174
E. Metral et al.
The modelling described in the previous subsections has been frequently applied
to explain collective instabilities observed in running machines, as well as to predict
instability thresholds (both in existing and future machines) and develop strategies
to circumvent limitations from collective effects. For instance, a detailed impedance
model of the SPS comprises the contributions from several accelerator components
and is used for deriving single-bunch wake fields, which are the driving terms for
HEADTAIL simulations. The kicks given to the beam particles by the different
wake fields can be then either applied at the real locations in which the sources
are situated, or weighted by the beta functions, summed up and applied in a
single location using a one-kick approximation. These simulations can be used for
predicting at which intensity transverse mode coupling occurs and the effects of
chromaticity on this threshold value [194]. This is very important to extrapolate
the beam stability limits in different conditions of operation, e.g. with a different
optics or to the upgraded machine, which will be in principle enabled to receive
higher intensity bunches. The mode shift can be plotted as a function of the bunch
intensity, because the main modes are detectable from the Fourier analysis of the
centroid motion. A typical plot of mode shift provided by simulations is displayed
in Fig. 4.10.
References
1. E. Métral et al., Beam Instabilities in Hadron Synchrotrons, IEEE Transactions on Nuclear
Science, Vol. 63, No. 2, 50 p, April 2016 (invitation for the 50th anniversary of the PAC
conference).
2. E. Métral (Issue Editor), ICFA Beam Dynamics Newsletter No. 69 devoted to the Collective
Effects in Particle Accelerators, 310 p, December 2016.
3. E. Métral and V.G. Vaccaro (chairs), ICFA Mini-Workshop on “Electromagnetic Wake Fields
and Impedances in Particle Accelerators”, Erice (Sicily, Italy), 2014: https://indico.cern.ch/
event/287930/
4. M.R. Masullo, S. Petracca and G. Rumolo (chairs), ICFA Mini-Workshop on “Impedances
and Beam Instabilities in Particle Accelerators”, Benevento (Italy), 2017: https://
agenda.infn.it/event/12603/
5. E. Métral, G. Rumolo and T. Pieloni (chairs), ICFA Mini-Workshop on “Mitigation of
Coherent Beam Instabilities in Particle Accelerators”, Zermatt (Switzerland), 2019: https://
indico.cern.ch/event/775147/
6. B. Zotter: Betatron Frequency Shifts due to Image and Self Fields, CERN Accelerator School:
General Accelerator Physics, CERN 85-19, Vol. I, p. 253, 1985.
7. K. Schindl: Space Charge, CERN-PS-99-012-DI, 1999.
8. A.W. Chao: Physics of Collective Beam Instabilities in High Energy Accelerators, New York:
Wiley, 371 p, 1993.
9. K.Y. Ng: Physics of Intensity Dependent Beam Instabilities, World Scientific, 776 p, 2006.
10. S. Andriamonje, et al.: Neutron TOF facility (PS213): Technical Design Report, CERNINTC-2000-004, 2000.
11. E. Métral, Some effects near transition, Proceedings of the CAS-CERN Accelerator School
on Intensity Limitations in Particle Beams on November 2015, CERN Yellow Reports: School
Proceedings, CERN-2017-006-SP.
12. E. Métral and G. Rumolo, USPAS course on “Collective Effects in Beam Dynamics” in
Albuquerque, New Mexico, USA, June 22–26, 2009: http://emetral.web.cern.ch/emetral/
E. Metral et al.
The modelling described in the previous subsections has been frequently applied
to explain collective instabilities observed in running machines, as well as to predict
instability thresholds (both in existing and future machines) and develop strategies
to circumvent limitations from collective effects. For instance, a detailed impedance
model of the SPS comprises the contributions from several accelerator components
and is used for deriving single-bunch wake fields, which are the driving terms for
HEADTAIL simulations. The kicks given to the beam particles by the different
wake fields can be then either applied at the real locations in which the sources
are situated, or weighted by the beta functions, summed up and applied in a
single location using a one-kick approximation. These simulations can be used for
predicting at which intensity transverse mode coupling occurs and the effects of
chromaticity on this threshold value [194]. This is very important to extrapolate
the beam stability limits in different conditions of operation, e.g. with a different
optics or to the upgraded machine, which will be in principle enabled to receive
higher intensity bunches. The mode shift can be plotted as a function of the bunch
intensity, because the main modes are detectable from the Fourier analysis of the
centroid motion. A typical plot of mode shift provided by simulations is displayed
in Fig. 4.10.
References
1. E. Métral et al., Beam Instabilities in Hadron Synchrotrons, IEEE Transactions on Nuclear
Science, Vol. 63, No. 2, 50 p, April 2016 (invitation for the 50th anniversary of the PAC
conference).
2. E. Métral (Issue Editor), ICFA Beam Dynamics Newsletter No. 69 devoted to the Collective
Effects in Particle Accelerators, 310 p, December 2016.
3. E. Métral and V.G. Vaccaro (chairs), ICFA Mini-Workshop on “Electromagnetic Wake Fields
and Impedances in Particle Accelerators”, Erice (Sicily, Italy), 2014: https://indico.cern.ch/
event/287930/
4. M.R. Masullo, S. Petracca and G. Rumolo (chairs), ICFA Mini-Workshop on “Impedances
and Beam Instabilities in Particle Accelerators”, Benevento (Italy), 2017: https://
agenda.infn.it/event/12603/
5. E. Métral, G. Rumolo and T. Pieloni (chairs), ICFA Mini-Workshop on “Mitigation of
Coherent Beam Instabilities in Particle Accelerators”, Zermatt (Switzerland), 2019: https://
indico.cern.ch/event/775147/
6. B. Zotter: Betatron Frequency Shifts due to Image and Self Fields, CERN Accelerator School:
General Accelerator Physics, CERN 85-19, Vol. I, p. 253, 1985.
7. K. Schindl: Space Charge, CERN-PS-99-012-DI, 1999.
8. A.W. Chao: Physics of Collective Beam Instabilities in High Energy Accelerators, New York:
Wiley, 371 p, 1993.
9. K.Y. Ng: Physics of Intensity Dependent Beam Instabilities, World Scientific, 776 p, 2006.
10. S. Andriamonje, et al.: Neutron TOF facility (PS213): Technical Design Report, CERNINTC-2000-004, 2000.
11. E. Métral, Some effects near transition, Proceedings of the CAS-CERN Accelerator School
on Intensity Limitations in Particle Beams on November 2015, CERN Yellow Reports: School
Proceedings, CERN-2017-006-SP.
12. E. Métral and G. Rumolo, USPAS course on “Collective Effects in Beam Dynamics” in
Albuquerque, New Mexico, USA, June 22–26, 2009: http://emetral.web.cern.ch/emetral/