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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.

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.

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.

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

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.

To determine the guide operating band, we derived the eigenvalue equations for a two dimensional photonic crystal rectangular waveguide, and found that the E(y), TEy, H(y) and TMy modes can exist in the photonic crystal rectangular waveguide. The calculation explains that this kind of waveguide can operate in single mode, if the height of the waveguide is low enough. And the bandwidth when the waveguide operates in single mode is determined by the cutoff frequency of the E(y)1 mode and that of the E(y)2 mode.

Application of ridged rectangular and circular waveguides has been found in many areas. In this paper，with the Rayleigh-Ritz method and polynomial representation，the wave propagation characteristics in the ridged elliptical waveguide are analyzed. The numerical results are in good agreement with calculation using electromagnetic field simulation software. The variation of bandwidth with physical dimensions has been studied. It is helpful for optimizing this kind of structure.

The sheath-helix model is used to analyze the helical slow-wave structure in which the helix turns are considered effectively shorted by the resistive coating on dielectric helix-support rods. Meanwhile, a gap is introduced to simulate the helix tape thickness, and the helix support rods are emulated by an effective dielectric tube and the difference of the radical propagation constant in different regions is taken into consideration. The dispersion equation and interaction impedance of arbitrary field modes are derived. On this basis, the effects of attenuation coating on the attenuation constant, phase constant and interaction impedance are discussed. The results presented here are useful for designing attenuator and improving the high-frequency characteristics of helical slow-wave structure as well as preventing the reflection oscillation and backward-wave oscillation of traveling-wave tubes.

Ion noise in output signal of klystrons was obtained by particle-in-cell method. The interactions between beam electron, ion, secondary electron and electromagnetic field are illustrated. The mechanism of ion noise is analyzed. It shows that phase fluctuation in output signal is caused by the change of the beam current DC velocity which is affected by the change of the amount of ions. The ion interacts with beam electron and has no equilibration state. The amount of secondary electrons is small and it has little effect on ion noise, but its behaviors reflect the process of ion noise. The amplitude fluctuation of output signal is caused by the change of beam velocity and beam radius. It is also affected by the ion behaviors.

In order to study 2D metallic photonic crystal, a new plane-wave expansion method was proposed. Based on traditional plane wave expansion method, the “original problem” to be solved was extended to a “new problem”. First, the relation between them were given, second, the “new problem” was transformed to an integral-differential eigen equation through an auxiliary function. The eigen equation was solved to obtain the band gap structures of the “new problem”. The band gap structures of the “original problem” were deduced according to “new problem”. Finally, numerical computations were done for 2D square-lattice square metallic rods photonic crystal, and excellent results were achieved.

The dispersion equation of a coaxial arbitrary-shaped-groove slow-wave structure 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 recta ngular steps，and the field continuity at the interface of two neighboring step s and the matching conditions at the interface between the groove region and central region are employed.The simulation results by CST MWS are in good agreement with the numerical calculation results of the dispersion equation.We have calculated the dispersion characteristics and the coupling impedance of the slo w-wave structures with some special groove shape.It shows that the dispersion c haracteristic of the triangle-groove structure is the weakest and the coupling i mpedance of it is the least, while the dispersion characteristic of the inverted -trapezoid-groove structure is the strongest and the coupling impedance of it is the largest.

The noise caused by ion relaxation oscillation becomes a research focus in the field of microwave tubes recently because of the improvement of radars and communications requirements. In this paper, electron beam is described by beam envelope equation, and ions generated from ionization of the background gas in microwave tubes are treated as discrete macro-particles. One dimensional Particle-in-Cell(PIC) simulation code was developed, and time series of ion relaxation oscillation are obtained by using the presented method. The ion relaxation oscillation is treated as the response of a complex nonlinear dynamical system, and the time series is analyzed by the power spectrum; the phase diagram and Lyapunov exponent are restructured. From the analysis results we find that the ion relaxation oscillation has a chaotic character. The reason of chaos was attributed to the dissipative Structure of the system. This would be useful for depressing relaxation oscillation and processing signals with relaxation oscillation noise.

Pulse shortening is an universal phenomenon in highpower microwave tubes, which hinders the improvement of microwave output energy. So far, it is also an unres olved problem in the field of high-power microwave devices. In this paper, the relativistic backward wave tube (RBWO) is treated as an example to study the pul se shortening phenomena. The influences of explosive emission in the inner surface of RBWO and fluctuation of the relativistic electron beam on the pulse width and output power are investigated by means of the particle in cell(PIC) method .Through the simulation results, some useful conclusions have been drawn. The explosive emission in the surface of the slow wave structure due to intense elec tric field is one of the most important factors causing pulse shortening in high-power microwave tube. The fluctuation of the electron beam can also lead to pulse shortening. Some methods to overcome pulse shortening are given in this paper.

The ridge-loaded helical traveling wave tube (TWT) is a new kind of high power millimeter wave device. The “hot” dispersion equation of this circuit loaded with an electronic beam is presented in this paper, and the Downhill method is used to solve the transcendental equation. The physical dimensions of a 474GHz ridge-loaded helical groove slow wave structure (SWS) with a 20kV electron beam are given and the investigations of the effect of the ridge dimensions and electron beam parameters on the small signal gain are carried out. It is indicated from the calculation results that this type of structure is suitable for use as s SWS of high power, high gain but narrow passband millimeter TWT, of which the 3dB gain bandwidth is 34%. In order to increase the bandwidth, the reduction of the ridge gap or the increase of the electron beam current in an allowable range may be useful. The presented analysis will be a guide to the design of this kind of traveling wave tube.