The design and performance of a magnetron-injection gun

The space-charge flow solutions described by Kino and others in connection with the crossed-field carcinotron gun can be generalized to form the basis of a magnetron-injection gun design suitable for the production of hollow electron beams. In the first part of the paper this generalization is described. From the resulting flow it is possible to determine by an approximate method the electrodes to produce a gun of desired perveance with nearly uniform current density at the cathode. This technique has been used to design guns having ratios of cathode length to a diameter considerably greater than unity. The close agreement between the results obtained on several experimental guns and the theoretical predictions is described, along with the effect of departures from the prescribed fields given by the design method.     

A Method for the Calculation of the Radiation-Pattern and Mode-Conversion Properties of a Solid-State Heterojunction Laser

A solution of the laser fields, both inside and outside the laser, is given in terms of the mode-conversion coefficients and an integral equation for the radiation pattern. It is shown how very accurate analytic solutions can be obtained by what, at first sight, appear to be extremely crude approximations. The reason is that mode conversion is taken implicitly into account by using a multiplier, whose exact form does not appear to be very critical, as a weighting function to average two different formulas for the function representing the radiation; and with the correct form for it, all the mode-conversion and reflection coefficients can be legitimately ignored. A plane-wave formula for this multiplier is a good first approximation, and a number of existing expressions occurring in the literature are obtained in this way. It is also shown rigorously that the results of an earlier obliquity-factor analysis apply. Further refinements are introduced to allow for higher order discrete modes, and good approximate analytic forms for the mode-reflection and conversion coefficients are obtained. A check with a rather extreme example shows excellent agreement with Ikegami's numerical computation for the dominant-mode reflection at the laser-air interface. The methods of this paper are applicable to general laser structures of cylindrical geometry with either continuous or discontinuous variations in refractive index. Very accurate numerical solutions should be obtainable after only one iteration of the integral equation, starting with the reflection-modified form of Hockham's formula as initiating function.     

基于FlexPDE的二维PSD数值分析

描述位置敏感探测器(PSD)的Lucovsky方程在一定简化条件下可求得解析解.提出了利用有限元分析软件FlexPDE对非简化Lucovsky方程进行二维区域数值求解的方法,并对四边型PSD进行了分析,结果表明该方法能够准确地分析二维PSD的光电特性,比解析法有更强的适应性.     

Electron Gun for Powerful Short Pulse Gyrotron with Operating Magnetic Field 8 T

High power short pulse gyrotron with operating frequency 395 GHz operating on the second cyclotron harmonic is now under developing at FIR FU. The gyrotron is planned to use in future experiments for plasma diagnostics. For this purpose the output power about 100 kW and pulse duration 100 ns at least are needed. Preliminary estimations of parameters of some versions of the electron guns with accelerating potential U_0?=?70-100 kV were performed. Possibilities of non-adiabatic as well as adiabatic guns were considered. It was shown that non-adiabatic system is not reliable for such rather low value of U₀, the adiabatic magnetron injection gun (MIG) is more preferable for the gyrotron design. Analytical estimations of the suitable MIG dimensions and operating regime to form good quality electron beam were fulfilled. Numerical optimization of the gun shape and position was performed. It was shown that in spite of the extremely big ratio of the operating current (I_0?=?18 A) to the Langmuir current of the gun, close to 0.4-0.5, the suggested MIG can form the helical electron beam (HEB) which is suitable for gyrotron operation properties.     

A simplified 2-D analytic model for the threshold-voltage of fullydepleted short gate-length Si-SOI MESFET's

We present a simplified form of the exact solution of the 2-D Poisson equation of fully depleted Si-SOI MESFET's by Hou and Wu (1995). The major improvement is that the Fourier coefficient of the electric displacement at the Si-SiO₂ interface is given in (finite) closed form, rather than infinite series. Their 2-D analytic model for the threshold-voltage can be simplified accordingly     

FIR digital filters with simultaneous conditions on amplitude and delay

A general analytic technique is given for the design of FIR digital filters with simultaneous conditions on both the amplitude and delay responses. It is shown that phase linearity can be maintained only within the passband, resulting in increased amplitude selectivity as compared with filters with exact linear phase at all frequencies.     

双传感器概率假设密度滤波解析实现方法

针对双传感器概率假设密度(PHD)理论的解析实现进行研究。Mahler给出的双传感器PHD理论,由于其中含有抽象的多目标积分,并且其中的二元分割过程计算量十分巨大,所以无法计算机实现。文中在线性高斯混合的假设条件下给出了严格双传感器PHD滤波的递推解析公式,并且通过提出“有效二元分割”算法极大降低了严格理论意义下的双传感器PHD算法的计算复杂度,从而解决了双传感器PHD滤波的计算实现问题。计算机模拟仿真验证了所提出算法的有效性。     

A new simplified charge pumping current model and its modelparameter extraction [MOSFET]

Using the Shockley-Read-Hall (SRH) theory, a simple analytic charge pumping current model has been developed and its accuracy verified by exact numerical analysis. It is shown that the derived analytic charge pumping current model with constant capture cross sections for electrons and holes does not correctly simulate the rising (falling) edges of the experimental charge pumping current. According to the slopes of the logarithmic charge pumping current, effective capture-cross-section models for elections and holes are proposed and are incorporated into the developed analytic charge pumping current model. It is shown that the experimental charge pumping current can be simulated very well by using the modified analytic model     

Time-Domain Analysis of a Lossy Nonuniform Transmission Line

An analytical solution of the coupled Telegrapher's equations for the voltage and current on a homogeneous lossy transmission line is presented. The resulting expression is obtained in the form of an exact time-domain propagator operating on the line voltage and current. It is shown that an application of Simpson's rule yields a simple accurate numerical representation of the propagator that can be used to analyze both homogeneous and inhomogeneous transmission lines. Numerical dispersion in lossy media is examined proving that this method has no numerical dispersion.      

Slow-Scale Instability of Single-Stage Power-Factor-Correction Power Supplies

This paper reports slow-scale instability in a single-stage power-factor-correction (PFC) power supply, which is a popular design solution for low power applications. The circuit employs a cascade configuration of a boost converter and a forward converter, which share an active switch and operate in discontinuous-conduction mode (DCM), to provide input PFC and tight output regulation. Main results are given by "exact" cycle-by-cycle circuit simulations. The effect of the slow-scale instability on the attainable power factor is illustrated in terms of total harmonic distortion which can be found by taking the fast Fourier transform of the input current. The slow-scale instability usually manifests itself as local oscillations within a line cycle. Based on the critical condition of DCM for the buck converter, the underlying mechanism of such instability is further investigated. It has been found that border collision is the underlying cause of the phenomenon. Moreover, it has been shown that the border collision observed here is effectively a nonsmooth Neimark-Sacker bifurcation. Finally, experimental results are presented for verification purposes.     

On simple methods for calculating ELF shielding of infinite planar shields

Simple approximate methods are developed and described for calculating the extremely low-frequency magnetic-shielding effectiveness for single- and double-layer infinite planar shields. In addition, exact expressions are given and "nearly exact" expressions are derived. Each expression has been compared to the exact expression in order to determine the range of parameters over which it is valid. Each approximate expression can be calculated rapidly and has a simple physical interpretation that leads to physical insight into the shielding process.     

Direct synthesis of crossed-field electron guns—A novel gun for producing Brillouin flow

A direct approach to the synthesis of crossed-field electron guns is presented. An iterative approximation to the desired beam form is achieved by application of the paraxial ray equation alternatively solving for potential and curvature along the beam while maintaining certain end-point conditions and the desired convergence pattern. When sufficient accuracy is obtained, polynomial approximations are used to express shapes of the trajectories and the electric fields along the beam edges in analytic form. The electrodes to produce the necessary electric fields along the beam edges are calculated by Kirstein's method. A conformal transformation is used to transform the beam edge into the real axis of a complex plane and analytic continuation of a suitable complex potential function is employed to find equipotential lines. These are transformed back into the plane of real coordinates and are surfaces along which electrodes can be placed. A novel short gun which produces a Brillouin beam has been designed using the iterative approach. The availability of beam curvature as a variable has made it possible to find an electrode system which controls the transition from the cathode-region flow characteristics used in Kino's short gun to a drift Brillouin beam. Detailed experimental evaluation of the gun reveals that the beam characteristics are in good agreement with those predicted theoretically.     

Dynamic Flow Control in Store-and-Forward Computer Networks

In a recent paper we presented an analysis of flow control in store-and-forward computer communication networks using a token mechanism. The analysis assumed equilibrium conditions for a selected set of system parameters which were not dynamically adjusted to stochastic fluctuations in the system load; this mechanism was referred to as "static flow control." In this paper we study a "dynamic flow control" in which parameters of the system are dynamically adjusted to match the availability of resources in the network. Based on Markov decision theory, an optimal policy to dynamically select the number of tokens is formulated. Because an exact solution to the problem is extremely difficult, an effective heuristic solution to the problem is presented. Numerical results are given and it is shown that the throughput-delay performance of a network is better with dynamic control than with static control.     

Experiments with a new type adiabatic crossed-field gun

In this paper experiments with a "long" crossed-field gun, designed by a method given by Kino, are described. This gun yielded the predicted value of current, but the other characteristics of the beam were not in accordance with the results of the theory. Experiments were carried out from which it may be concluded that there are RF instabilities present in the beam, instabilities which grow in the drift region and are generated at the cathode. The rate of growth of these instabilities is of the same order as the rate of growth of RF fields given by the theory of McFarlane and Hay.     

The design and performance of grid-controlled, high-perveance electron guns

The focusing electrode and a probe projecting through the cathode serve as control electrodes for the current from a convergent-beam electron gun. The principal advantage of this type of "grid" is that there is no interception of the high-current-density beam by the probe-grid. This paper presents the design procedure and experimental results for typical probe-gridded guns. The design procedure is used to obtain the desired perveance, beam diameter, and approximate laminar electron flow. The probe geometry that results in a minimum beam distortion is discussed. The range of values of amplification factor obtainable and the influence of probe geometry on this factor are discussed. The magnetic field required for focusing the beam from a probe-gridded gun is compared with that required for perfect laminar flow and for focusing the beam from a nongridded gun of similar design. An electrolytic tank in conjunction with an analog computer was used to plot electron trajectories, with the effect of space charge included, for the probe-gridded gun and a similar nongridded gun. A comparison of the electron optics of the gridded and nongridded gun is made. Electrical breakdown and beam current during the interpulse time are problems considered. Methods used to minimize electrical breakdown and interpulse beam current are presented. Several models of probe-gridded guns were constructed. The measured characteristics of these guns demonstrate that the advantages of grid control can be obtained with only a minor effect on gun perveance and beam focusing.     

Testing of geometrized models of 2D electron beams

Geometrized models of a dense electron beam are tested using two sets of references: solutions with multiplicative separation of variables and analytic solutions with additive separation of variables. The effectiveness of the geometrized approach for describing nonparaxial flows with the nonuniform distribution of parameters over the cross section is demonstrated. Models are considered in which the length of the base current tube or the potential plays the role of the longitudinal coordinate. The effect of remarking the transverse coordinate, which determines the geometry of the current tube, is studied. The asymptotic theory is compared with the first-approximation geometrized theory. It is shown that each exact axially symmetric solution to the equations of a beam in elementary functions corresponds to the exact solution to the equation for a tubular beam in the asymptotic theory. For optimal utilization of possibilities of the geometrized approach, it is proposed to use the value of discrepancy as a criterion oor accuracy.     

An application of the boundary element method to the magnetic fieldintegral equation

A boundary element method (BEM) for the solution of electromagnetic scattering problems using the magnetic field integral equation (MFIE) is discussed. The discretized form of the MFIE is written in indicial notation with no limitations placed on the order of either the geometric or functional approximation. By considering several different types of boundary elements, it is determined that geometric errors can be significant and degrade the accuracy of the numerical solution. It is shown that a higher-order approximation for the current could significantly improve the accuracy of the numerical solution. The superparametric boundary element in which the geometry was given quadratic approximation and the current was given linear approximation was more efficient than elements using lower-order approximations. The BEM results are compared to the results obtained using the dielectric bodies of revolution (DBR) code     

广义变系数Burgers-Kadomtsev-Petviashvili方程的自B?cklund变换和精确解析解

应用Painlevé分析法研究了广义变系数Burgers-Kadomtsev-Petviashvili方程。结果显示该方程不具有Painlevé性质。通过截断的Painlevé展开方法，在条件 ( 为任意常数)下, 得到了该方程的自B?cklund变换。基于自B?cklund变换，给出了一些新的解析解如多孤子解和周期解。     

Space-charge recombination in a forward-biased diffused p-n junction

Exact numerical solutions have been obtained for a practical diffused-junction silicon diode at forward-bias voltages such that the current through the diode is mainly governed by space-charge recombination. A comparison has been made of these solutions with the analytical solutions based on the representation of the diffused junction by a linearly-graded junction. It is shown that, as applied to the linearly-graded junction, the Sah-Noyce-Shockley theory of space-charge recombination, which assumes a linear electrostatic potential variation across the space-charge region, gives closed-form solutions which agree to within 40 per cent with the exact numerical solutions over the range of bias voltages considered. Considerably better agreement, to within 15 per cent, can be obtained, however, by employing in the calculation of the recombination rate, an improved electrostatic potential distribution resulting from the first iteration of the linearized Poisson's equation as given in Sah's linearly-graded-junction theory. In this case, the solution for the recombination current is no longer available in closed form; however, it can be readily obtained by a simple numerical integration.     

An improved design theory of a magnetron-injection gun

An improved design theory of a magnetron-injection gun is presented, which is based on a "constant radius" approximation. This theory derives a correction term to be added to the solution of Kino-Taylor's planar theory. It is found that, within the adopted approximation, the only correction necessary to Kino-Taylor's theory is to take into account the effect of the centrifugal force. The corrected electron trajectories and the corrected electrode shapes are shown for specific examples.