JACoW is a publisher in Geneva, Switzerland that publishes the proceedings of accelerator conferences held around the world by an international collaboration of editors.
TY - CONF AU - Mounet, N. AU - Dadiani, E. AU - Métral, E. AU - Rahemtulla, A. AU - Zannini, C. ED - Gianfelice, Eliana ED - Nagaitsev, Sergei ED - Kim, Dong Eon ED - Marx, Michaela ED - Schaa, Volker R. W. TI - Closed Form Formulas of the Indirect Space Charge Wake Function for Axisymmetric Structures J2 - Proc. of HB2021, Batavia, IL, USA, 04-08 October 2021 CY - Batavia, IL, USA T2 - ICFA Advanced Beam Dynamics Workshop on High-Intensity and High-Brightness Hadron Beams T3 - 64 LA - english AB - Indirect space charge contributes significantly to the impedance of non ultrarelativistic machines such as the LEIR, PSB and PS, at CERN. While general expressions exist in frequency domain for the beam coupling impedance, the time domain wake function is typically obtained numerically, thanks to an inverse Fourier transform. An analytical expression for the indirect space charge wake function, including the time dependence as a function of particle velocity, is nevertheless highly desirable to improve the accuracy of time domain beam dynamics simulations of coherent instabilities. In this work, a general formula for the indirect space charge wake function is derived from the residue theorem. Moreover, simple approximated expressions reproducing the time and velocity dependence are also provided, which can even be corrected to recover an exact formula, thanks to a numerical factor computed once for all. The expressions obtained are successfully benchmarked with a purely numerical approach based on the Fourier transform. PB - JACoW Publishing CP - Geneva, Switzerland SP - 65 EP - 70 KW - impedance KW - space-charge KW - vacuum KW - simulation KW - coupling DA - 2024/03 PY - 2024 SN - 2673-5571 SN - 978-3-95450-225-7 DO - doi:10.18429/JACoW-HB2021-MOP10 UR - https://jacow.org/hb2021/papers/mop10.pdf ER -