Theoretical And Simulation Study On Longitudinal Beam Intensity Effects In The Heavy Ion Accelerator HIAF/BRing

Booster Ring?BRing?is the key component of the High Intensity heavy-ion Accel-erator Facility?HIAF?,which is designed to supply beams with high intensity,such as78Kr¹⁹⁺(3×10¹¹particles per pulse?ppp?),²³⁸U³⁵⁺(1×10¹¹ppp),and proton(6×10¹²ppp).Thus it is important to study the longitudinal collective instabilities,which can lead to deterioration of beam quality and even lead to beam loss,during the design phase of the HIAF.In the BRing,magnetic alloy?MA?loaded cavities with low quality factor?value?will be employed to provide high acceleration voltage in limited space and cover wide frequency sweeps of the beams during acceleration.The impedance of the MA cavities,which is the main part of the longitudinal impedance in the BRing,will result in beam loading effects and coasting beam instabilities that have large influence on beam quality.The BRing have many characteristics compared to the other proton or heavy ion accelerators in the world.Firstly,the beam species,including almost all heavy ion beams from proton to Uranium,are complicated.Secondly,the beam states,includ-ing single bunch,multiple bunches,and coasting beams,are complicated.Thirdly,the manipulation of the beams is complicated including beam capture,acceleration,de-bunching,merging,and longitudinal compression.The main target of this thesis is to study the influence of longitudinal collective effects on the beams in the BRing includ-ing beam loading effects,coasting beam instabilities,and space charge effects.With the use of a self-developed code,Longitudinal Particle Tracking Code?LPTC?,the longitu-dinal collective effects are studied.Methods to compensate the effects or suppress the instabilities are also studied,which is the fundamental work for reducing the impact of the longitudinal collective effects during the design,construction,and commissioning phases of the BRing.In this thesis,longitudinal impedance in the BRing is analysed firstly.The basic theory of longitudinal beam dynamics including longitudinal collective effects is repro-duced and generalized to describe heavy ion beams.Then the manipulation of several typical beams,as well as the corresponding RF curves,are described.The study of longitudinal collective effects is based on these typical beams.Numerical methods are important tools to study the longitudinal collective effects.Thus the code LPTC is devel-oped to simulate the longitudinal beam dynamics in the BRing with complicated beam manipulation,beam states,and beam species.LPTC,which is optimized for heavy ion beams,can be used for calculating wake voltage induced by the impedance of cavities withvalues less than 0.5 in both frequency and time domains.LPTC is proved to be accurate and reliable with several benchmarks,and thus it can be used for simulating the longitudinal collective effects in the BRing.In the BRing,beam loading effects can cause potential well distortion which leads to the growth of momentum spread and bunch length of the beams by 111%and 119%,respectively.In the debunching-rebunching scenario of⁷⁸Kr¹⁹⁺beam,the growth of bunch length results in the decrease of transfer efficiency from the BRing to Spectrom-eter Ring?SRing?to 78.2%.In the merging scenario of⁷⁸Kr¹⁹⁺beam,couple-bunch effect appears when two bunches approach each other,which leads to the oscillation of bunch center after merging.In the longitudinal-compression scenario of²³⁸U³⁵⁺,the bunch length exceeds the design value.A multi-harmonic feedforward system is proposed to compensate the transient beam loading effects caused by the broadband impedance of the MA cavities.To compensate the beam loading effects,the feedfor-ward system should compensate at least 6 harmonic with the largest wake voltage of8.2 kV and frequencies of 0.29?3.2 MHz.Growth contours and the Keil-Schnell Cri-terion are used to study the coasting beam instabilities.The threshold of the RMSE value of momentum spread for the⁷⁸Kr¹⁹⁺coasting beam is 0.000375 which is larger than the momentum spread that can be obtained without the influence of wake.Thus the⁷⁸Kr¹⁹⁺beam is unstable and the growth rate is about 260 s^-1.The growth rate given by LPTC simulations is 274 s^-1,which agrees well with the theoretical calcula-tion.During the debunching stage,debunching time,debunching RF voltage curves,and the multi-harmonic feedforward system have large influence on the coasting beams obtained.With adiabatic debunching RF voltage,debunching time larger than 5 ms and harmonic current larger than 11 mA compensated by the feedforward system,a coasting beam with uniform distribution is obtained.The multi-harmonic feedforward system and MA cavities being short-circuited by switches in the acceleration gaps are better passive and active methods to suppress the coasting beam instabilities.The space charge effects have small influence on the beams except for the compression process of the²³⁸U³⁵⁺beam,during which short bunch length is desired.The bunch length increases by 5%with space charge effects,and thus RF voltage should be increased from 240 kV to 262 kV to compensate the space charge voltage.The acceleration sce-nario of proton beam is different from heavy ion beams because the proton beam will cross the transition energy during acceleration stage.To avoid beam loss before cross-ing the transition energy and carry out beam merging quickly,an acceleration scenario of merging bunches at low energy?500 MeV?with larger RF voltage and smaller RF phase is designed.With the use of transition energy ?_tjump,harmonic currents at h=1?25 compensated,and ?_toptimized to 7.5,influence of the longitudinal collective ef-fects are effectively reduced,which is the foundation for the subsequent study of proton beam dynamics.