Update on MEIC Nonlinear Dynamics Work V.S. Morozov Teleconference with SLAC March 24, 2015 F. Lin

Outline Update on the MEIC ion collider ring design Review of milestones Discussion of chromaticity compensation options Discussion of short-term plans

Ion Collider Ring Figure-8 ring with a circumference of 2153.9 m Two 261.7 arcs connected by two straights crossing at 81.7 geom. match #3 disp. supp./ disp. supp./ geom. match #2 norm.+ SRF Arc, 261.7 tune tromb.+ match elec. cool. R = 155.5 m 81.7 future 2nd IP Polarimeter det. elem. disp. supp. ions beam exp./ match IP disp. supp./ geom. match #3 disp. supp./ geom. match #1

Ion Collider Ring Parameters All design goals achieved Resulting collider ring parameters Proton energy range GeV 20(8)-100 Polarization % > 70 Detector space m -4.6 / +7 Luminosity cm-2s-1 > 1033 Circumference m 2153.89 Straights’ crossing angle deg 81.7 Horizontal / vertical beta functions at IP *x,y cm 10 / 2 Maximum horizontal / vertical beta functions x,y max ~2500 Maximum horizontal dispersion Dx 3.28 Horizontal / vertical betatron tunes x,y 24(.38) / 24(.28) Horizontal / vertical natural chromaticitiesx,y -101 / -112 Momentum compaction factor  6.45  10-3 Transition energy tr 12.46 Normalized horizontal / vertical emittance x,y µm rad 0.35 / 0.07 Horizontal / vertical rms beam size at IP *x,y µm ~20 / ~4 Maximum horizontal / vertical rms beam size x,y mm 2.8 / 1.3

Arc FODO Cell Basic building block of the arcs Dipoles Quadrupoles Length of 22.8 m = 1.5  electron FODO cell lengths (26 cells per arc) Betatron phase advance of 90 in each plane Dipoles Magnetic/physical length of 8/8.28 m (implemented as two 4 m long pieces) Bending angle of 73.3 mrad (4.2), bending radius of 109.1 m, sagitta of 18.3 mm Field of 3.06 T at 100 GeV/c x aperture = (4 cm+sagitta/2) = 5 cm, y aperture = 3 cm (10 + 1 cm orbit allowance) Quadrupoles Magnetic/physical length of 0.8/0.9 m Field gradients of 52.7/-52.9 T/m at 100 GeV/c Field of 2.1/-2.1 T at 40 mm radius Sextupole/corrector package next to each quadrupole Magnetic/physical length of 0.5/0.6 m 3 T at 40 mm focusing sextupole adds 34.8/-7.1 units of x/y chromaticity 3 T at 40 mm defocusing sextupole adds -3.7/18.1 units of x/y chromaticity BPM next to each quadrupole Physical length of 0.15 m

Ion IR Optics IR design features Modular design Based on triplet Final Focusing Blocks (FFB) Asymmetric design to satisfy detector requirements and reduce chromaticity Spectrometer dipoles before and after downstream FFB, second focus downstream of IP No dispersion at IP, achromatic optics downstream of IP detector elements match/ beam compression IP match/ beam expansion geom. match/ disp. suppression FFB FFB ions

Complete Ion Collider Ring Lattice Optics of a complete ring with all sections incorporated and matched ions Arc 1 Straight 2 IP Arc 2 Straight 1

Milestones of Funded 1-Year Grant First and Second quarters Optimization of the detector region design Comparison of different non-linear compensation schemes and selection of the optimal one Optimization of the non-linear dynamics compensation scheme Third and fourth quarters Continuation of the momentum acceptance and dynamic aperture optimization Consideration of lattice imperfections: magnet field errors and misalignments Development of the beam diagnostics and correction scheme

Milestones of Submitted Proposal MDI and IR Studies: Quarter 1: Further optimization of the detector region design. Achieve a scheme with acceptable detector background levels that meshes smoothly with the nearby accelerator requirements. Quarter 2: Collaborate with the JLab group to optimize the chromaticity correction scheme. This potentially impacts details of the IR layout and requires a certain amount of design iteration. Quarter 3: With the latest data in hand, continue to refine the IR masking design to maintain low detector background levels. Develop a vacuum chamber for the interaction region that satisfies detector and accelerator requirements. Quarter 4: Evaluate the effect of lattice imperfections and alignment errors on the performance of the IR design, background etc. Investigate vacuum pumping requirements in the IR region. Nonlinear Beam dynamics: Quarter 1-2: Ongoing optimization of the hadron-ring lattice, including examining variants as the design evolves. Goals for the acceptance are about 8 sigma in the transverse dimensions and about 0.4% in energy spread. Development of the beam diagnostics and correction concepts. Quarter 3-4: Once estimates for the magnet field harmonics become available, investigate the effect of these on the acceptance of the lattice. Ultimately these results will be used to generate magnet specifications. Compensation of the detector solenoid effects.

Chromaticity Compensation Options All potential schemes work in a similar way Sextupoles placed in a dispersive region generate a chromatic  wave with a phase such that it cancels the chromatic kick of the final focusing blocks Sextupoles are positioned in a way that cancels their unwanted nonlinear effects Additional sextupoles are used to compensate the residual chromaticity Compensation scheme options Minus-identity sextupole pairs in the arcs: chromatic beta waves add up, geometric kicks cancel CCB proposed by JLab: –I sextupole pairs and sextupoles at low-x locations Distributed sextupole scheme: multiple –I pairs build up a chromatic wave Distributed sextupole scheme with -beat: lower-strength sextupoles General considerations when selecting a scheme Larger  functions at sextupole locations mean lower sextupole strengths and generally better chromatic compensation but cause larger amplitude-dependent tune shift Smaller  functions generally mean smaller amplitude dependent tune spread but require stronger sextupoles and cause larger higher-order chromaticities We probably need to find a balance of the two effects

Chromaticity Compensation Compensation of momentum dependence of betatron tunes (primarily due to strong focusing at IP) using properly-phased sextupole families Distributed sextupole compensation strategy Build-up chromatic  wave in the arcs to cancel FFB’s chromatic kick Arc FODO cells with 90 phase advance in x/y Two sextupole families, each with an even number of magnets  phase advance between individual sextupoles of each family n+/2 phase advance from the last sextupole of each family to IP Option of exciting  beat in the arcs if needed Compensation of ~1/6 residual linear chromaticity Two sextupole families, each with a multiple of 4 magnets /2 phase advance between individual sextupoles of each family Control of chromatic driving terms ((2), D(2), / ) and cancellation of geometric resonance driving terms to first order in sextupole strength FFB IP  /2 

Chromatic Amplitude Functions Adjust sextupole strengths & phase advance by minimizing W function at IP Compensate residual linear chromaticity by two additional families Before compensation After sextupole compensation

Suggested Short-Term Goals Note: a postdoc, Guohui Wei, joining whose main focus will be on this work Down selection of a chromaticity compensation scheme A quick check and comparison of most promising schemes by analysis of nonlinear parameters and tracking Use linear matrices for matching and adjusting the phase advance, enough flexibility is built into the lattice for an actual optical implementation later Determine optimum -function values at the sextupole locations Relevant questions to think about Consider compensating both FFBs using the nearest arc at the expense of chromatic smear at the IP Optimization of betatron tunes Evaluate the need for geometric sextupoles and octupoles Error sensitivity study, First use BPMs and correctors included in the lattice next to each quadrupole Part of the diagnostics and correction scheme development Somewhat longer-term goals Consider impact of magnet multipole components, can collaborate with P. McIntyre of Texas A&M University