Nuclear Physics and Atomic Energy

ядерна ф≥зика та енергетика
Nuclear Physics and Atomic Energy

  ISSN: 1818-331X (Print), 2074-0565 (Online)
  Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine
  Languages: Ukrainian, English
  Periodicity: 4 times per year

  Open access peer reviewed journal

 Home page   About 
Nucl. Phys. At. Energy 2022, volume 23, issue 4, pages 230-233.
Section: Nuclear Physics.
Received: 01.11.2022; Accepted: 30.12.2022; Published online: 6.02.2023.
PDF Full text (en)

Nonlinear field effects in the collector ring due to large-amplitude particle oscillations

M. E. Dolinska1,2,*, N. L. Doroshko1, O. V. Dolinskyy2

1 Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kyiv, Ukraine
2 GSI Helmholtz Centre for Heavy Ion Research, Darmstadt, Germany

*Corresponding author. E-mail address:

Abstract: In the frame of the FAIR project, the Collector Ring (CR) is planned to be built for efficient cooling of antiprotons and rare isotope beams [1]. In order to accept hot beam from separators large acceptances are required. This paper examines the effects which can influence the beam dynamics due to large betatron oscillation amplitude and momentum spread. Using analytic expressions, the amplitude-dependent tune shifts driven by sextupole magnets, the fringe field of quadrupole magnets, and kinematics effects have been calculated. The obtained results have been compared with numerical simulations by means of precise multi-turn particle tracing. The tracking analysis for the CR has been performed considering the real shape of the magnetic field of the wide aperture quadrupole. We report on quantitative studies of the effects on the dynamic aperture of the rings.

Keywords: collector ring, tune shift, chromaticity, kinematic effect, sextupole effect, fringe field.


1. A. Dolinskii, F. Nolden, M. Steck. Lattice considerations for the collector and the accumulator ring of the FAIR project. In: Workshop on Beam Cooling and Related Topics. Proc of COOL07, TUA2C08, Bad-Kreuznach, Germany, Sept. 9 - 14, 2007 (Germany, Darmstadt, 2007) p. 106.

2. A. Dolinskii et al. Amplitude dependent tune spread in the CR operated as an antiproton collector. In: 2nd International Particle Accelerator Conference, Proc. of IPAC2011, WEPC054, San Sebastian, Spain, Sept. 4 - 9, 2011, p. 2136.

3. E. Forest, D. Robin, A. Zholents. Sources of amplitude-dependent tune shift in the PEP-II design and their compensation with octupoles. In: 4th European Particle Accelerator Conference, Proc. of EPAC94, London, England, 27 June - 1 July, 1994, p. 1033.

4. E. Levichev, P. Piminov. Analytic estimation of the non-linear tune shift due to the quadrupole magnet fringe field. arXiv:0903.3028 [physics.acc-ph].

5. Z. Parsa, S. Tepikian, E. Courant. Second-order perturbation theory for accelerators. Particle Accelerators 22 (1987) 205.

6. 7-GeV Advanced Photon Source Ц Conceptual Design Report. Argonne National Laboratory Reports, ANL-87-15 (USA, Argonne National Laboratory, 1987) 528 p.

7. P. Krejik. Nonlinear quadrupole end-field effect in the CERN antiproton accumulator. IEEE CH2387-9/87/0000/-1278.