Electron Ring Optics Design Alex Bogacz for MEIC Collaboration Center for Advanced Studies of Accelerators MEIC Review September 2010

Figure-8 Collider Rings total ring circumference ~1000 m 60 deg. crossing Collider Ring size is a compromise between synchrotron radiation and space charge 3-11 GeV electrons 20-60 GeV ions (with 6 Tesla dipoles)

Collider Ring Architecture Larger Figure-8 Rings (~1000 m circumference) 6 Tesla bends for ions at 60 GeV Additional straights to accommodate ‘snakes’ (ions) and RF (electrons) Horizontal IR crossing, dispersion free straights Spin Rotators (4) at arcs ends Electron Collider Ring based on emittance preserving Optics FODO (1350 phase adv/cell) FMC/DBA Optics TEM Optics?

Electron Ring - 1350 FODO Cell E = 11 GeV 4.03051 15 0.15 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y 4.03051 0.5 PHASE_X&Y Q_X Q_Y phase adv/cell: Dfx,y= 1350 Arc dipoles: $Lb=110 cm $B=12.5 kGauss $ang=2.14 deg. $rho = 29.4 meter Arc quadrupoles $Lq=40 cm $G= 9 kG/cm 1350 FODO offers emittance preserving optics – 〈H〉 minimum for FODO lattices Synchrotron radiation power per meter less than 20 kW/m

Emittance preserving Optics 4.03051 15 0.3 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y 1350 FODO F ~〈H〉 Minimized 〈H〉 over bends H = gD2 + 2aDD’ + bD’2 F  100 Equilibrium rms emittance at 5 GeV: ex = 1.87 ×10-8 m

Quarter Arc Achromat 60 × 1.1 meter dipoles 120 deg. Arc 15 0.15 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y 120 deg. Arc 2 dis. sup. cells 2 dis. sup. cells 26 FODO cells 60 × 1.1 meter dipoles

Electron Ring - Arc Optics 260 15 0.15 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y 240 deg. Arc quarter Arc – 120 meter Straight – 20 meter quarter Arc – 120 meter

Electron Half-Ring - Lattice 494.097 15 0.15 -0.15 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y ×2 Arc ‘inward’ – 260 m Straight – 234 m Ring circumference – 988 m

Spin Rotator - Ingredients… 320 230 15 0.15 -0.15 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y Arc end 4.4 0 8.8 0 Spin rotator ~ 46 m BL = 11.9 Tesla m BL = 28.7 Tesla m

Locally decoupled solenoid 17.9032 15 5 BETA_X&Y[m] BETA_1X BETA_2Y BETA_1Y BETA_2X BL = 28.7 Tesla m solenoid 4.16 m solenoid 4.16 m decoupling quad insert M = C - C

Locally decoupled solenoid 17.9032 15 1 -1 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y BL = 28.7 Tesla m solenoid 4.16 m solenoid 4.16 m decoupling quad insert M = C - C

Spin Rotator - Optics 5 GeV 4.4 0 8.8 0 Spin rotator ~ 46 m 374 288 30 1 -1 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y 4.4 0 8.8 0 Spin rotator ~ 46 m BL = 11.9 Tesla m BL = 28.7 Tesla m

Emittance preserving Optics 46 28.5 20 1 -1 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y BL = 28.712 Tesla m Solenoid 2 Solenoid 1 8.8 deg. bend Minimized 〈H〉 over bends H = gD2 + 2aDD’ + bD’2

Spin Rotator Pair - Optics 5 GeV 374 288 30 1 -1 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y 575 490 30 1 -1 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y 4.40 8.80 BL = 11.8 T m BL = 28.7 T m -4.40 -8.80 BL = -11.8 T m BL = -28.7 T m

Lower emittance - upgrade path E = 5 GeV E = 11 GeV 4.03051 15 0.3 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y 4.03051 15 0.3 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y 1350 FODO FMC Cell F = 100 F = 30 exeg = 1.87 ×10-8 m Minimize 〈H〉 over bends H = gD2 + 2aDD’ + bD’2

Extreme emittance preserving Optics E = 11 GeV FMC Cell TEM like Cell 4.03051 15 0.3 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y 4.06 20 0.2 BETA_X&Y[m] DISP_X&Y[m] BETA_X BETA_Y DISP_X DISP_Y F = 30 F = 3

Summary Complete design of Figure-8 Collider Rings (~ 1000 m circumference) Emittance preserving Arcs based on 1350 FODO lattice Compact spin rotators ‘meshed’ into the arcs No dispersion suppression at arc end Locally decoupled solenoid inserts Beyond 1350 FODO Optics in the arcs FMC Optics TEM Optics?