Beam Dynamics @ Collector Ring Dmitry Shwartz BINP, Novosibirsk 6th BINP-GSI-FAIR workshop 01.12.2014

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...

Collector Ring layout Antiprotons Rare isotopes Perimeter, П 221.451 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.

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

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

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

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

Beam sizes, p-bar mode  

Chromatic effects, RIB mode

Beam sizes, RIB mode

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)

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

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

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

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

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

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 = -0.015 p/p = 0 p/p = +0.015

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

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. ...

Thank you!