Damping Ring Requirements for 3 TeV CLIC

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2 Damping Ring Requirements for 3 TeV CLIC Quantity Symbol Value Bunch population N b No. of bunches/train k bt 154 Repetition frequency f r 100 Hz Horizontal emittance γε x m Vertical emittance γε 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 εêm 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 EêGeV CLIC Damping Rings, LC02, SLAC, 4/2/2001 1

3 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

4 ! Vertical emittance from opening angle of synchrotron radiation Vertical emittance limit? ε y 13λ/ = 32 e 13 ceλ/ e β 12 3π 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 < 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

5 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

6 TME cell CLIC Damping Rings, LC02, SLAC, 4/2/2001 5

7 Full ring CLIC Damping Rings, LC02, SLAC, 4/2/2001 6

8 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 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

9 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 ÅÅÅÅ t "drv116" tês Evolution of emittances during 5 damping times. No IBS case = dashed lines Slow growth of ε x log 10 HeêmL ÅÅÅÅÅ t "drscale10" tês Closer to target emittances in higher energy ring TME arcs Wigglers Snapshots of detailed IBS growth rates at onset of pseudo-equilibrium. Element no. PAC2001 paper Element no CLIC Damping Rings, LC02, SLAC, 4/2/ TME arcs Wigglers Close to 3 TeV requirement

10 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

11 Examples of results Loss rate CLIC Damping Rings, LC02, SLAC, 4/2/

12 EGeV N t 77 N cell 222. θ Arc Meter C dr LArc cell LArc bend N W L W λ W LArc cell Meter " βw " Meter Meter 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 Kilogram Ampere Second Meter3ê2 " β W L W +LArc bend Ncell C dr ρ Arc B arc α c τ x τ r Meter Kilogram Ampere Second2 n DT i Meter Meter2 y k β W { Meter Second Second Meter ε xdr Meter ε xno Meter σ ε h ε 0.5 D m Meter β m Meter µ xtme f RF Second h RF I dr Ampere Second 2 U dr Kilogram Meter Kilogram Meter P 2 dr Second 3 P dr Kilogram Meter C dr Second3 τ pdr Second P dr

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