Damping Ring Requirements for 3 TeV CLIC Quantity Symbol Value Bunch population N b 9 4.1 10 No. of bunches/train k bt 154 Repetition frequency f r 100 Hz Horizontal emittance γε x 7 4.5 10 m Vertical emittance γε 9 3 10 m Bunch spacing! CLIC 3 TeV emittance requirements are very demanding in comparison to other projects.! Work in progress many problems remain. l b y 0.2 m Min. kicker rise time T kicker 25 ns Table 1: Beam parameters required for 3 TeV CLIC 1. 10 8εêm 1. 10 9 1. 10 10 1. 10 11 1. 10 12 13 1. 10 ATF achieved NLC e+ main TESLA e+ CLIC 500 GeV ATF achieved NLC e+ main CLIC 500 GeV Emittances Horizontal Vertical CLIC 3 TeVe TESLA e+ CLIC 3 TeVe 1.5 2 2.5 3 3.5 4 4.5 5 EêGeV CLIC Damping Rings, LC02, SLAC, 4/2/2001 1
Approach to Damping Ring Design! Follow conventional scheme of racetrack ring TME cells in arcs Damping wigglers in straight sections! Established semi-analytic design recipes do not take account of intensity-dependent effects: Intra-beam scattering Electron Cloud Fast beam-ion instability Bunch-lengthening Etc CLIC Damping Rings, LC02, SLAC, 4/2/2001 2
! Vertical emittance from opening angle of synchrotron radiation Vertical emittance limit? ε y 13λ/ = 32 e 13 ceλ/ e β 12 3π 2.3 10 β y 14 3 () s G () s 3 G () s ds W B E W ds, [ BW / T] β [ E / GeV] W G = 1/ ρ (wiggler - dominated machine)! CLIC case: this is a significant fraction (say 20%) of the design vertical emittance! Independent of energy of damping ring ε y 1.53 10 < β W [ E / GeV] < 66 m m [ B / T] W 12 required for CLIC 3 TeV 30 m CLIC Damping Rings, LC02, SLAC, 4/2/2001 3
Lattice example! Arcs: many TME cells Minimises quantum excitation of ε x high tune, 2.4 km circumference! Wiggler-dominated Rapid radiation damping! Relatively high energy, 4-64 GeV Counteracts intra-beam scattering Design must include compensation of IBS effect CLIC Damping Rings, LC02, SLAC, 4/2/2001 4
TME cell CLIC Damping Rings, LC02, SLAC, 4/2/2001 5
Full ring CLIC Damping Rings, LC02, SLAC, 4/2/2001 6
Intra-beam Scattering! Emittances evolve with IBS and radiation (3 coupled ODEs) ε& µ = 2ε µ τ µ 123 Radiation damping + 2ε µ 0 ( µ + ), µ { x, y, t} τ µ Tµ ε x, ε y, ε t { Quantum excitation ε 14243 Intra -beam scattering! No stationary solution in general IBS growth times from Bjorken-Mtingwa theory to sum local values over all elements of our lattices. Plots show evolution of σ x (blue), ε y (red) and ε t (black) from injection to extraction (5 damping times). Dashed lines correspond to the absence of IBS. CLIC Damping Rings, LC02, SLAC, 4/2/2001 7
Comparison: 2 lattices with similar wiggler sections & TME cells Lattice example drv16 Symbol Value Beam energy E 1.98 GeV Circumference C 538 m Insertion length L insertion 60 m Wiggler length L wig 10.8 m Wiggler peak field B 1.8 T Wiggler period w λ 0.2 m w Lattice example drs10 Symbol Value Beam energy E 4.63 GeV Circumference C 2419 m Insertion length L insertion 60 m Wiggler length L wig 10.8 m Wiggler peak field B 1.8 T Wiggler period w λ 0.2 m w log 10 HeêmL -5-6 -7-8 -10-11 -12 120 1 ÅÅÅÅ t "drv116" 0.02 0.04 0.06 0.08 0.1 0.12 0.14 tês Evolution of emittances during 5 damping times. No IBS case = dashed lines Slow growth of ε x log 10 HeêmL -6-10 -12 40 1 ÅÅÅÅÅ t "drscale10" 0.02 0.04 0.06 0.08 0.1 tês Closer to target emittances in higher energy ring. 100 30 80 60 40 20 TME arcs Wigglers 500 1000 1500 2000 Snapshots of detailed IBS growth rates at onset of pseudo-equilibrium. Element no. PAC2001 paper Element no. 2000 4000 6000 8000 CLIC Damping Rings, LC02, SLAC, 4/2/2001 8 20 10 TME arcs Wigglers Close to 3 TeV requirement
Increasing energy is only way! Study of parametrised generic damping ring lattice modules JMJ, Bruce Knuteson (Univ. Chicago), to appear CLIC Damping Rings, LC02, SLAC, 4/2/2001 9
Examples of results Loss rate CLIC Damping Rings, LC02, SLAC, 4/2/2001 10
EGeV 4.62681 N t 77 N cell 222. θ Arc 0.0283026 2956.8 Meter C dr LArc cell LArc bend N W L W λ W LArc cell 5.29568 Meter 25.8229 " βw " Meter 7.2413 Meter 0.280421 Meter 3ê2 " β W Spin - tune ν = 10.5 Energy loss ratio FI 2W = 2, Quantum excitation ratio FI 2W = 0.9, TME cell detuning factor f = 3 TME B W g W 2.10196 Kilogram Ampere Second2 0.0280421 Meter3ê2 " β W L W +LArc bend Ncell 0.400055 C dr ρ Arc B arc α c τ x τ r 187.109 Meter 0.0824832 Kilogram Ampere Second2 n DT 3.65594 0.000338203 i 0.177741 Meter 0.000133775 Meter2 y k β W { Meter 0.210616 Second 0.0000712311 Second Meter ε xdr 3.31329 10 11 Meter ε xno 4.5 10 7 Meter σ ε 0.00111292 h ε 0.5 D m 0.022044 Meter β m 2.05101 Meter µ xtme 0.231934 f 1.49896 10 9 RF Second h RF 14784 I dr 0.80904 Ampere 6.24151 10 12 Second 2 U dr Kilogram Meter2 0.649999 525875. Kilogram Meter P 2 dr Second 3 P dr 177.853 Kilogram Meter C dr Second3 τ pdr 17319.4 Second P dr 0.0208702
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