Abstract
The aim of this study is to quantify longitudinal resistive wall impedances, corresponding wake functions, and wake potentials for different accelerator machines of interest. Accurate calculations of wake potentials by particle-in-cell codes are extremely difficult for the investigated parameters; therefore, we use an analytical approach and consider large domains with fine discretization for the required numerical integrations. The semianalytical wake potential computations are benchmarked against numerical general purpose 2D/3D Maxwell solver software codes and a different analytical approach for a certain set of parameters. We report examples to illustrate limitations of wake potential estimations from coupling impedances, and computations for the machines using realistic beam parameters and machine conditions. A numerical example where the aim is to find the wake potential of the machine from the 5$\%$ noisy impedance data is given.
Highlights
In particle accelerators, the coupling impedance is used to define the electromagnetic interaction of the particle beam with its environment
The main physical components of the impedances are the space charge impedance, which is caused by the bunch distribution and resistive wall impedance which is related to the medium parameters of the wall
In this study we focus on the machine parameters of an accumulator ring such as those used at the Spallation Neutron Source (SNS), the synchrotron of the Japan Proton Accelerator Research Complex (JPARC), the booster rings of the CERN Proton Synchrotron (PS), the electron-cyclotron resonance ion source (ECR), and the GSI heavy-ion-synchrotron (SIS18), see [5, 10, 19,20,21,22]
Summary
The coupling impedance is used to define the electromagnetic interaction of the particle beam with its environment. In this study we omit the space charge impedance calculations and focus on the numerical evaluations of resistive wall impedance and wake representations which can be used for micrometer/millimeter length short bunches up to long bunches in order of meters, and can be applied to ultrarelativistic ( β ≈ 1 ) and low-β ( β ≈ 0.07 ) machines, with β = υ/c where υ is the beam velocity, c is the speed of light. A promising approach to compute the wake potential of circular cylindrical beam pipe structures in extreme conditions is based on fundamental analytical calculations In this manuscript we are interested in the calculation of the longitudinal monopole impedance Z|(|0) via the Al-khateeb et al.’s [7] approach, since this mode has a stronger accelerating or decelerating effect on the beam compared to the higher-order modes, and it is very relevant for our parameter space.
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