Study on transient beam loading compensation for China ADS proton linac injectorⅡ

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 mA 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.

Study of the beam loading effect in the CSNS/RCS

The China Spallation Neutron Source/Rapid Cycling Synchrotron （CSNS/RCS） accelerates a high-intensity proton beam from 80 MeV to 1.6 GeV. Since the beam current and beam power is high, the beam loading is a severe problem for the stability of the circulating beam in the RCS. To study the beam loading effect in the CSNS/RCS theoretically, the RLC circuit model of the rf cavity, the method of Fast Fourier Transform and the method of Laplace transform have been employed to obtain the impedance of the rf system, the beam spectrum and the beam-induced voltage, respectively. Based on these physical models, the beam dynamics equations have been revised and a beam loading model has been constructed in the simulation code ORIENT. By using the code, the beam loading effect on the rf system of the CSNS/RCS has been investigated. Some simulation results have been obtained and conclusions have been drawn.

Analytical solution to the transient beam loading effects of a superconducting cavity

Transient beam loading is one of the key issues in any high beam current intensity superconducting accelerators, and needs to be carefully investigated. The core problem in the analysis is to obtain the time evolution of effective cavity voltage under transient beam loading. To simplify the problem, the second order ordinary differential equation describing the behavior of the effective cavity voltage is intuitively simplified to a first order one, with the aid of two critical approximations which lack proof of their validity. In this paper, the validity is examined mathematically in some specific cases, resulting in a criterion for the simplification. It is popular to solve the approximate equation for the effective cavity voltage numerically, while this paper shows that it can also be solved analytically under the step function approximation for the driven term. With the analytical solution to the effective cavity voltage, the transient reflected power from the cavity and the energy gain of the central particle in the bunch can also be calculated analytically. The validity of the step function approximation for the driven term is examined by direct evaluations.After that, the analytical results are compared with the numerical ones.

Optimization of the beam quality in ionization injection by a tailoring gas profile

A new scheme is proposed to improve the electron beam quality of ionization-induced injection by tailoring gas profile in laser wakefield acceleration.Two-dimensional particle-in-cell simulations show that the ionization-induced injection mainly occurs in high-density stage and automatically truncates in low-density stage due to the decrease of the wakefield potential difference.The beam loading can be compensated by the elongated beam resulting from the density transition stage.The beam quality can be improved by shorter injection distance and beam loading effect.A quasi-monoenergetic electron beam with a central energy of 258 MeV and an energy spread of 5.1%is obtained under certain laser-plasma conditions.

Shear deformable finite beam elements for composite box beams

The shear deformable thin-walled composite beams with closed cross-sections have been developed for coupled flexural, torsional, and buckling analyses. A theoretical model applicable to the thin-walled laminated composite box beams is presented by taking into account all the structural couplings coming from the material anisotropy and the shear deformation effects. The current composite beam includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Seven governing equations are derived for the coupled axial-flexural-torsional-shearing buckling based on the principle of minimum total potential energy. Based on the present analytical model, three different types of finite composite beam elements, namely, linear, quadratic and cubic elements are developed to analyze the flexural, torsional, and buckling problems. In order to demonstrate the accuracy and superiority of the beam theory and the finite beam elements developed by this study,numerical solutions are presented and compared with the results obtained by other researchers and the detailed threedimensional analysis results using the shell elements of ABAQUS. Especially, the influences of the modulus ratio and the simplified assumptions in stress-strain relations on the deflection, twisting angle, and critical buckling loads of composite box beams are investigated.

Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be non- linearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by com- paring them with results from previous studies and with a laboratory experiment.

Codimension-two bifurcation of axial loaded beam bridge subjected to an infinite series of moving loads

A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.

Limit Load Solution for Electron Beam Welded Joints with Single Edge Weld Center Crack in Tension

Limit loads are widely studied and several limit load solutions are proposed to some typical geometry of weldments.However,there are no limit load solutions exist for the single edge crack weldments in tension（SEC（T））,which is also a typical geometry in fracture analysis.The mis-matching limit load for thick plate with SEC（T） are investigated and the special limit load solutions are proposed based on the available mis-matching limit load solutions and systematic finite element analyses.The real weld configurations are simplified as a strip,and different weld strength mis-matching ratio M,crack depth/width ratio a/W and weld width 2H are in consideration.As a result,it is found that there exists excellent agreement between the limit load solutions and the FE results for almost all the mis-matching ration M,a/W and ligament-to-weld width ratio（W-a）/H.Moreover,useful recommendations are given for evaluating the limit loads of the EBW structure with SEC（T）.For the EBW joints with SEC（T）,the mis-matching limit loads can be obtained assuming that the components are wholly made of base metal,when M changing from 1.6 to 0.6.When M decreasing to 0.4,the mis-matching limit loads can be obtained assuming that the components are wholly made of base metal only for large value of（W-a）/H.The recommendations may be useful for evaluating the limit loads of the EBW structures with SEC（T）.The engineering simplifications are given for assessing the limit loads of electron beam welded structure with SEC（T）.

Discharge Characteristics of Large-Area High-Power RF Ion Source for Positive and Negative Neutral Beam Injectors

A large-area high-power radio-frequency（RF） driven ion source was developed for positive and negative neutral beam injectors at the Korea Atomic Energy Research Institute（KAERI）. The RF ion source consists of a driver region, including a helical antenna and a discharge chamber, and an expansion region. RF power can be transferred at up to 10 kW with a fixed frequency of 2 MHz through an optimized RF matching system. An actively water-cooled Faraday shield is located inside the driver region of the ion source for the stable and steady-state operations of high-power RF discharge. Plasma ignition of the ion source is initiated by the injection of argongas without a starter-filament heating, and the argon-gas is then slowly exchanged by the injection of hydrogen-gas to produce pure hydrogen plasmas. The uniformities of the plasma parameter,such as a plasma density and an electron temperature, are measured at the lowest area of the driver region using two RF-compensated electrostatic probes along the direction of the shortand long-dimensions of the driver region. The plasma parameters will be compared with those obtained at the lowest area of the expansion bucket to analyze the plasma expansion properties from the driver region to the expansion region.

A phenomenological model of the fundamental power coupler for a superconducting resonator

In this study,a phenomenological model of the radio frequency(RF)behavior of a superconducting cavity fundamental power coupler is proposed by analyzing the simulation results of a transient beam-loading process in an extremely overcoupled superconducting cavity.Using this phenomenological model,the calculation of the transient reflected power from a superconducting cavity under beam loading can be mathematically simplified to algebraic operations without solving the differential equation governing the transient beam-loading process,while maintaining the calculation accuracy.Moreover,this phenomenological model can facilitate an intuitive understanding of the significant surge in the time evolution of reflected power from a superconducting cavity in certain beam-loading processes.The validity of this phenomenological model was carefully examined in various beam-loading processes and cavity conditions,and the method based on this phenomenological model was utilized in the transient RF analysis of the superconducting cavity system of the CAFe Linac,achieving satisfactory results.

Cavity fundamental mode and beam interaction in CEPC main ring

Background CEPC is a 100-kilometer-long electron-position collider,aiming to produce Higgs,W and Z-pole.Double ring(DR)is the baseline design of its main ring,and advanced partial double ring(APDR)is the alternative one.Purpose The purpose of this paper is to study the beam loading effects and the corresponding longitudinal beam dynamics of CEPC DR and APDR.Methods The phase shift of the bunches modulated by the bunch gap is calculated with the approximation formulas and simulated with the program.All these methods are compared,and the application conditions of them are also elaborated.In addition,the longitudinal coupled-bunch instability in CEPC main ring is calculated by analytical formulas.Results In CEPC DR high-lumi Z,the phase shift can be reduced to 0.51 deg(°).Besides,the total number of unstable longitudinal modes is 15 in CEPC DR high-lumi Z when no feedback system is added.Conclusion The phase shift of the bunches in CEPC can be reduced to an acceptable value if the optimal filling pattern is chosen.For CEPC APDR,the RF parameters are calculated and the beam loading effects are tolerable.

Closed-form solution of beam on Pasternak foundation under inclined dynamic load

The dynamic response of an infinite Euler–Bernoulli beam resting on Pasternak foundation under inclined harmonic line loads is developed in this study in a closed-form solution.The conventional Pasternak foundation is modeled by two parameters wherein the second parameter can account for the actual shearing effect of soils in the vertical direction.Thus,it is more realistic than the Winkler model,which only represents compressive soil resistance.However,the Pasternak model does not consider the tangential interaction between the bottom of the beam and the foundation;hence,the beam under inclined loads cannot be considered in the model.In this study,a series of horizontal springs is diverted to the face between the bottom of the beam and the foundation to address the limitation of the Pasternak model,which tends to disregard the tangential interaction between the beam and the foundation.The horizontal spring reaction is assumed to be proportional to the relative tangential displacement.The governing equation can be deduced by theory of elasticity and Newton’s laws,combined with the linearly elastic constitutive relation and the geometric equation of the beam body under small deformation condition.Double Fourier transformation is used to simplify the geometric equation into an algebraic equation,thereby conveniently obtaining the analytical solution in the frequency domain for the dynamic response of the beam.Double Fourier inverse transform and residue theorem are also adopted to derive the closed-form solution.The proposed solution is verified by comparing the degraded solution with the known results and comparing the analytical results with numerical results using ANSYS.Numerical computations of distinct cases are provided to investigate the effects of the angle of incidence and shear stiffness on the dynamic response of the beam.Results are realistic and can be used as reference for future engineering designs.

Location estimating of load for bending beam

We propose a method by which location of load for bending beam can be approxi- mately retrieved by matching the measured and theoretically forecasted displacement distribu- tion. To show the method validity, a principal experiment is performed.

Suppression of longitudinal coupled-bunch instabilities with RF feedback systems in CEPC main ring

Background Circular electron positron collider(CEPC)is a 100-km electron positron collider proposed by IHEP.The longitudinal coupled-bunch instability(LCBI)of CEPC main ring operating to study the Z particle(Z machine)may be a limiting factor of CEPC and needs to be considered seriously.Purpose The purposes of this paper are to calculate the LCBI caused by the fundamental mode of superconducting RF cavities in CEPC main ring,which is the most critical impedance,and to complete the design of the RF feedback systems suitable for CEPC,whose specifications can suppress the LCBI to a manageable level.Methods The LCBI growth rate in the CEPC main ring is calculated in the frequency domain.Two kinds of RF feedback,i.e.,direct feedback and one-turn delay feedback,are simulated with the program to suppress the LCBI.And according to the suppression effect of LCBI growth rate after adding RF feedback,the required design parameters are given.Results Two operation conditions of Z machine have severe LCBI without suppression,and dozens of longitudinal modes are unstable.Only the direct RF feedback is needed to suppress LCBI in the case of Z-30 MW,while both the direct RF feedback with maximum gain and one-turn feedback are needed in the case of Z-50 MW.The LCBI growth rates can be reduced to the order of half frequency of the synchronous oscillation.Conclusion The LCBI of CEPC Z machine has been studied.Selecting appropriate feedback RF feedback can reduce the LCBI to an acceptable value that bunch by bunch feedback can suppress.

Physical design of a 10 MeV LINAC for polymer radiation processing

In China, polymer radiation processing has become one of the most important processing industries. The radiation processing source may be an electron beam accelerator or a radioactive source. Physical design of an electron beam facility applied for radiation crosslinking is introduced in this paper because of it’s much higher dose rate and efficiency. Main part of this facility is a 10 MeV travelling wave electron linac with constant impedance accelerating structure. A start to end simulation concerning the linac is reported in this paper. The codes Opera-3d, Poisson-superfish and Parmela are used to describe electromagnetic elements of the accelerator and track particle distribution from the cathode to the end of the linac. After beam dynamic optimization, wave phase velocities in the structure have been chosen to be 0.56, 0.9 and 0.999 respectively. Physical parameters about the main elements such as DC electron gun, iris-loaded periodic structure, solenoids, etc, are presented. Simulation results proves that it can satisfy the industrial requirement. The linac is under construction. Some components have been finished. Measurements proved that they are in a good agreement with the design values.

Tracking code simulation for passive harmonic cavity in the SSRF storage ring

Background A passive third harmonic cavity is planned to install in the Shanghai Synchrotron Radiation Facility(SSRF)storage ring to increase the beam lifetime.Transient beam loading effect generated by the gap between the bunch trains can suppress the bunch lengthening effect of the third harmonic cavity.Besides,the field excited in the passive operation of the harmonic cavity depends on the bunch distribution.Purpose To estimate the effect of transient beam loading,the tracking codes have been developed.Methods The tracking simulation has been performed for three uniform filling cases and a nonuniform filling case.The lengthened bunch distribution has also been included into tracking code simulation.The effect of the lengthened bunch has also been investigated.Results The uniform filling pattern with shorter bunch trains shows lower transient beam loading effect and can give much higher bunch lengthening factors compared to those of non-uniform filling case.The effect caused by the reduction of the harmonic voltage generated by lengthened bunch distribution causes a great reduction on bunch lengthening effect in uniform filling case,while the lengthening factor of non-uniform filling case does not affect much in this issue.Conclusion The tracking codes have been developed to estimate the effect of transient beam loading for three uniform filling cases and a non-uniform filling case.The larger gap in the filling pattern can cause the higher transient beam loading effect and lower bunch lengthening effect.The lengthened bunch distribution has also been included into tracking code simulation.The effect of the lengthened bunch has also been investigated.The more the bunch is lengthened,the greater reduction on bunch lengthening effect.

Frequency tuning with RFQ temperature in China ADS Injector Ⅱ

A 162.5 MHz four-vane radio frequency quadruple（RFQ） accelerator has been developed at the Institute of Modern Physics（IMP） for Injector II of the China ADS linac. The RFQ will operate in continuous wave mode at 100 k W. For the designed 10 mA beam, the additional RF power dissipation will induce a very large reflection of power. A water-temperature controlling system will be used to reduce the power reflection by tuning the frequency of the RFQ. The tuning capability of the water temperature is studied under different configurations of cooling water.Simulations and experiment are compared in this paper. The experimental results agree well with simulation using ANSYS. This can be used as a reference to tune the RFQ in beam commissioning.