JLEIC Electron Ring Nonlinear Dynamics Work Plan F. Lin, V.S. Morozov Teleconference with SLAC January 26, 2016 F. Lin

Outline JLEIC electron collider ring for nonlinear dynamics studies Not the baseline design Reduced-emittance optics design: some sections have been optimized to reduce the emittance by ~30% Review of submitted proposal IR design for both rings Beam dynamics for ion ring only, but can be applied to electron ring Discussion of chromaticity compensation options Discussion of short-term plans

Reduced-Emittance Electron Ring Circumference of 2185.55 m = 2 x 811.84 m arcs + 2 x 280.92 straights Chromaticities: (H,V) = (-138, -125) Figure-8 crossing angle 81.7 Reduced-emittance ring layout is very similar to the baseline design layout (below). e- R=155m RF Spin rotator CCB Arc, 261.7 81.7 Forward e- detection IP Tune trombone & Straight FODOs Future 2nd IP

Electron Ring Optics Parameters Electron beam momentum GeV/c 10 Circumference m 2185.55 Beta stars at IP *x,y cm 10/2 Detector space -3 / 3.2 Maximum horizontal / vertical  functions x,y 949/692 Maximum horizontal / vertical dispersion Dx,y 0.78 / 0 Horizontal / vertical betatron tunes x,y 47.(49) / 49.(15) Horizontal / vertical chromaticitiesx,y -138 / -125 Momentum compaction factor  1.9 10-3 Transition energy tr 22.7 Energy spread 10-3 0.9 Hor./ver. emittance x,y (normalized/un-normalized) @10GeV µm rad 779 / 156 (0.040/0.008) Energy spread @ 5GeV 0.45 Hor./ver. emittance x,y (normalized/un-normalized) @ 5GeV 97 / 19 (0.01/0.002)

Normal Arc FODO Cell Complete FODO (Each arc has 39 such normal FODO cell) Length 15.2 m (arc bending radius 155 m) 2 dipoles + 2 quadrupoles + 2 sextupoles 108/108 x/y betatron phase advance (every 5 cells create five –I (3) sextupole pairs) Dipoles Magnetic/physical length 5.4/5.68 m Bending angle 48.9 mrad (2.8), bending radius 110.5 m 0.3 T @ 10 GeV Sagitta 3.3 cm Quadrupoles Magnetic/physical length 0.56/0.62 m -13.0 and 12.8 T/m field gradients @ 10 GeV 0.65 and 0.64 T @ 50 mm radius Sextupoles Magnetic/physical length 0.25/0.31 m -176(?) and 88(?) T/m2 field strengths @ 10 GeV for chromaticity compensation only in two arcs (strengths will be determined in DA simulations) BPMs and Correctors Physical length 0.05 and 0.3 m

Reduced-Emittance Sections End of arc Dispersion suppression Matching between arcs and spin rotators Spin rotator Regular arc FODO cell Spin rotator Dipole set 2nd sol. + decoupling quads 1st sol. + decoupling quads

Chromaticity Compensation Upstream local Chromaticity Compensation Block (CCB) Two 5m-long dipoles and four 2m-long dipoles with a maximum field 0.58 T @ 10 GeV 13 quads (7 families) have a maximum field ~25 T/m @ 10 GeV 4 sextupoles (2 families) are used for a compensation of local chromaticities from the FFQs SXT1 SXT2 SXT1 SXT2 Ion CCB From V. Morozov Re Im h21000 0.04 h30000 -0.013 h10110 -0.18 h10020 1.85 0.09 h10200 2.04 -0.09

Compton polarimetry region IP Region IP region Final focusing quads with maximum field gradient ~63 T/m Four 3m-long dipoles (chicane) with 0.44 T @ 10 GeV for low-Q2 tagging with small momentum resolution, suppression of dispersion and Compton polarimeter IP e- forward e- detection region FFQs Compton polarimetry region x(m), y(m) Dx(m)

Complete Electron Ring Optics Along the ion beam direction (in order to match the ion ring optics design easily) ion e- IP Upstream CCB

Complete Electron Ring Optics Along the electron beam direction e- IP Upstream CCB

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. From V. Morozov

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 (upstream CCB only now, downstream CCB has to be in the arc) Distributed sextupole scheme: multiple –I pairs (every 5 arc FODO cells) build up a chromatic wave (slides 13,14) 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 Electron emittance growth has to be minimized Modified based on V. Morozov’s ion compensation options

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 (39 cells each arc) with 108 phase advance in x/y Five 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 (last consideration) Compensation of residual linear chromaticity Two sextupole families, each with a multiple of 4 magnets (4 arc FODD cells) /2 (108  90) 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  Modified based on V. Morozov’s ion compensation options

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 From V. Morozov

Comparison to KEKB

Suggested Short-Term Goals 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 Use PEP-II magnet multipole field errors, misalignment and rotation parameters First use BPMs and correctors included in the lattice next to each quadrupole Part of the diagnostics and correction scheme development From V. Morozov