s-wave bound and scattering state wave functions for a velocity-dependent Kisslinger potential

A relation linking the normalized s-wave scattering and the corresponding bound state wave functions at bound state poles is derived. This is done in the case of a non-local, velocity-dependent Kisslinger potential. Using formal scattering theory, we present two analytical proofs of the validity of the theorem. The first tackles the non-local potential directly, while the other transforms the potential to an equivalent local but energy-dependent one. The theorem is tested both analytically and numerically by solving the Schr?dinger equation exactly for the scattering and bound state wave functions when the Kisslinger potential has the form of a square well. A first order approximation to the deviation from the theorem away from bound state poles is obtained analytically. Furthermore, a proof of the analyticity of the Jost solutions in the presence of a non-local potential term is also given. Received: 3 March 2001 / Accepted: 9 June 2001     

Far-field structural property of a Gaussian beam diffracted by a phase aperture

Based on the angular spectrum representation of an arbitrary electromagnetic beam and the method of stationary phase, an analytically vectorial structure of a Gaussian beam diffracted by a phase aperture has been derived in the far-field. Moreover, the derivation is performed without any approximation. The analytical expressions of the energy flux of the TE term, the TM term, and the apertured Gaussian beam are also presented in the far-field, respectively. The influence of the phase delay on the energy flux distributions of the TE term, the TM term, and the apertured Gaussian beam is discussed in the far-field.     

Study on transient beam loading compensation for China ADS proton linac injector Ⅱ

Significant transient beam loading effects were observed during beam commissioning tests of prototype II of the injector for the accelerator driven sub-critical(ADS) system, which took place at the Institute of Modern Physics, Chinese Academy of Sciences, between October and December 2014. During these tests experiments were performed with continuous wave(CW) operation of the cavities with pulsed beam current, and the system was configured to make use of a prototype digital low level radio frequency(LLRF) controller. The system was originally operated in pulsed mode with a simple proportional plus integral and deviation(PID) feedback control algorithm,which was not able to maintain the desired gradient regulation during pulsed 10 m A beam operations. A unique simple transient beam loading compensation method which made use of a combination of proportional and integral(PI) feedback and feedforward control algorithm was implemented in order to significantly reduce the beam induced transient effect in the cavity gradients. The superconducting cavity field variation was reduced to less than 1.7% after turning on this control algorithm. The design and experimental results of this system are presented in this paper.     

Beam lifetime measurement and analysis in Indus-2 electron storage ring

In this paper, the beam lifetime measurement and its theoretical analysis are presented using measured vacuum pressure and applied radio frequency (RF) cavity voltage in Indus-2 electron storage ring at 2 GeV beam energy. Experimental studies of the effect of RF cavity voltage and bunched beam filling pattern on beam lifetime are also presented. An equation of stable beam current decay is evolved and this equation closely follows the observed beam current decay pattern. It shows that the beam is stable and the beam current decay is due to the beam–residual gas interaction (vacuum lifetime) and electron–electron interaction within a bunch (Touschek lifetime). The estimated vacuum, Touschek and total beam lifetimes from analytical formulations are also compared with the measured beam lifetime.     

A uniform approximation for the eigenmodes of a planar dielectric waveguide

This paper derives a new approximation for the eigenmodes of a planar waveguide. The approximation is uniformly valid at both the high and low frequency regions of the dispersion relation. It is shown that a Pade approximation of the frequency equation leads to very accurate solutions. The new approximate solution is used to compute the frequency spectrum and the results compared with the exact analytical solution. The solutions presented here are ideal for analytically studying transient wave fields by means of modal summation.     

Vectorial structure of the far-field of an apertured four-petal Gaussian beam

Based on the theorem of vectorial structure and the method of stationary phase, an analytical vectorial structure of the far-field of an apertured four-petal Gaussian beam has been derived without any approximation. The analytical expressions of the energy flux of the TE term, the TM term, and the apertured four-petal Gaussian beam are also presented in the far-field reference plane, respectively. The energy flux distributions of the TE term, the TM term, and the apertured four-petal Gaussian beam are graphically demonstrated in the far-field plane. The dependences of the energy flux distributions of the TE term, the TM term, and the apertured four-petal Gaussian beam on the f-parameter, the truncation parameter, and the beam order are also examined.     

Resonant reflection of Bose-Einstein condensate by a double delta-function barrier within the Gross-Pitaevskii equation

Resonant reflection of a Bose-Einstein condensate by a double delta-function barrier has been considered analytically using the Gross-Pitaevskii approximation for nonlinearity. The reflection coefficient has been derived taking into account a weak nonlinearity of the Schrödinger equation produced by the interaction between cold alkali atoms. Nonlinear term is given in the limit of asymptotically weak interaction and zero temperature. The one-dimensional potential is approximated by two repulsive delta-function barriers. The analytical solution was obtained for the reflection coefficient using a multiple-scale analysis in order to remove secular terms. The most interesting case corresponds to the condensate energies for which reflection is absent without nonlinear term. Thus, reflection is determined only by the nonlinearity. The reflection coefficient is derived in the first order on the nonlinearity parameter.     

Analytic vectorial structure of circular flattened Gaussian beams

By means of the method of vector angular spectrum representation and the mathematical techniques, the analytically vectorial structure of the circular flattened Gaussian beam (CFGB) is derived without any approximation, which can be applicable to an arbitrary observation plane. In the far-field, the analytical formulae of the TE and the TM terms are further simplified using the method of stationary phase. The analytical expressions of the energy flux for the TE term, the TM term, and the CFGB are also presented. The energy flux distributions of the TE term, the TM term, and the CFGB are demonstrated in different reference planes, and the evolvement of the patterns of the TE term, the TM term, and the CFGB upon propagation are graphically illustrated.     

相对论速调管中间腔与调制电子束间的非线性互作用

在强流相对论电子束驱动的相对论速调管放大器中, 由于强流和高场强的影响, 尤其是中间腔具有高Q值, 微波腔与电子束之间的非线性作用很明显, 严重影响器件性能. 根据麦克斯韦方程组以及电子在微波场作用下运动方程给出了中间腔的束-波互作用自洽方程. 从这些方程出发, 研究了调制深度和调制频率对间隙电压幅度和相位的影响. 对比常规速调管的等效电路模型, 自洽公式给出的间隙电压幅值同粒子模拟结果更接近, 尤其是较高调制深度的情况. 同时器件带宽随调制深度的增加而变宽, 这也同粒子模拟结果一致. 由此设计了一个S波段高增益相对论放大器, 在LTD (长脉冲螺旋线)加速器上开展了相应的实验工作, 实验上获得了1.1 GW的输出功率, 器件增益49 dB. 关键词： 相对论速调管 非线性互作用 自洽方程     

Independent waves in complex source point theory

The full-wave generalization of the scalar Gaussian paraxial beam is determined by an analytical continuation of the field of a point source for the Helmholtz equation. The regions of validity of the analytically continued fields are investigated for the outgoing and the incoming waves. The two independent wave functions valid for the two half-spaces separating the secondary source plane are deduced.     

Analytically vectorial structure of an apertured Laguerre-Gaussian beam in the far-field

Based on the angular spectrum representation of an arbitrary electromagnetic beam and the method of stationary phase, an analytically vectorial structure of an apertured Laguerre-Gaussian beam in the far-field has been derived without any approximation. The analytical expressions of the energy flux of the TE term, the TM term, and the apertured Laguerre-Gaussian beam are also presented in the far-field, respectively. The energy flux distributions of the TE term, the TM term, and the apertured Laguerre-Gaussian beam are numerically demonstrated in the far-field reference plane. The influences of the f-parameter, the truncation parameter, the radial and angular mode numbers, and the dependent relation of angle on the energy flux distributions in the far-field of the TE term, the TM term, and the apertured Laguerre-Gaussian beam are also discussed in detail.     

2D Pauli Equation with Hulthén Potential in the Presence of Aharonov-Bohm Effect

The 2D Pauli equation with Hulthén potential for spin-1/2 particle in the presence of Aharonov-Bohm (AB) field is solved analytically, on the assumption that an effective approximation is used for the centrifugal term.Singular and regular solutions of the problem are obtained. It is shown that the AB field lifts the degeneracy of the energy levels. The range of the flux parameter for which singular solutions are allowed is modified compared to the pure AB case. When the screening parameter vanishes, it is shown that the obtained energy spectrum becomes the same as that of the Aharonov-Bohm Coulomb problem.     

The dynamic response of an inhomogeneous plasma diode to an appliedpotential drop

Recent measurements of the response to an applied step voltage in collisionless plasmas have demonstrated the importance of the initial ion density distribution for the resulting time evolution and the formation of electric double layers. The dynamic response of a plasma diode to an applied step voltage is studied by particle-in-cell simulations and an analytical model. It is shown that an ion-density cavity (a local ion-density minimum with a width of many Debye lengths) can support large potential drops for several electron transit times. The potential drop extends over a distance related to the cavity width. When the applied potential drop exceeds a certain critical value, which depends on the cavity depth, the drop instead concentrates in a cathode sheath, which also is the response obtained for homogeneous initial plasma. The existence regions for the two different response in the appropriate parameter plane are found from the simulations and shown to agree with the regions predicted analytically. The analytical potential profiles agree with those simulated     

Acoustical analysis of multiple cavities connected by necks in series with a consideration of evanescent waves

In this paper, a new analytical method was developed to obtain the natural frequencies and natural modes of multiple cavities connected by necks or slits in series, which strongly affect the longitudinal acoustic modes. At the interface between a cavity and a neck, discontinuity in the cross-sectional area generates an evanescent wave in addition to a plane wave. The evanescent wave with a set of cross-modes decays along a distance from the neck, but the evanescent wave forces length correction term to be added to the characteristic equation of the enclosure. Therefore, the effective length, instead of the physical length of the neck, is used in the characteristic equation. We examined the validity of the proposed method by using finite element analysis for five cases. We also investigated the effect of changing the neck's position on the acoustical characteristics and the relation between added length and natural frequency.     

Multiquadric Finite Difference (MQ-FD) Method and Its Application

The conventional finite difference (FD) schemes are based on the low order polynomial approximation in a local region. This paper shows that when the polynomial approximation is replaced by the multiquadric (MQ) function approximation in the same region, a new FD method, which is termed as MQ-FD method in this work, can be developed. The paper gives analytical formulas of the MQ-FD method and carries out a performance study for its derivative approximation and solution of Poisson equation and the incompressible Navier-Stokes equations. In addition, the effect of the shape parameter $c$ in MQ on the formulas of the MQ-FD method is analyzed. Derivative approximation in one-dimensional space and Poisson equation in two-dimensional space are taken as model problems to study the accuracy of the MQ-FD method. Furthermore, a lid-driven flow problem in a square cavity is simulated by the MQ-FD method. The obtained results indicate that this method may solve the engineering problem very accurately with a proper choice of the shape parameter $c$.     

Acceleration and focusing of intense ion beams in rf undulator structures

Bunching, acceleration, and transverse focusing of intense ion beams in an undulator linac are considered. Such an accelerator features the absence of an rf field harmonic synchronous with the beam. A 3D equation of motion in the Hamiltonian form is derived in the smooth approximation, and the general conditions for ion beam acceleration and transverse focusing in the undulator linac are formulated. Basic analytical results are compared with the results of numerical simulation of the beam dynamics in the polyharmonic field of an accelerating cavity.     

Propagation of elegant Hermite cosine Gaussian laser beams

In this paper, a more generalized beam containing an elegant Hermite Gaussian beam and a cosine Gaussian beam, which is called elegant Hermite cosine Gaussian (EHcoG) beam, is introduced and studied. The propagation properties of the EHcoG laser beams through a first-order paraxial optical system are demonstrated analytically and numerically. The recurrence propagation equations of the EHcoG beams through a first-order paraxial optical system with and without aperture are derived, from which the analytical propagation expression for EHcoG beams of any order can be obtained by means of the recursive procedures. The validity of the analytical results is confirmed by the numerical results.     

新型高功率径向强流速调管振荡器

 提出了一种新结构的高功率径向强流速调管振荡器,该器件利用折叠式同轴谐振腔的微波场与接近空间电荷限制电流的径向电子束强烈相互作用产生高功率微波。首先对这种器件的实现机理进行了初步的分析，提出了有间隙电压情况时的径向同轴间隙的空间电荷限制电流1维近似估计模型。分析表明：对于电子束直流接近但小于直流空间限制电流的径向速调管，当有调制间隙电压时，空间限制电流要小于无调制间隙电压情况下的直流空间限制电流，径向强流电子束电流接近和超过空间电荷限制电流时会出现强烈的调制。然后用PIC程序对其特性进行了粒子模拟，在二极管输入电压500 kV、电子束电流为30 kA条件下，最终得到了峰值功率6 GW、频率1.3 GHz的微波输出。     

Comparison of exact and mean beam length results for a radiating hydrogen plasma

The purpose of this work is to investigate the accuracy of the mean beam length technique in high-temperature radiative heat transfer, combined with other modes of heat transfer. In order to study the validity of the mean beam length method, Nusselt numbers are presented for fully developed channel flow of a radiating nonisothermal hydrogen plasma. Black isothermal boundaries are considered. Numerical results obtained from the exact integrodifferential equation have been obtained previously for this problem. Linearized radiation and local thermodynamic equilibrium are assumed.The results show that the Nusselt numbers obtained by using the geometric mean beam length are in close agreement with results obtained by using the mean beam length. Therefore the complicated calculations needed to obtain the mean beam length are unnecessary.A comparison of the results obtained in the present work with previously reported work shows that the mean beam length technique is a better approximation to the exact solution than the optically-thick, or nongray differential approximation solutions.     

Surface tension,shear viscosity and isothermal compressibility of liquid C60 along the liquid-vapour coexistence

The correlations between the surface tension, shear viscosity, and isothermal compressibility, are investigated for liquid C₆₀ at extended regions of temperature and pressure. An improved equation of state [EOS] is employed, based on hard-core plus three Yukawa potential [HC3YK] which facilitates the analytically accurate series mean spherical approximation [SMSA] formalism for the free energy. The present equation of state is utilized to obtain analytical expressions for the thermodynamic functions of interest and discuss the validity of their mutual relations along the spinodal curve of C₆₀.