The Theoretical And Simulation Study On The Transverse Collective Instabilities In The HIAF/BRing

Booster Ring(BRing)which is the main accelerator in the High Intensity heavy ion Accelerator Facility(HIAF)can accelerate high intensity beams with a wide range of heavy ion species from proton to uranium(proton 2 × 1012 ppp,Kr19+ 3 × 1011 ppp,U34+ 1× 1011 ppp).The research on the transverse collective instabilities stimulated by the coupling impedances plays a significant role in reaching the required intensity or keeping the high beam quality in the BRing.It is also the fundamental work for the design of octupole magnets for Landau damping or feedback systems.Compared with other accelerator facilities,like colliders,synchrotron light sources or spallation neutron sources,the operations are very complicated in the BRing.So,three transverse dipole collective instabilities should be analyzed under proton and heavy ion operation modes with complicated beam manipulations,which is also very complex.In this thesis,the Vlasov mode approach and the numerical approach for these transverse dipole collective instabilities are studied.A code,named Simulation Platform for Collective Instabilities(CISP)is developed in order to simulate all these instabilities.Both two methods are used to analyze the transverse collective instabilities in the BRing with three typical beams including proton beam,Krl9+ beam and U34+ beam.Firstly,Vlasov mode approach is employed in this thesis to study the frequency shifts due to transverse dipole collective instabilities under a general condition in the proton and heavy ion beams.And the general method of analyzing transverse dipole collective instabilities in the proton and heavy ion beam is reproduced.Meantime,based on the general results,the thresholds or growth rates of transverse mode-coupling insta?bility,transverse coupled-bunch instability and transverse unbunched beam instability have been obtained and they are used in the calculations with the parameters of the BRing.The Vlasov mode approach shows that transverse mode-coupling instability can limit the intensity of the proton beam to 8 x 1011 ppp which is much less than the required intensity 2 × 1012 ppp.However,the Kr19+ beam and the U34+ beam are not influenced by this instability.The growth times of transverse coupled-bunch instabil-ity and transverse unbunched beam instability are less than the corresponding duration times,which shows that both two transverse collective instabilities can influence all typical beams.As to the numerical approach,there are some codes for several specific transverse collective instabilities in some heavy ion beams,but no one for all these instabilities.They cannot cover all transverse collective instabilities in the BRing.In this thesis,the numerical models for wake,6D tracking,nonlinear magnets and space charge are studied.And with these numerical models,the simulation code CISP is developed.It can simulate all these transverse collective instabilities now.CISP simulations show that the intensity of the proton beam is limited to 6 x 1011 ppp by transverse mode-coupling instability.And transverse coupled-bunch instability can introduce the beam loss which is about 95%in the Kr19+ beam and increase the normalized emittance of the proton beam and the U34+ beam by 3?4 times.Besides,transverse unbunched beam instability can also increase the normalized emittance of the three typical beams by about 40%.With the comparisons,simulation results and theoretical results agree with each other,which tests the validity of both two methods.How to stabilize these transverse dipole collective instabilities is also an important issue.In this thesis,the stabilization from chromaticity,octupole magnets and feed-back systems is discussed.The difference of physics among different methods is also analyzed.The research shows that chromaticity-0.04 can stabilize the transverse mode-coupling instability in the BRing very well.And chromaticity-2,an octupole magnet whose integral strength is 1.8 m-3 or a bunch-by-bunch feedback system can stabilize transverse coupled-bunch instability very easily.However,for transverse unbunched beam instability,introducing a feedback system with large bandwidth is the best way to stabilize it.This research is the fundamental work for the design of the stabilization systems related to these transverse dipole collective instabilities.