MEIC Alternative Design Part III Ion ring by super-ferric magnets Luminosity performance Improving luminosity at low ion energy (and not be afraid of the hour-glass effect) MEIC Accelerator R&D Meeting Sept. 4, 2014

MEIC Ion Ring by Super-ferric Magnets (2.5 km) Super-ferric only Super-ferric High field SC Maximum kinetic energy GeV 87.6 (100) 100 Dipole length m 9.45 0.75 Dipole maximum field T 2 (2.28) 2 6 Bending radius / angle m / deg 146/3.71° 167/3.24° 55.5 / 0.77° BDL split 100% 81% 19% Dipoles in each arc 74 68 FODO cells in each arc 37 34 Cell length/packing factor 24.3 / 0.78 26.2 / 0.78 Figure-8 crossing angle deg 95° Arc length / radius m / m 899.4 / 187.4 896 / 186.8 Straight length 343.4 342 Ring circumference 2486 2477 Super-ferric magnet 9.45 m, up to 2 T High field magnet 0.75 m, up to 6 T

MEIC Ion Ring by Super-ferric Magnets (2.25 km) Super-ferric only Super-ferric High field SC Maximum kinetic energy GeV 79.5 (100) 100 Dipole length m 9.45 1.53 Dipole maximum field T 2 (2.5) 2 6 Bending radius / angle m / deg 132.5/4.1° 167/3.24° 55.5/1.58° BDL split 100% 67% 33% Dipoles in each arc 66 56 FODO cells in each arc 33 28 Cell length/packing factor 24.3 / 0.78 28.2 / 0.78 Figure-8 crossing angle deg 90° Arc length / radius m / m 801 / 170 789 / 167.5 Straight length 340 334 Ring circumference 2283 2249 Super-ferric magnet 9.45 m, up to 2 T High field magnet 1.5 m, up to 6 T

Luminosity As a Function of Electron Energy Luminosity per IP (1033 cm-2s-1) CM energy (GeV)

Luminosity As a Function of Electron Energy Luminosity per IP (1033 cm-2s-1) CM energy (GeV)

Luminosity As a Function of CM Energy Luminosity per IP (1033 cm-2s-1) CM energy (GeV)

Luminosity & Space Charge at Low Ion Energy Proton Electron Beam energy GeV 25 3 Collision frequency MHz 750 Beam current / particles per bunch A /1010 0.047 / 0.039 3 / 2.5 RMS bunch length cm 1 0.75 Emittance, norm. (x/y) µm 0.35 / 0.07 9.9 / 2.0 Horizontal and vertical β* 10/2 (4/0.2) 77.5/15.5 (31/6.2) Vert. beam-beam tune shift 0.015 Laslett tune shift 0.06 Small Dist. from IP to 1st FF quad m 7 (4.5) 3.5 Luminosity per IP, 1033 cm-2s-1 0.22 (0.56) High luminosity  High bunch charge  long bunch length

Slava’s Idea and “Recipe” Long bunch length + traveling final focusing Keep the ion bunch length at the limit due to the space charge, Maintain the ion beta-star possibly short (making it equal to the e- bunch length, optimally, thus it becomes small compared to the i-bunch length) Increase the electron beta-star to the ion bunch length, thus restoring the e- beam transverse area to make it equal to that of the i- beam (that is easy!). Introduce a proper sextupole field to the FFB (final focusing block) of ions. Meaning that the crab cavity is there, sextupole will cause the focal point of ions run through the i-bunch length while following the the e- bunch, in this way integrating collisions of e-bunch through all the i- bunch.

Bunch Length and Hour-Glass Effect M. Furman, LBL-30833, 1999 Hour glass reduction factor Hhg is a slow varying function, this provides a way to exploit luminosity The trick is played in the FCC & CepC proposals: with a fixed aspect ratio, L~Hhg/β*y Circular e+e- collider FCC CepC Z W H tt Bunch length mm 2.56 1.49 1.17 2.42 β*x m 0.5 1 0.8 β*y 1.2 Luminosity reduction Hhg 0.64 0.77 0.83 0.78 0.704

Function Behavior

Luminosity vs. Bunch change/length Full acceptance detector, 25 GeV x 3 GeV Bunch length (cm) Current (mA) Hour-class effect Combined factor Luminosity (1033 cm-2s-1) 1 47 0.977 0.215 2 94 0.944 1.882 0.414 3 141 0.895 2.685 0.591 4 188 0.848 3.392 0.746 5 235 0.803 4.015 0.883 6 282 0.761 4.566 1.005 7 329 0.722 5.054 1.112 8 376 0.686 5.488 1.207 9 423 0.654 5.886 1.295 10 470 0.624 6.24 1.373 Ion beam nominal current ~500 mA

Luminosity vs. Bunch change/length High luminosity detector, 25 GeV x 3 GeV Bunch length (cm) Current (mA) Hour-class effect Combined factor Luminosity (1033 cm-2s-1) 1 47 0.894 0.497 2 94 0.791 1.582 0.880 3 141 0.697 2.091 1.161 4 188 0.620 2.480 1.379 5 235 0.557 2.785 1.548 6 282 0.505 3.030 1.685 7 329 0.462 3.234 1.798 8 376 0.426 3.408 1.895 9 423 0.395 3.555 1.977 10 470 0.368 3.68 2.046 Ion beam nominal current ~500 mA

Hour-glass reduction Factor Hour Glass Reduction Factor Hhg Bunch length (cm)

Luminosity As a Function of Bunch length Luminosity per IP (1033 cm-2s-1) CM energy (GeV)

A Modest(?) Parameter Set at Low Ion Energy Proton Electron Beam energy GeV 25 3 Collision frequency MHz 750 Current / particles per bunch A /1010 0.047/0.039 3 / 2.5 0.188/0.156 RMS bunch length cm 1 0.75 6 Emittance, norm. (x/y) µm 0.35 / 0.07 9.9 / 2.0 Horizontal and vertical β* 10/2 (4/0.2) 77.5/15.5 (31/6.2) Vert. beam-beam tune shift 0.015 Laslett tune shift 0.06 Small 0.04 Dist. from IP to 1st FF quad m 7 (4.5) 3.5 Luminosity per IP, 1033 cm-2s-1 0.22 (0.56) 0.67 (1.13) Increase the bunch length from 1 cm to 6 cm Increase the bunch charge a factor of 4 Reduce the space charge tune-shift from 0.6 to 0.4