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S2E optics design and particles tracking for the ILC undulator based e+ source Feng Zhou SLAC ILC e+ source meeting, Beijing, Jan. 31 – Feb. 2, 2007

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Main parameters ParameterSymbolValueUnits Positrons per bunch at IPnbnb 2 x 10 10 (1 x 10 10 ) † number Bunches per pulseNbNb 2820 (5600) † number Pulse Repetition Ratef rep 5Hz Positron Energy (DR injection)E0E0 5GeV DR Dynamic Aperture γ(Ax +Ay)<0.09m-rad DR Longitudinal AcceptanceAlAl ( 3.46)x( 25) cm-MeV Electron Drive Beam EnergyEeEe 150GeV Undulator Period 1.15cm Undulator StrengthK0.92- Undulator Type-Helical- Photon Energy (1 st harm cutoff)E c10 10.06MeV Target Material-Ti-6%Al-4%V- Target ThicknessLtLt 0.4 / 1.5r.l. / cm Incident Spot Size on Target ii >0.75mm, rms Positron Polarization † P60%

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Layout of the ILC e+ source Target to capture system (125 MeV) Target hall: 125 MeV dogleg,125-400 MeV NC pre- acceleration, and 400 MeV dogleg 5.03 km 400 MeV transport SC boost linac to 5 GeV Linac-to-Ring: spin rotations, energy compression, and beam collimation. 5-GeV beam dump

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Transport in Target hall OMD (6T-0.5T): to transform e+ with small spot size and large divergence at the target into large size and small divergence at the capture cavities. N.C. RF capture cavities system embedded in a 0.5 T of solenoid to accelerate e+ beam to 125 MeV. PCAP - 125 MeV e+ beam dogleg: to separate e+ from e- and photons using a dogleg with 2.5 m of horiz. offset (by Nosochkov). PPA - NC pre-accelerator consisting of L-band structures embedded in a 0.5 T of solenoid to accelerate e+ from 125 MeV to 400 MeV. PPATEL - a 400-MeV horiz. and vert. dogleg to deflect the beam by 5 m and 2 m in the horiz. and vert. planes, respectively (by Nosochkov).

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PCAP PPA PPATEL PCAP PPA PPATEL X (m) Y (m) Z (m)

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400 MeV 5-km Transport PTRANa – to follow e- main linac tunnel for 4 km. PTRANb – to bring e+ from e- main linac tunnel to e+ booster linac tunnel. PTRANc – 479 m of transport to connect with booster linac. Y (m) X (m) Z (m) PTRANa PTRANb PTRANc

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5-GeV e+ booster linac Accelerate e+ beam from 400 MeV to 5 GeV. Have 3 sections: - 400 MeV to 1.083 GeV (4 non-standard ILC CM, each CM has 6 9-cell cavities and 6 quads) - 1.083 GeV to 2.626 GeV (6 ILC CM, each has 2 quads) - 2.626 GeV to 5 GeV (12 standard ILC CM, each has 1 quad )

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LTR – Linac to Ring Spin rotations to preserve polarization in DR: - Bending magnets: from longitudinal to horizontal plane =n 7.929 at 5 GeV; here n=7 to get reasonable R56. - Solenoid: from horizontal to vertical, parallel or anti-parallel to the magnetic field in the DR: = 26.23 T.m at 5 GeV. Energy compression: R56 and RF section Collimations: to reduce beam loss in the DR Emittance measurement, and 3 PPS stoppers Matching section

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collimation 7X7.929 collimation solenoid RF solenoid RF section 7X7.929 Emitt. station

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5-GeV e+ beam dump As a beam dump: for 0.1% and 10% of energy spread, the half edge beam sizes x/ y are 3.9cm/8.3cm and 14.3cm/8.3cm, respectively, which meet the dump window specifications (see D. Walz, Snowmass, 2005). As an energy spectrometer: 0.1% of resolution. 1 st Bend of PLTR arc, its power off for dump Dump bendMonitor for energy spectrometer Dump window

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Overall e+ source optics

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X (m) Y (m) Z (m) PCAP, PPA, and PPATEL PTRAN PBSTR LTR Overall e+ source geometry

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Multi-particle Tracking from the Target to the DR injection line Multi-particle tracking from the Target to the capture system (125 MeV) (by Y. Batygin). Elegant code is used to track the e+ beam through the rest of the beamline including the PCAP, PPA, PPATEL, PTRAN, PBSTR, and LTR. Energy compression is optimized to accommodate more e+ within the DR 6-D acceptance: m, and ( 25MeV) ( 3.46cm)

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ComponentsHalf aperture in x/y (cm) Capture cavities2.3/2.3 PCAP7.5/7.5 PPA2.3/2.3 PPATEL7.5/7.5 PTRAN7.5/7.5 PBSTR3.7/3.7 LTR RF section Solenoid Others 3.7/3.7 2.0/2.0 7.5/3.5 ILC e+ source physical apertures

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Undulator parameter: K=1, =1cm. Target: 0.4 r.l., immersed B 0 =6T. OMD: B=B 0 /(1+g.z), g=0.6/cm, z=18.3cm. Target Time (s) y’ (rad) y (m) 125 MeV Y. Batygin, www.slac.stanford.edu/~batygin/

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ILC e+ loss distribution along the beamline

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Time (s) With LTR, but w/o collimation 2X3.46cm 50 MeV Time (s) With LTR and collimation 2X3.46cm 50 MeV Time (s) W/o LTR

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RMS values of magnet errors for tracking Misalignment in x and y plane Field errorRotation error Quad x = 200 m y = 200 m 0.1% Sextupole x = 200 m y = 200 m 0.1% Bend x = 200 m y = 200 m 0.1%0.3 mrad

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No error x (m) x (rad) No error y (m) y (rad) with errors but no correction x (m)y (m) with errors but no correction With errors and correction x (m)y (m) y (rad) x (rad) y (rad)

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Comparisons of capture efficiency Survived in physical apertures Captured within DR Trans. acceptance Captured within DR 6-D acceptance W/o LTR With LTR55.4%53.3% 32.3% 49.8% With LTR and collimation49.6%48.8%48.5% W/ errors W/o orbit correction54.9%42.8%40.2% With errors and orbit correction55.4%53.0%49.8%

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Summary and outlook S2E optics for e+ source is developed. S2E tracking w/o and w/ errors is performed: 49.8% of e+ from the target are captured within the DR 6-D acceptance after energy compression. e+ loss into DR is ~1% after LTR collimation; additional betatron collimators are needed to collimate 0.8% of e+. Field and alignment errors and orbit correction are analyzed. Toward EDR: optics and physical aperture optimizations; reducing e+ loss in the DR; modeling activation of the 5- GeV collimations; tolerances definition; and tuning requirements. F. Zhou, Y. Batygin, Y. Nosochkov, J, C.Sheppard, and M. D. Woodley, “Start-to-end optics development and multi-particle tracking for the ILC undulator-based positron source”, SLAC-PUB-12239, Jan. 2007.

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