1. Beam Dynamics @ Collector Ring
Dmitry Shwartz
BINP, Novosibirsk
6th BINP-GSI-FAIR workshop

2. CR: three operation modes
Antiprotons (p-bar mode), x,z = 240 mm mrad, p/p = ±3%
Radioactive ions (RIB mode), x,z = 200 mm mrad, p/p = ±1.5%
Isochronus mode...

3. Collector Ring layout
Antiprotons
Rare isotopes
Perimeter, П  m
Rigidity, B
13 Tm
Number of particles, N
108
109
Kinetic energy, K
3 GeV
740 MeV/u
Velocity, v
0.971c
0.830c
Relativistic factor , 
4.20
1.79
Betatron tunes, x, y
4.26, 3.61
3.26, 3.29
Revolution frequency, 0
1.35 MHz
1.16 MHz
RF harmonic, q 1
CR lattice is kind of two fold symmetric, but it is not.

4. CR lattice (pbar mode) Lattice functions of one half-period. beamsizes
RF system Rmax=75mm
Wide quads’ Rin = 160mm aperture

5. CR lattice (rib mode)
Lattice functions of one half-period.
beamsizes

6. Beam size crossections
p-bar
RIB
Injected
...7 different “wide” quads,
R = 160 mm aperture
...6 different “narrow” quads,
R = 100 mm aperture

7. Chromatic effects, p-bar mode
2-nd order dispersion function
x = D1*(p/p)2
~ 1 cm
Beta-functions chromaticity

8. Beam sizes, p-bar mode

9. Chromatic effects, RIB mode

10. Beam sizes, RIB mode

11. Survival plot (DA), p-bar mode
p-bar mode. SAD code. Nturns=300, resolution: 60x15
chromatic sextupoles - on, quads fringes - on, sextupole error 10% + rotation 10mrad, quad error 1% + rotation 10mrad, quads high order harm x^9 dB/B=10^-4
z (cm)
p/p = -0.03
p/p = 0
p/p = +0.03
x (cm)
Particle with given initial conditions survival for N turns, from N=0 (red) to N=300 (blue)

12. What limits the DA?
p-bar mode. SAD code. on-energy, Nturns=300, resolution: 60x15
linear
Sextupoles
Quads’ fringe fields
SVD sextupoles + fringe fields

13. Quads field quality, x5 linear x5, dB/B= 10-4, Rref=185/160/100mm
Systematic nonlinearity is introduced into all quads with amplitude:

14. Quads field quality, x9 510-4 linear
x9, dB/B= 10-4, Rref=185/160/100mm
510-4
x9, dB/B= 10-3, Rref=185/160/100mm
x9, dB/B= 10-2, Rref=185/160/100mm

15. p-bar mode, tunescan p/p = -0.03 p/p = 0 p/p = +0.03 3 1
RIB mode. SAD code. Nturns=300, resolution: 32x32
chromatic sextupoles - on, quads fringes - on, sextupole error 10% + rotation 10mrad, quad error 1% + rotation 10mrad, quads high order harm off

16. RIB mode, tunescan
5.5
RIB mode. SAD code. Nturns=300, resolution: 32x32
chromatic sextupoles - on, quads fringes - on, sextupole error 10% + rotation 10mrad, quad error 1% + rotation 10mrad, quads high order harm off

17. Survival plot, RIB mode p/p = -0.015 p/p = 0 p/p = +0.015
RIB mode. SAD code. Nturns=300, resolution: 60x15
chromatic sextupoles - on, quads fringes - on, sextupole error 10% + rotation 10mrad, quad error 1% + rotation 10mrad, quads high order harm x^9 dB/B=10^-4
p/p =
p/p = 0
p/p =

18. Footprints z
3 batches of particles (on- and off-energy), seeded on the border of beam emittance, tracked for 1000 turns. x
p-bar
RIB

19. Sextupole schemes 3. ... 1. SVD technique for chromaticity correction
2. "Best pairs" optimization scheme (E.Levichev, P.Piminov, EPAC'2006).
Portion of chromaticity is compensated by one pair (SXi, SZi), that gives the largest DA.
N(N-1)/2 pairs for N sext families
The tunes chromaticity correction itself is not the target.
DA – is (the only?) the target...
3. ...

20. Thank you!