Quantification of resistive wall instability for particle accelerator machines

The aim of this study is to quantify longitudinal resistive wall impedances, corresponding wake functions, andwake potentials for different accelerator machines of interest. Accurate calculations of wake potentials by particle-in-cellcodes are extremely difficult for the investigated parameters; therefore, we use an analytical approach and consider largedomains with fine discretization for the required numerical integrations. The semianalytical wake potential computationsare benchmarked against numerical general purpose 2D/3D Maxwell solver software codes and a different analyticalapproach for a certain set of parameters. We report examples to illustrate limitations of wake potential estimations fromcoupling impedances, and computations for the machines using realistic beam parameters and machine conditions. Anumerical example where the aim is to find the wake potential of the machine from the 5% noisy impedance data isgiven.

PDF

___

[1] Zotter BW, Kheifets SA. Impedances and Wakes in High Energy Particle Accelerators. Singapore: World Scientific, 1998.
[2] Boine-Frankenheim O, Gjonaj E, Petrov F, Yaman F, Weiland T et al. Energy loss and longitudinal wakefield of relativistic short proton bunches in electron clouds. Physical Review Special Topics-Accelerators and Beams 2012; 15 (5): 054402. doi: 10.1103/PhysRevSTAB.15.054402
[3] Laslett LJ, Neil VK, Sessler AM. Transverse resistive instabilities of intense coasting beams in particle accelerators. Review of Scientific Instruments 1965; 36 (4): 436-448. doi: 10.1063/1.1719595
[4] Gluckstern RL. Analytic Methods for Calculating Coupling Impedances 2000-011. Meyrin, Switzerland: CERN, 2000.
[5] Zimmermann F, Oide K. Resistive wall wake and impedance for nonultrarelativistic beams. Physical Review Special Topics-Accelerators and Beams 2004; 7 (4): 044201. doi: 10.1103/PhysRevSTAB.7.044201
[6] Zimmermann F, Oide K. Resistive wall wake and impedance for non-ultrarelativistic beams. In: Particle Accelerator Conference (PAC 2003); Portland, OR, USA; 2003. pp. 2604-2606.
[7] Al-Khateeb AM, Boine-Frankenheim O, Hofmann I, Rumolo G. Analytical calculation of the longitudinal space charge and resistive wall impedances in a smooth cylindrical pipe. Physical Review E 2001; 63 (2): 026503. doi: 10.1103/PhysRevE.63.026503
[8] Mounet N. The LHC transverse coupled-bunch instability. PhD, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, 2012.
[9] Quatraro D, Rumolo G. Non relativistic resistive wall wake fields and single bunch stability. In: 23rd Particle Accelerator Conference (PAC09); Vancouver, BC, Canada; 2009. pp. 3217-3219.
[10] Quatraro D. Collective effects for the LHC injectors: non-ultrarelativistic approaches. PhD, Bologna University, Bologna, Italy, 2011.
[11] Hänichen L, Mueller W, Weiland T, Al-Khateeb AM, Boine-Frankenheim O. Comparison of analytical and numerical results for broadband coupling impedance. In: 23rd Particle Accelerator Conference (PAC09); Vancouver, BC, Canada; 2009. pp. 3420-3422.
[12] Al-Khateeb AM, Boine-Frankenheim O, Hasse RW, Hofmann I. Longitudinal impedance and shielding effectiveness of a resistive beam pipe for arbitrary energy and frequency. Physical Review E 2005; 71 (2): 026501. doi: 10.1103/PhysRevE.71.026501
[13] Zannini C, Rumolo G, Rijoff T, Biancacci N. Electromagnetic simulations for non-ultrarelativistic beams and applications to the cern low energy machines. In: International Particle Accelerator Conference (IPAC2014); Dresden, Germany; 2014. pp. 1718-1720.
[14] Macridin A, Spentzouris P, Amundson J. Impedances and Wake Functions for Non-ultrarelativistic Beams in Circular Chambers Fermilab-Pub-12-518-CD. Batavia, IL, USA: FERMILAB, 2012.
[15] Métral E, Argyropoulos T, Bartosik H, Biancacci N, Buffat X et al. Beam instabilities in hadron synchrotrons. IEEE Transactions on Nuclear Science 2016; 63 (2): 1001-1050. doi: 10.1109/TNS.2015.2513752
[16] Zagorodnov I, Schuhmann R, Weiland T. Long-time numerical computation of electromagnetic fields in the vicinity of a relativistic source. Journal of Computational Physics 2003; 191(2): 525-541. doi: 10.1016/S0021-9991(03)00329- 2
[17] Zagorodnov I, Schuhmann R, Weiland T. Conformal FDTD-methods to avoid time step reduction with and without cell enlargement. Journal of Computational Physics 2007; 225 (2): 1493-1507. doi: 10.1016/j.jcp.2007.02.002
[18] Al-Khateeb AM, Hasse R, Boine-Frankenheim O. Comparison of the longitudinal coupling impedance from different source terms. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 2008; 593 (3): 171-176. doi:10.1016/j.nima.2008.05.011
[19] Henderson S. SNS Parameters List SNS-100000000-PL0001-R13. Oak Ridge, TN, USA: ORNL, 2005.
[20] Plum MA. Private Communication on SNS Parameters, 2017.
[21] Yaman F, Gjonaj E, Weiland T. 3D EM PIC code to study E-cloud effects for short bunches (< 50ns). In: CERN-GSI Electron-Cloud Workshop; Meyrin, Switzerland; 2011.
[22] Franczak B. SIS Parameter List GSI-SIS-TN/87-13. Darmstadt, Germany: GSI, 1987.
[23] Danilov V, Cousineau S, Aleksandrov A, Assadi S, Blokland W et al. Accumulation of high intensity beam and first observations of instabilities in the SNS accumulator ring. In: 39th ICFA Advanced Beam Dynamics Workshop HB2006; Tsukuba, Japan; 2006. pp. 59-63.
[24] Zagorodnov I, Dohlus M. Steady-State Resistive Wake with Oxid Layer and Roughness, Start to End Simulations (S2E). Hamburg, Germany: DESY, 2008.
[25] Zagorodnov I. Wakefield Code ECHO 2(3)D. In: ICFA mini-Workshop on Electromagnetic Wake Fields and Impedances in Particle Accelerators; Erice, Sicily, Italy; 2014.
[26] Zagorodnov I. Computation of electromagnetic fields generated by relativistic beams in complicated structures. In: North American Particle Accelerator Conference (NAPAC’16); Chicago, IL, USA; 2016. pp. 642-646.