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Register a new userAnalytical Solution to the Transient Beam Loading Effects of the Superconducting Cavity
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Transient beam loading effect is one of the key issues in any superconducting accelerators, which needs to be carefully investigated. The core problem in the analysis is to obtain the time evolution of cavity voltage under the transient beam loading. To simplify the problem, the second order ordinary differential equation describing the behavior of the cavity voltage is intuitively simplified to a first order one, with the aid of the two critical approximations lacking the proof for their validity. In this paper, the validity is examined mathematically in some specific cases, resulting in a criterion for the simplification. Its popular to solve the approximated equation for the 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 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.
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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 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 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 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.
The fast beam-ion instability (FII) is caused by the interaction of an electron bunch train with the residual gas ions. The ion oscillations in the potential well of the electron beam have an inherent frequency spread due to the nonlinear profile of the potential. However, this frequency spread and associated with it Landau damping typically is not strong enough to suppress the instability. In this work, we develop a model of FII which takes into account the frequency spread in the electron beam due to the beam-beam interaction in an electron-ion collider. We show that with a large enough beam-beam parameter the fast ion instability can be suppressed. We estimate the strength of this effect for the parameters of the eRHIC electron-ion collider.
We report on the experience with long-range beam--beam effects in the LHC, in dedicated studies as well as the experience from operation. Where possible, we compare the observations with the expectations.
During the proton-anti proton collider run several experiments were carried out in order to understand the effect of the beam-beam interaction on backgrounds and lifetimes. In this talk a selection of these experiments will be presented. From these experiments, the importance of relative beam sizes and tune ripple could be demonstrated.
We first introduce the design parameters of the Beijing Electron-Positron Collider II (BEPCII) and the simulation study of beam-beam effects during the design process of the machine. The main advances since 2007 are briefly introduced and reviewed. The longitudinal feedback system was installed to suppress the coupled bunch instability in January 2010. The horizontal tune decreased from 6.53 to 6.508 during the course of data taken in December, 2010. The saturation of the beam-beam parameter was found in 2011, and the vacuum chambers and magnets near the north crossing point were moved 15 cm in order to mitigate the long range beam-beam interaction. At the beginning of 2013, the beam-beam parameter achieved 0.04 with the new lower $alpha_{p}$ lattice and the peak luminosity achieved 7 x 10$^{32}$ cm$^{-2}$ s$^{-1}$.
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