1. 10 October 2013 1 st -Stored Beams meeting Sergey Litvinov Isochronous Optics of the CR+

2. Motivation (Why is the Isochronous Mode?) Motivation (Why is the Isochronous Mode?) Principle of the Isochronous Mass Measurements Principle of the Isochronous Mass Measurements Different Isochronous Requirements Different Isochronous Requirements 3 Isochronous Modes of the CR (ver. CR72) 3 Isochronous Modes of the CR (ver. CR72) Sextupole Corrections Sextupole Corrections Octupole Corrections Octupole Corrections Magnets’ Fields Imperfections (Nonlinear Lattice) Magnets’ Fields Imperfections (Nonlinear Lattice) Further Steps Further Steps + Outline

3. 3. How were the heavy elements from iron to uranium made? National Research Council's board on physics and astronomy 02.01.2002 The 11 Greatest Unanswered Questions of Physics Resolution of these profound questions could unlock the secrets of existence and deliver a new age of science within several decades by Eric Haseltine, Illustrations by Dan Winters & Gary Tanhauser

4. typical lifetimes for unstable nuclei far from the valley of  stability: 10 -4 – 10 -2 s Requiring n capture time:  n ~ 10 -4 s  N n ~ 10 20 n/cm 3 termination point: fission of very heavy nuclei explosive scenarios needed to account for such high neutron fluxes waiting points Rolfs & Rodney: Cauldrons in the Cosmos, 1988 The r (rapid neutron capture) - process

5. Are Supernovae IIa the sites of the r-process?? A possible scenario: Supernovae IIa provide in the second of their outbreak a huge neutron flux creating a plenty of unstable neutron-rich nuclei that decay by a chain of beta decays towards the valley of stability

6. masses and lifetimes of key r- and rp-nuclei; β decay of highly charged ions key nuclear properties of nucleosynthesis and atomic shell effects The r (rapid neutron capture) –process creates about 50% of nuclei; its site is still unknown

7. Limits of nuclear stability: superheavies; p- and n- drip lines; pathways of stellar nucleosynthesis To measure: Ground state properties of exotic nuclei: masses and β decay half-lives masses determine the pathways of s-, rp- and r-processes β half-lives the accumulated abundances

8. NuSTAR Annual Meeting, 28 February 2013, GSI Darmstadt Super-FRS RESR NESR СR FAIR - CORE Facility FAIR - Modularized Start Version (MSV) Isomeric Beams, Lifetimes and MAsses

9. NuSTAR Annual Meeting, 28 February 2013, GSI Darmstadt Requirement #1 Sensitivity and quickness Requirement #2 Large acceptance Requirement #3 High accuracy for mass measurements Requirement #4 Calibration masses  lower energy Solution: Isochronous Mode

10. FRS-ESR Ion-Optical Matching Isochronous Mass Spectrometry (IMS) Isochronous Mass Spectrometry 3. Isochronous condition:  = t  = t 1. Revolution frequency difference (or revolution time) of two particles with different m/q ratio circulating in the ring can be written as: 2. Transition energy  t is: Thus, all particles with the same m/q at different velocities travel rigidly around the ring with equal revolution times. In other words, the ring can be used as a Time-Of-Flight (TOF) mass spectrometer. H. Wollnik et al., “Experiment Proposal for the SIS-FRS-ESR Facilities”, (1986).

11. FRS-ESR Ion-Optical Matching Isochronous Mode of the CR Different Isochronous Settings of the CR 1. γ t = γ = 1.84 (E = 782.5 MeV/u) 2. γ t = γ = 1.67 (E = 624.1 MeV/u) 3. γ t = γ = 1.43 (E = 400.5 MeV/u) Mass analysis becomes very complicated due to a small number of reliable reference masses. if at lower energies, the less-exotic isobars in different atomic charge states are stored in the ring simultaneously with the nuclides of interest. At high energies the exotic nuclei are produced mainly as fully-ionized atoms and no (less-exotic) isobars are present.

12. FRS-ESR Ion-Optical Matching CR72 asymetric Collector Ring (ver.72-asymetric) 1m 0.5 m 7 wide quadrupoles are to be replaced. One can get totally 3.5 m of additional free space in the straight sections. There are 10 wide quadrupoles in the CR straight sections.

13. FRS-ESR Ion-Optical Matching Isochronous Mode of the CR72 Isochronous CR72 (Horizontal Beam Size) Combined horizontal beam size of all three modes for a corresponding maximum momentum spread. The beam size is close to ±19 cm in the arcs.

14. FRS-ESR Ion-Optical Matching Isochronous CR72 (Vertical Beam Size) Beam size of the optics γ t = 1.84, γ t = 1.67 and γ t = 1.43 are marked by yellow, red and blue colors correspondingly. Isochronous Mode of the CR72

15. FRS-ESR Ion-Optical Matching Isochronous CR72 (Injection) The injection setting is the same for all three modes, which allows a fast switching between isochronous settings during machine operation. Beam size of the optics γ t = 1.84, γ t = 1.67 and γ t = 1.43 are marked by yellow, red and blue colors correspondingly. Isochronous Mode of the CR72

16. FRS-ESR Ion-Optical Matching Isochronous Mode of the CR Analysis of Revolution Frequency  Transverse beam emittance ( ε )  Closed Orbit Distortion (COD)  Field errors of the ring magnets (err.)  Fringe fields of the magnets (ff.) Contributions: A. Dolinskii, S. Litvinov et al., NIM A 574, 207-212 (2007).).

17. FRS-ESR Ion-Optical Matching Influence of Transverse Emittance Isochronous Mode of the CR In order to reach the necessary mass resolving power of 10 5 the transverse emittance would have to be limited to 10 mm mrad in both planes. As a result, the transmission of the ions into the ring would be reduced drastically. We consider ions of one species in the ideal isochronous ring, where only pure betatron motion exists. For such a ring the frequency spread is directly related to the transverse emittance: A. Dolinskii, S. Litvinov et al., NIM A 574, 207-212 (2007).)., are the Twiss parameters averaged over the whole circumference of the ring.

18. FRS-ESR Ion-Optical Matching Revolution Time in 2 nd -Order Isochronous Mode of the CR However, the mass resolving power can be improved using second-order corrections and keeping the transverse emittance large. Let us assume a beam of one species circulating in the ring turn by turn. We observe it in the symmetry plane of the ring where the phase-space ellipse is upright (Twiss =0) and this condition is restored after each turn. Statistical uncertainty gets reduced with increasing number of revolutions, and for accuratemassmeasurements it is essential to measure the revolution time of the particle over many turns. Therefore, the relative revolution time deviation between an arbitrary and the reference particle can be expressed in terms of the initial coordinates as a Taylor However, the mass resolving power can be improved using 2 nd -order corrections and keeping the transverse emittance large. We observe a beam of one species circulating in the ring turn by turn at the symmetry plane, where the phase-space ellipse is upright and this condition is restored after each turn. Statistical uncertainty gets reduced with increasing number of revolutions, and for accurate mass measurements it is essential to measure the revolution time of the particle over many turns. Therefore, the relative revolution time deviation (or revolution frequency) between an arbitrary and the reference particle can be expressed in terms of the initial coordinates as a Taylor series: where (x,y) are the transverse coordinates and angles (a, b). The index c stamps for the coefficients normalized by the total time-of-flight t = nT 0 (n is the number of turns). Achromatic RingIsochronous Ring 2 nd -order Isochronous Ring X-transverse contribution Y-transverse contribution Usually small

19. FRS-ESR Ion-Optical Matching Chromaticity and Revolution Time Isochronous Mode of the CR However, the mass resolving power can be improved using second-order corrections and keeping the transverse emittance large. Let us assume a beam of one species circulating in the ring turn by turn. We observe it in the symmetry plane of the ring where the phase-space ellipse is upright (Twiss =0) and this condition is restored after each turn. Statistical uncertainty gets reduced with increasing number of revolutions, and for accuratemassmeasurements it is essential to measure the revolution time of the particle over many turns. Therefore, the relative revolution time deviation between an arbitrary and the reference particle can be expressed in terms of the initial coordinates as a Taylor Evolution of the relative 2 nd -order geometric time aberrations as a function of the number of turns in the CR (ver. 65) for a single ion with start positions x and a on the edge of the acceptance of 100 mm mrad. The inserted numbers show the limit over many turns. S. Litvinov et al., Proc. of RUPAC’12, TUPPB037.. Therefore, correcting chromaticity with 2 sextupole families (for x and y directions) +1 sextupole family for the 2 nd -order isochronicity we significantly improve the time resolution

20. FRS-ESR Ion-Optical Matching Further Sextupole Corrections Isochronous Mode of the CR However, the mass resolving power can be improved using second-order corrections and keeping the transverse emittance large. Let us assume a beam of one species circulating in the ring turn by turn. We observe it in the symmetry plane of the ring where the phase-space ellipse is upright (Twiss =0) and this condition is restored after each turn. Statistical uncertainty gets reduced with increasing number of revolutions, and for accuratemassmeasurements it is essential to measure the revolution time of the particle over many turns. Therefore, the relative revolution time deviation between an arbitrary and the reference particle can be expressed in terms of the initial coordinates as a Taylor For an achromatic ring we can write: and:, where (x|  ) and (a|  ) are 2 nd -order dispersion and its derivative Therefore, if one correct (x|  ) or (a|  ) with an additional sextupole,then the other term turns to zero and time chromaticterms (t|x  ) and (t|a  ) turn to zero too. Correction of 2 nd -order dispersion gives a best dispersion adjustment in the arcs, but including additional sextupole affect the time resolution. It would be important to correct nonlinear dispersion in Pbar and RIB modes where the larger momentum acceptance. Standard deviation of relative ToF as function of turns. S. Litvinov et al., NIM A 724 (2013), 20-26

21. FRS-ESR Ion-Optical Matching Octupole Corrections Isochronous Mode of the CR However, the mass resolving power can be improved using second-order corrections and keeping the transverse emittance large. Let us assume a beam of one species circulating in the ring turn by turn. We observe it in the symmetry plane of the ring where the phase-space ellipse is upright (Twiss =0) and this condition is restored after each turn. Statistical uncertainty gets reduced with increasing number of revolutions, and for accuratemassmeasurements it is essential to measure the revolution time of the particle over many turns. Therefore, the relative revolution time deviation between an arbitrary and the reference particle can be expressed in terms of the initial coordinates as a Taylor Applying the octupole magnets for correction 3 rd -order isochronicity and 2 nd -order chromaticity we can reach:

22. FRS-ESR Ion-Optical Matching Dipole Inhomogeneity The CR dipole field homogeneity is crucial for the time resolution. It can be written in terms of normal multipole coefficients (bn) as: The b n values are normalized with respect to the dipole component b 0 and are expressed in units of 10 -4 at the reference radius r 0 =190 mm. B =1.6 T. Sextupole (b 2 ) and octupol (b 3 ) components affect the time resolution, but can be completely compensated using sextupole and octupole magnets. Decapole component (b 4 ) is the largest. Within its influence on dT the goal of 10 -6 of mass resolution can be reached only for dp/p=±0.2% (for γ t =1.67 ). Using one family of decapole magnet would compensate this effect.

23. FRS-ESR Ion-Optical Matching Fringing Fields The effect of the dipole B-Field inhomogeneity is so strong, that in order to distinguish effects of fringing fields the decapole component was compensated in the simulations. The fringe fields of the dipole and quadrupole magnets lead to a small mismatch of the phase space and dispersion, to the change of betatron tunes, chromaticity and isochronicity. Therefore, the quadrupole and sextupole settings have to be recalculated. 100 turns Quadrupole fringe fields represent a major contribution to the limit of the time resolution. Their influence is more difficult to compensate. Contrary to the dipole dipole inhomogeneity it does not correspond to a simple multipole component which can be compensated with an opposite field nearby. Correcting significant third-order time aberrations with 4 octupole families the time resolution is improved a bit. Finally, one can reach a resolution of up to: S. Litvinov et al., NIM A 724 (2013), 20-26

24. FRS-ESR Ion-Optical Matching Further Steps Isochronous Mode of the CR 1. In present calculations 4 octupole families have been used (inside Q-8,9,10,11). However, there is possible to install only 3 octupole families inside quadrupole magnets: either in Q-7,9,11 or Q-6,8,10, because of BPMs installation. So, the octupole correction scheme has to be recalculated and optimum positions have to be found. The magnets’ strength could be increased in comparison with present values: 2. Ripple of Power Supplies of Dipoles gives additional systematic error to the revolution time determination. It possible, that this error would not allow to reach the best time resolution with decapole or even octupoles. This question has to be also clarified. 3. The simulation result of reduction transverse emittance effect has to be experimentally proofed. B max oct. =0.002 T. B max dec. =0.001 T

25. FRS-ESR Ion-Optical Matching CR71s-Pbar +CR68-CR71s CR68CR71s γtγt 3.8514.667 Ƞ -0.010760.01076 ε x = ε y [mm mrad] 240 ∆p/p max [%]±2.3±3.5 Q x /Q y 4.27/4.845.17/4.09 ∆µ x (SC) [deg]107100 ∆µ y (SC) [deg]85100 B quad. max [T]0.920.83

26. FRS-ESR Ion-Optical Matching CR71s-Pbar Injection

27. FRS-ESR Ion-Optical Matching CR72-Pbar CR71s-Tunes Tunes line in linear approximation. Tunes line in nonlinear optics Sextupole correction is necessary!

28. Thank You For Your Attention!