribution test sample number and makes it easier to build model.

Ion noise in output signal in klystron was obtained by particle in cell method. The phase fluctuation in output signal is caused by the change of the beam current DC velocity which is affected by the change of the ion amount. The phase of output signal changed with the change of beam electron amount.

This article modified the Tunneladder circuit expecting to widen the bandwidth and hope to carry on its merits. In this modified Tunneladder circuit, 'forward-wave' was assumed. Cross-section resembling the idealized unmodified circuit of Tunneladder is analyzed. Through making the longitudinal electronic fields satisfying the boundary condition at one point along the boundary, the dispersing equation and interaction impedance expression of Tunnelplane was derived. Good accordance between theory and HFSS of dispersion characteristics of Tunnelplane is acquired.

A systematic theoretical and experimental study on 35 GHz 45 kV third-harmonic gyrotron with a permanent magnet system is presented in this paper. A complex cavity with gradual transition, and a diode magnetron injection electron gun (MIG) are employed in the gyrotron. The permanent magnet system provided the axial magnetic field of about 4.5 kG in the cavity region. The Ka band third-harmonic gyrotron with a permanent magnet system has been designed, constructed and tested. A peak output power of 147.3 kW was obtained at a beam voltage of 45 kV with beam current of 32.2 A, corresponding to an efficiency of 10.2%.

By field matching method, we have derived strictly out the dispersion equation and coupling impedance of ridge-loaded helical groove. Through numerical calculation of these formulas, we could get the relative curves of dispersion and coupling impedance with geometrical dimensions. The analysis in this paper has provided theoretic basis of the designing and calculating for ridge-loaded helical groove millimeter TWT.

A systematic study on Ka band low-voltage third-harmonic gyrotron is presented in this paper. Two types of complex cavity structures with gradual and abrupt transitions are employed in the gyrotrons. A nonlinear theoretical investigation and numerical simulation for interaction between electron beam and RF fields in complex cavities are given. A diode magnetron injection electron gun utilized in the gyrotrons is simulated numerically. The Ka band third harmonic complex cavity gyrotrons with a permanent magnet system are designed and constructed. The experiments of these gyrotrons are in progress.

The dispersion equation of the coaxial interlaced disk-loaded waveguide slow-wave structure is derived by the multi-conductor transmission line method. The simulation results by HFSS are in good agreement with the calculation results obtained from the dispersion equation. Influences of structure parameters on dispersion characteristics are discussed. It can be concluded that with the increase of inner conductor and the decrease of the period length, the bandwidth of the slow-wave structure becomes greater. The dispersion characteristics of the coaxial interlaced disk-loaded waveguide and those of the coaxial disk-loaded waveguide are compared. The results show that the coaxial interlaced disk-loaded structure can obtain a wide bandwidth and weak dispersion. This study will be a guide to the research of the coaxial interlaced disk-loaded waveguide slow wave structure used in the traveling-wave tube.

The drought vulnerability characteristics from 1971 to 2012 in Northeast China are analysed and the risk in Northeast China is calculated based on the theory of information distribution and diffusion, combining with the standardized precipitation index (SPI) and the drought damage index (DDI) in Northeast China, with considering the meteorological factors and social factors. The probability density function (PDF) of DSI is estimated by using the method of information distribution. The vulnerability of the relationship between DSI and DDI is constructed by using the method of two-dimensional normal information diffusion. Then the average risk can be obtained by calculating the sum (discrete distribution) or integral (continuous distribution) of the product of the PDF of DSI and the vulnerability curve. The results show that the introduction of information distribution and diffusion method to analyze the problem of vulnerability for the situation of small sample could render the PDF of DSI smoother. What is more, the vulnerability of the relationship between DSI and DDI through the DSI to obtain the DDI has clearer physical meaning. Therefore the results could be realistic. More significantly, similar results can be obtained with different simple lengths, which means that the method is insensitive to the simple length and it can well overcome the instability of analysis of the small sample.

Lyapunov exponent is an important physical quantity indicating a system is in regular motion or in chaotic motion. In view of this, in this paper, we use the Lyapunov exponent to study the chaotic properties of the system, and the mutations in climate. The results show that the Lyapunov exponent is a reliable mutation detection method. For the ideal sequence or actual atmosphere sequence the method can be used to accurately find out the mutation position; the predictability of nonlinear local Lyapunov exponent is used to evidence the reliability of the early warning signals of abrupt climate change based on the phenomenon of critical slowing down, through calculating the largest Lyapunov exponent of each time the system intrinsic properties can be reflected and the chaos characteristics can be studied, thereby providing a theoretical basis for the wide applications of the present method in real observation data.

Based on the combination of a staggered double vane slow wave structure (SWS) and round electron beam, a 200-W W-band traveling-wave tube (TWT) amplifier is studied in this paper. The main advantages of round beam operation over the sheet beam is that the round beam can be formed more easily and the focus requirement can be dramatically reduced. It operates in the fundamental mode at the first spatial harmonic. The geometric parameters are optimized and a transition structure for the slow wave circuit is designed which can well match the signal that enters into and goes out from the tube. Then a TWT model is established and the particle-in-cell (PIC) simulation results show that the tube can provide over 200-W output power in a frequency range of 88 GHz-103 GHz with a maximum power of 289 W at 95 GHz, on the assumption that the input power is 0.1 W and the beam power is 5.155 kW. The corresponding conversion efficiency and gain at 95 GHz are expected to be 5.6% and 34.6 dB, respectively. Such amplifiers can potentially be used in high power microwave-power-modules (MPM) and for other portable applications.

An open-styled dielectric-lined azimuthally periodic circular waveguide (ODLAP-CW) for a millimeter-wave traveling-wave tube (TWT) is proposed, which is a modified form of a dielectric-lined azimuthally periodic circular waveguide (DLAP-CW). The slow-wave characteristics of the open-styled DLAP-CW are studied by using the spatial harmonics method, which includes normalized phase velocity and interaction impedance. The complicated dispersion equations are numerically solved with MATLAB and the results are in good agreement with the simulation results obtained from HFSS. The influence of structural parameters on the RF properties is investigated based on our theory. The numerical results show that the optimal thickness of the metal rod can increase the interaction impedance, with the dielectric constant held fixed. Finally, the slow-wave characteristics and transmission properties of an open-styled structure are compared with those of the DLAP-CW. The results validate that the mode competition is eliminated in the improved structure with only a slight influence on the dispersion characteristics, which may significantly improve the stability of an open-styled DLAP-CW-based TWT, and the interaction efficiency is also improved.

A novel slow-wave structure called V-shape folded rectangular groove waveguide is proposed. This structure evolves from a conventional rectangular groove waveguide bending the groove with V-shape along its longitudinal direction, and the gap between metal plates forms a sheet electron beam channel naturally. Compared with the traditional U-shape structure, it can increase the interaction area without changing good high-frequency properties, which can adopt the sheet electron beam with a larger area to acquire more output power. In this paper, the high-frequency properties of this structure are analyzed, the interaction circuit for the V-band TWT is designed and the PIC simulation is performed to predict the operating characteristics. From our calculations, this tube can produce average saturation output power over 1000 Watts in a frequency range from 58 GHz to 64 GHz when the cathode voltage and beam current are set to be 12.8 kV and 600 mA respectively. The corresponding saturation gain and electron efficiency can reach over 33 dB and 13.2% respectively.

The folded double-ridged waveguide structure is presented and its properties used for wide-band traveling-wave tube are investigated. Expressions of dispersion characteristics, normalized phase velocity and interaction impedance of this structure are derived and numerically calculated. The calculated results using our theory agree well with those obtained by using the 3D electromagnetic simulation software HFSS. Influences of the ridge-loaded area and broad-wall dimensions on the high frequency characteristics of the novel slow-wave structure are discussed. It is shown that the folded double-ridged waveguide structure has a much wider relative passband than the folded waveguide slow-wave structure and a relative passband of 67% could be obtained, indicating that this structure can operate in broad-band frequency ranges of beam-wave interaction. The small signal gain property is investigated for ensuring the improvement of bandwidth. Meanwhile, with comparable dispersion characteristics, the transverse section dimension of this novel structure is much smaller than that of conventional one, which indicates an available way to reduce the weight of traveling-wave tube.

A novel mm-wave high power microwave device, the ridge-loaded folded waveguide traveling wave tube (TWT), is presented and its linear gain properties are investigated. The perturbed dispersion equation is derived and the small signal growth rate is calculated for different dimensions of ridge and parameters of electron beam. For a cold beam, the linear theory predicts a gain of 1.15 dB/period and a 3-dB small-signal gain bandwidth of 18.51% in Kα-band. The investigation reveals that, with the same beam parameters, the novel slow-wave structure (SWS) has advantage over the folded waveguide SWS in its gain and efficiency. The dimensions of ridge and the beam current may be increased in order to raise the gain.

A novel slow-wave structure (SWS)， the folded double-ridged waveguide structure， is presented and its properties used for wide-band traveling-wave tube (TWT) are investigated. A Ka-band folded double-ridged waveguide TWT is modeled by Magic 3D and the beam-wave interaction is simulated and analyzed. Within the same beam condition， it is concluded from the comparison of folded double-ridged waveguide TWT and folded waveguide TWT that: in the condition of similar gain maximum， the folded double-ridged waveguide TWT has wider bandwidth of which is 22%， and higher electron efficiency of which is 9％.

In this paper a dielectric-loaded folded waveguide slow-wave circuit is presented. The "hot" dispersion relation for slow wave interaction between the traveling wave and linear beam is derived from the fluid dynamical treatment. In the special case where εr=1, the dispersion relation can be simplified with a closed form of the conventional Pierce’s small-signal equation, which confirms the validity of the derivations. By giving the specific parameters, the effects of dielectric loading on the small-signal gain have been studied. The results indicated that in the case of "weak loading" (where d/a

A novel slow-wave structure (SWS), the folded double-ridged waveguide structure, is presented and its linear gain properties are investigated. The perturbed dispersion equation is derived and the small signal growth rate is calculated for dimensions of the ridge-loaded region and the parameters of the electron beam. The novel structure has potential applications in the production of high power and broad band radiation. For a cold beam, the linear theory predicts a gain of 1.1–1.27 dB/period and a 3-dB small-signal gain bandwidth of 30% in W-band. A comparison between the folded double-ridged waveguide SWS and folded waveguide SWS (FWSWS) shows that with the same physical parameters, the novel SWS has an advantage over the FWSWS on the bandwidth and electron efficiency.

A novel Ka-band folded waveguide (FW) amplifier for traveling wave tubes (TWT) is investigated. The dispersion curve and interaction impedance are obtained and compared to the normal FW circuit by numerical simulation. The interaction impedance is higher than a normal circuit through the whole band. We also study the beam-wave interaction in this novel circuit, and the nonlinear large-signal performance is analyzed by a 3-D particle-in-cell code MAGIC3D. A much higher continuous-wave (CW) output power with a considerably shorter circuit compared to a normal circuit is predicted by our simulation. Moreover, the novel FW even has a broader 3-dB bandwidth. It therefore will be useful in designing a miniature but high-power and broadband millimeter-wave TWT.

We report on experimental test of a 7.8 GHz power extractor using a dielectric loaded rectangular waveguide structure. This work is conducted at the Argonne wakefield accelerator (AWA) facility. The wakefield is excited by an electron beam travelling through a dielectric loaded rectangular waveguide, and the generated rf power is then subsequently extracted with a properly designed rf coupler. In the experiment, 30 MW of output power is excited by a 66 nC single electron bunch, and wakefield superposition by a train consisting of four bunches is also demonstrated. Both the results agree well with theoretical predictions.

To utilize the interaction between the field and the electron beam in a traveling wave tube （TWT）, the velocity of electrons and the longitudinal phase velocity of field should be made approximately equal. But when the electromagnetic energy increases, the electrons are slowed down and the synchronization condition is no longer satisfied in periodic structures. However, the varying-period slow-wave structure can be used to maintain the synchronization in the whole interaction section. This structure also has the advantages of space harmonic selectivity and wide bandwidth. The space harmonic in varying-period slow-wave structures is analyzed here. The synchronization condition of one space harmonic with the electron beam during the whole interaction process is presented in this paper. And the folded waveguide with varying period is analyzed as an example.

The coupled Helmhotz-type differential equations for a general cylindrical structure containing chiral material were transformed into a pair of decoupled equations, and this new set was solved to find expressions for Ez and Hz with the expansion of the complete eigen functions in elliptical chiralwaveguide. There are no pure TE （TM） or even-type （odd-type） modes existing individually in the elliptical structure if Ez and Hz are coupled with each other. The influences of eccentricity and chiral admittance on dispersion of modes are discussed in this paper.

In this article, dielectric photonic crystals (PhC) with finite dimensions and exposed in air is analyzed for its potential value in traveling wave tubes (TWTs). The modes existing in finite dielectric PhC are EH and HE, and also E if the finite PhC is two-dimensiond. The E1 mode is the E polarization in infinite dielectric PhC. Calculation shows that only the existence of gaps of pass-bands is necessary for PhC in TWTs, while the complete photonic crystal band gaps are superfluous.

The rectangular waveguide grating slow-wave structure (SWS) is a new type of RF system of millimeter traveling wave tube (TWT). However, it has narrow pass band. For the purpose of broadening the bandwidth of this circuit, it is necessary to study the influence of groove shapes on the characteristics. In this paper, the dispersion equation of a rectangular waveguide grating SWS with arbitrary grooves is derived by means of an approximate field-theory analysis, in which the continuous profile of the groove is approximately replaced by a series of steps, and the field continuity at the interface of two neighboring steps and the matching conditions at the interface between the groove region and the interaction region are ensured. The cold test on dispersion characteristics of a rectangular groove SWS shows that the theoretical results are in good agreement with the experimental results. We have calculated the dispersion characteristics and the coupling impedance of the slow-wave structures with some special groove shapes. It shows that the dispersion characteristics of the triangle-groove structure is the weakest and the coupling impedance of it is the lowest, while the dispersion characteristics of the inverted-trapezoid-groove structure is the strongest and the coupling impedance of it is the highest.