Non-linear Beam Dynamics Studies for JLEIC Electron Collider Ring Fanglei Lin, Vasiliy Morozov, Guohui Wei, Yuhong Zhang (JLAB) Yunhai Cai, Yuri Nosochkov (SLAC) Min-Huey Wang JLEIC Collaboration Meeting Spring 2017 April 3-5, 2017 F. Lin

Outline The goal of the study is to identify the lattice design of the electron collider ring with the best overall properties: low emittance, adequate chromatic correction and large dynamic aperture (DA) Optimized baseline design based on FODO arc cells and PEP-II magnets Recap of chromaticity compensation and update on DA Design based on TME-like arc cells and new magnets Chromaticity compensation and DA Design based on short FODO arc cells and new magnets Conclusions and Outlook

Recap of the Optimized Baseline Design PEP-II type FODO arc cells and PEP-II magnets Circumference: C = 2185.54 m = 2 x 811.84 m arcs + 2 x 280.92 m straights Natural chromaticity: [xH, xV] = [-113, -120] Optimized for minimum emittance Emittance at 5 GeV (from Elegant) without chromaticity correction blocks (CCB) Before optimization: ge = 138 mm-rad, e = 14 nm-rad After optimization: ge = 92 mm-rad, e = 9.5 nm-rad (8.9 nm-rad from MAD) Complete ring without non-linear chromaticity correction blocks IP, b*=10/2cm

Chromatic Sextupoles – Optimized Baseline Linear chromaticity correction: conventional 2-family sextupoles in 108o arc cells (30 cells with sextupoles per arc  compensation of high order effects due to ~2p phase advance in every 10 cells) Non-linear correction: Chromaticity Correction Blocks (CCB) on each side of IP, where sextupoles are set nearly in phase with the FFQ for correction of non-linear chromaticity e- R=155m RF Spin rotator Arc, 261.7 81.7 Forward e- detection IP Tune trombone & Straight FODOs Future 2nd IP CCB Arc sextupoles Future CCB for 2nd IP

CCB Schemes FODO type CCB, ex = 19.4 nm SBCC (scheme-6), ex = 8.3 nm Interleaved –I sextupole pairs in regular FODO arc cells  no impact on emittance, but strong sextupoles, residual non-linear effects, insufficient correction, small off-energy DA Compact CCB with 3 interleaved sextupoles  adequate chromaticity correction, but residual non-linear effects, small DA, large emittance (~15 nm-rad @ 5 GeV) FODO type CCB with non-interleaved –I sextupoles pairs and high b finctions  adequate chromaticity correction and DA, but large emittance (>15 nm-rad) SuperB type CCB (SBCC) with non-interleaved –I sextupole pairs and missing dipoles  adequate correction and DA, lowest 8.3 nm-rad emittance (with short dipoles) ‒ Best -I S2 S1 FODO type CCB, ex = 19.4 nm SBCC (scheme-6), ex = 8.3 nm

Correction and DA Update – Optimized Baseline Best SBCC option with short dipoles (scheme-6), ex = 8.3 nm-rad @ 5 GeV Tune vs Dp/p b* vs Dp/p Qx = 48.22 Qy = 50.16 No errors: DA = ±23sx×72sy (LEGO) PEP-2 MP field errors (except FFQ): DA = ±20sx×46sy 10 seeds Dp/p=0

Summary – Optimized Baseline Design Chromaticity Correction Schemes x/x,0 DA: x/σx , y/σy Range of (p/p)/σ p/p=0 p/p=0.4% Linear correction: conventional 2-family arc sextupoles (v1) Non-linear: no dedicated correction 1 ±20, ±48 0, 0   9 Linear correction: conventional 2-family arc sextupoles Non-linear: interleaved –I sext pairs in regular arc cells (v1a) Non-linear: FODO type CCB with 2 non-interleaved –I sextupole pairs, optimized phase advance (v1b3) 2.1 ±15, ±40 ±4.5, ±10   9 Non-linear: FODO type CCB with 2 non-interleaved –I sextupole pairs, optimized phase advance, reduced beta functions for lower emittance (v1d2) 1.7 ±17, ±41 ±5, ±10 Non-linear: compact CCB with 3 interleaved sextupoles, optimized phase advance ±8.5, ±18 ±5, ±7.3 Non-linear: SuperB type scheme (SBCC) with regular length dipoles and large bending angles (scheme-3 ) 1.4 ±25, ±60 ±10, ±15 Non-linear: SBCC with short dipoles and small bending angles (scheme-6, optimized, ring geometry not yet matched) 0.93 ±23, ±72 ±7, ±26 11 Best option

Work Plan – since 2016 Fall Meeting Optimize SBCC for low emittance in the optimized baseline design ‒ Done Can emittance be further reduced? Implement the SBCC in the low emittance design with TME-like arc cells and new magnets; match ring’s geometry; optimize chromaticity correction; check dynamic aperture If DA is good, continue with studies in bullet # 4 Otherwise  study the low emittance design with short FODO-arc-cell and new magnets; optimize chromaticity correction; check dynamic aperture Further studies Replace thin-lens trombones with quadrupole adjustment, verify performance Tune scan to find optimal tune for maximum DA Effects of misalignment and field errors on DA Implement orbit correction scheme (BPMs and correctors) Specify tolerances Effects of non-linear field errors on DA Regular magnets: start with the PEP-II specs FF quads: specify tolerances Next  bullet # 2: study performance of ring design based on TME arc cells

Design Based on TME Arc Cells Matched geometry, C = 2276.58 m = 2 x 925.18 m arcs + 2 x 213.11 m straights Low emittance TME-like arc cells with new magnets Low emittance SBCC scheme Two options studied: 4 high-b SBCCs or 2 high-b + 2 low-b SBCCs Emittance @ 5 GeV: e = 3.2 nm-rad, ge = 30.9 mm-rad without SBCCs, e = 3.0 nm-rad, ge = 29.4 mm-rad with 4 high-b SBCCs IP SBCC Design with 4 high-b SBCCs Design with 2 high-b + 2 low-b SBCCs

Arc Cell and SBCC – TME Design SD,SF,SF,SD TME-like arc cell with new magnets Length 22.8 m (same as ion ring arc cell) Arc bending radius 155.45 m (as in the baseline) Phase advance 270o / 90o (x/y) 4 dipoles Length 4 m, bending angle 2.1o Field 0.37 T @ 12 GeV Sagitta 1.83 cm 4 quadrupoles Length 0.56 m Gradient 24 T/m @ 12 GeV 4 sextupoles (2 families) Arc IP S1 S2 Low emittance SBCC (high-b) Short dipoles with small bending angles  low H-function  low emittance contribution Two non-interleaved –I sextupole pairs per SBCC with sufficiently high beta functions Optimized phase advance (np + Dm) from SBCC sextupoles to FFQs for best correction of non-linear chromaticity

Chromaticity Correction – TME design Non-linear correction: previously designed low emittance SBCC 4 high-b SBBCs ‒ for nominal IP and future 2nd IP 2 high-b SBCCs (near IP) + 2 low-b SBCCs ‒ lower natural chromaticity Linear correction (in arcs): Conventional 2-family sextupoles in 24 TME cells per arc (non-linear compensation properties due to ~2p phase advance in every 4 cells ) -I sextupole pairs (non-interleaved or interleaved); various options as shown in the table X, Y indicate X or Y sextupoles in a given cell; empty cells have no sextupoles 90o between same family pairs to cancel 1st order chromatic beta Sextupole strengths of “1” and “2” families in scheme 3d are fixed at X1 = X2/2 and Y1 = Y2/2 Cell # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 3a X Y 3b 3c 3d X1 X2 Y1 Y2 3e 3f

Correction Performance and DA – TME design Schemes with –I pairs in arcs require strong arc sextupoles Large local chromatic beta variation in arcs leading to non-linear chromaticity and poor correction with insufficient momentum range Best performance with: Conventional 2-family arc sextupoles ‒ lowest sextupole strengths and chromatic non-linearities 2 high-b SBCCs (to correct FFQ) + 2 low-b SBCCs ‒ lowest natural chromaticity Tune vs Dp/p 15σx 29σy Dynamic aperture w/o errors Qx = 65.22 Qy = 35.16 Dynamic aperture is smaller than in the optimized baseline design

Short Summary – TME Design Chromaticity Compensation Schemes Arc Sexts K2 (1/m3) x , x DA: x/σx , y/σy (p/p)/σ =0 =0.4% Linear correction: conventional 2-family arc sextupoles Non-linear: 4 high-b SBCCs – 2 SBCCs for FFQ correction, 2 other SBCCs not used for correction 14.71, -22.92 -159, -196 -9, +5 Non-linear: 4 high-b SBCCs – all used for correction 13.93, -22.04 8.8, 23 7, 12 -12, +12 Linear correction: conventional 2-family arc sextupoles, but different position of focusing sextupoles in TME cell Non-linear: 4 high-b SBCCs – 2 SBCCs for FFQ correction, 2 other SBCCs for local correction 43.81, -9.61 Non-linear: 2 high-b SBCCs for FFQ correction, 2 low-b SBBCs not used for correction 10.13, -16.44 -145, -166 15, 29 7, 14 30.53, -7.25 -9, +9 Linear correction: -I pairs in arcs (schemes 3a, 3b) 29.71, -48.56 -5, +5 Best option Lowest 3 nm-rad emittance, but DA of 15s w/o errors may not be large enough ! Next  bullet # 3: study performance of ring design based on short FODO cells

Design Based on Short FODO Arc Cells Short FODO arc cells for low emittance, and new magnets Circumference: C = 2276.45 m = 2 x 926.27 m arcs + 2 x 211.95 m straights Natural chromaticity: [xH, xV] = [-116, -147] Two SBCCs near IP for non-linear chromaticity correction Emittance at 5 GeV (from Elegant): e = 5.5 nm-rad, ge = 54 mm-rad SBCCs 1x 3x 2y 4y IP

Arc Cell and SBCC – Short FODO Design FODO arc cell with new magnets Length 11.4 m (half of ion ring arc cell) Arc bending radius 155.45 m (as in the baseline) Phase advance 108o (x & y) 2 dipoles Length 3.6 m, bending angle 2.1 0.41 T @ 12 GeV Sagitta 1.65 cm 2 quadrupoles Length 0.56 m 21 T/m @ 12 GeV 2 sextupoles (2-family) New Arc IP Spin rotator SBCC FODO cells S1 S2 Low emittance SBCC Short dipoles with small bending angles  low H-function  low emittance contribution Two non-interleaved –I sextupole pairs per SBCC with sufficiently high beta functions Optimized phase advance from SBCC sextupoles to FFQs for best correction of non-linear chromaticity

Correction Performance – Short FODO Design 4 sextupole families in two SBCCs K2L = 2.2, -4.5, -2.6, 3.9 (1/m2) Optimized phase advance from sextupoles to IP 1x=3.7531, 2y=4.2535, 3x=5.2434, 4y=6.2413 Conventional 2-family arc sextupoles (opposite polarities in two arcs) 50 cells with x/y sextupoles per arc K2 = 14.7 and 6.0 (1/m3), L = 0.25 m Sufficiently large momentum range W functions IP  13σ Tune vs Dp/p b* vs Dp/p Qx = 57.22 Qy = 55.16

Dynamic Aperture – Short FODO Design Dynamic aperture at IP, no magnet errors, sx = 23.4 mm, sy = 4.7 mm @ 5 GeV 38σx 70σy So far, the best overall dynamic aperture (w/o errors)

Work Plan – Updated Optimize SBCC for low emittance in the optimized baseline design ‒ Done Can emittance be further reduced? Implement the SBCC in the low emittance design with TME-like arc cells and new magnets; match ring’s geometry; optimize chromaticity correction; check dynamic aperture ‒ Done If DA is good, continue with studies in bullet # 4 ‒ DA is “not good enough” Otherwise  study the low emittance design with short FODO-arc-cell and new magnets; optimize chromaticity correction; check dynamic aperture ‒ Done Further studies for the short FODO-arc-cell design Replace thin-lens trombones with quadrupole adjustment, verify performance Tune scan to find optimal tune for maximum DA Effects of misalignment and field errors on DA Implement orbit correction scheme (BPMs and correctors) Specify tolerances Effects of non-linear field errors on DA Regular magnets: start with the PEP-II field quality FF quads: specify tolerances

Conclusions and Outlook The study confirms that the SBCC scheme with sufficiently short dipoles provides an adequate non-linear chromaticity correction and yields a low emittance contribution in all the studied designs of the electron collider ring The optimized baseline design based on PEP-II magnets provides adequate chromaticity correction and DA, but a relatively high emittance of ~9 nm-rad @ 5 GeV The design based on TME-like arc cells with new magnets provides the lowest emittance of 3 nm-rad, but requires strong arc sextupoles leading to stronger non-linearities and smaller dynamic aperture The design based on short FODO arc cells with new magnets appears to be the best option so far. It provides a relatively low emittance of 5.5 nm-rad, adequate chromatic compensation and the best dynamic aperture (without errors). The plan for further studies is to focus on the short FODO ring design including: finalizing the optics; implementing orbit correction system; optimizing the tune for maximum DA; and investigating the impact of magnet errors and tolerance specification

Non-linear Beam Dynamics Studies for JLEIC Electron Collider Ring Thank You

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PEP-II Measured Multipole Field Errors Systematic errors (DBN/Bref) Dipole at R = 30 mm N= 3 1.00E-5 Quadrupole at R = 44.9 mm N= 3 1.03E-3 4 5.60E-4 5 4.80E-4 6 2.37E-3 10 -3.10E-3 14 -2.63E-3 Sextupole at R = 56.52 mm N= 9 -1.45E-2 15 -1.30E-2 Random errors (DBN/Bref) Dipole at R = 30 mm N= 3 3.20E-5 4 3.20E-5 5 6.40E-5 6 8.20E-5 Quadrupole at R = 44.9 mm N= 3 5.60E-4 4 4.50E-4 5 1.90E-4 6 1.70E-4 10 1.80E-4 14 7.00E-5 Sextupole at R = 56.52 mm N= 5 2.20E-3 7 1.05E-3