Update for ion ring lattice chromaticity correction Y. Nosochkov, M-H. Wang 04-21-2015

Outline Ion ring lattice v15c.0 04/07/2015 Outline Ion ring lattice v15c.0 Update for the correction with two –I sextupole pairs: tune scan and dynamic aperture Example of distributed system of interleaved x and y –I sextupole pairs in the arcs without beta modulation np+p/2 phase advance from the –I pairs to the IP Correct linear chromaticity using the remaining periodic sextupoles Verify dynamic aperture

Dynamic aperture tune scan for correction with two –I sextupole pairs 04/07/2015 Dynamic aperture tune scan for correction with two –I sextupole pairs The selected tune Q=[24.22,23.16] is based on maximum dynamic aperture and momentum range.

Chromaticity for two –I sextupole pairs at selected tune 04/07/2015 Chromaticity for two –I sextupole pairs at selected tune Linear chromaticity is set to +2 units. Chromatic tune and b* are reasonable within the range of Dp/p = ±0.4%. W-function in the arcs seems affected by the choice of tune. This could be due to contribution from quads not in phase with FFB.

Dynamic aperture with –I sextupole pairs using LEGO 04/07/2015 Dynamic aperture with –I sextupole pairs using LEGO Sufficient dynamic aperture (at IP) for up to Dp/p = ±0.4%.

Schematic of distributed sextupoles in arcs 04/07/2015 Schematic of distributed sextupoles in arcs Use arc sextupoles nearest to IP for FFB chromaticity correction. Make interleaved x and y –I pairs by using sextupoles in every 2nd cell. Use the remaining periodic sextupoles for linear chromaticity correction. 5 (x) + 5 (y) –I pairs 4 (x) + 4 (y) 8 (x) + 8 (y) sextupoles Extra –I pairs due to higher beta in downstream FFB

Complete ring lattice with distributed correction 04/07/2015 Complete ring lattice with distributed correction Make np phase advance from –I sextupole pairs to FFB. Tune is not optimized: Q=[24.625, 24.320], x =[-101.5, -112.2]. 5+5 pairs, 8+8 sext 8+8 sext, 4+4 pairs

04/07/2015 W-functions Minimize IP W-function using –I sextupole pairs, and correct linear chromaticity with periodic cell sextupoles. K2 (m-3) for x = 0 : 0.476, -1.424 (upstream pairs), -1.423, 2.785 (downstream pairs), 1.489, -2.925 (arcs). More impact from out-of-phase chromatic kick in –I sextupoles due to modest bx(y) / by(x) ratio.

04/07/2015 Chromatic tune and b* Larger high-order chromaticity effects. This may be, in part, due to accumulation of out-of-phase chromatic kicks in –I sextupole pairs.

Dynamic aperture using LEGO 04/07/2015 Dynamic aperture using LEGO On-momentum dynamic aperture is sufficient, but it is reduced compared to the lattice with two –I sextupole pairs. This could be due to geometric aberrations from stronger sextupoles and interleaved x and y –I pairs. The momentum range is also limited to less than ±0.3%. One can try to improve it by creating large beta ratio at –I sextupoles for more orthogonal correction. Optimization of tune may also help.