COMPENSATION OF DETECTOR SOLENOID FIELD WITH L*=4.1M Glen White, SLAC April 20, 2015 ALCW2015, KEK, Japan

Overview The overlap of the main detector solenoid fields with the final doublet generates beam aberrations at the IP Coupling and vertical dispersion terms These can be partially corrected for using a compensating “anti-solenoid” field “Compensation of detector solenoid effects on the beam size in a linear collider” PRST-AB 8, (2005) Y. Nosochkov & A. Seryi Provided for by pair of “force-neutral anti-solenoid” windings within QD0 cryostat. Generates no net longitudinal force on internal quadrupole magnet. Create simulation environment for optimizing parameters of anti-solenoid. Results presented for current SiD & ILD detector solenoid field maps, with & without “anti-DID” dipole fields.

Anti-Solenoid Field Region in QD0 Cryostat QD0 cryostat package currently being re-designed by B. Parker, as shown for illustration purposes only Considering yoke over outer half of QD0 magnet package which would shield detector solenoid field there. Not included in simulations shown here. Also considering additional fine-correction coil wound directly on QD0 Force-neutral anti-solenoid is 2 concentric coils centered in detector reference frame. R 2 inner /R 2 outer = 0.5 and I inner /I outer = -2 for force cancelation to work R inner = 77mm R outer = 112mm Parameters used to optimize anti-solenoid field for beam aberration cancelation: Length of solenoid coils (inner=outer), assuming end of anti- solenoid coil fixed at d/s QD0 end Solenoid field strength (maintaining required inner:outer ratio) Dipole windings on QD0 to achieve beam centering at IP. Anti-Solenoid Region in QD0 Inner/outer force neutral anti-solenoid coils. (QD0 Cryostat design by B. Parker, BNL)

Solenoid Field Description Implement code within Matlab (Lucretia) to generate anti- solenoid field maps according to analytic formula shown. Cross-check with field generation code from BNL used for magnet design.

Simulation Environment and Optimization Procedure Lucretia (Matlab) tracking model of IR region, utilizing recent addition to call GEANT4 for tracking through arbitrary 3D EM field D macro-particle bunch representation for optimization, 10 5 for final results. Quadrupole and sextupole fields directly calculated for tracking inside SD0 & QD0. Set GEANT4 tracking options and verify correct beam tracking to IP (compared with standard Lucretia tracking) OC0 is treated as a thin-lens element in the center of SD0 and tracked by Lucretia. Superimpose detector solenoid field description in beam reference frame. Generate anti-solenoid and dipole fields based on parameterized optimization, superimpose onto global fields for tracking. Provide optimizer anti-solenoid length and strength parameters as input variables. Optimizer tracks beam, applies required dipole field strengths in QD0 to IP and minimizes parameters for (1/σ x /σ y ) Main detector solenoid field values linearly interpolated from provided maps. Third-order stepper (“G4SimpleHeum”) required for GEANT4 field tracking instead of standard fourth-order Runge-Kutta for stability. GEANT particle tracking includes incoherent synchrotron radiation process. Other physics processes deactivated.

IR Solenoid Field Maps (no Anti-DID) 3D field maps provided by detector collaborations Transform to beam reference frame (14 mrad horizontal x-ing) Common L*=4.1m Fields superimposed onto QD0 and SD0 fields (not shown) Also use dipole field windings on QD0 to correct IP trajectory (not shown here). ILD has larger impact on beam aberrations due to larger integrated solenoid field overlap with QD0. Using larger field strength option of 4T to assess worse-case scenario SiD ILD QD0 SD0 QD0 SD0 QD0 SD0 QD0 SD0

Beam Tracking with/without Optimized Anti-Solenoid & Dipole Corrections SiD ILD QD0 SD0 QD0 SD0 QD0 SD0 QD0 SD0

Optimization of Anti-Solenoid TDR 500 GeV baseline: σ x = 475nm σ y =5.9nm Figures show minimum beam sizes for given anti-solenoid lengths (beam collision maintained with QD0 dipole fields) Max length restricted to 1.1m (Overlap with QD0A) Optimizer has set solenoid strength in each case based on (1/σ x /σ y ) SiD ILD

Optimal Anti-Solenoid and QD0 Dipole Fields SiD ILD QD0 SD0 QD0 SD0 QD0 SD0 QD0 SD0

Detector “Anti-DID” Fields “Anti-DID” dipole fields included in detector fields directs beamstrahlung pair radiation to minimize detector backgrounds. Field profiles as provided by detector groups. Optimized for RDR configuration, need to be re-optimized for TDR parameters. Deflects incoming beams away from each other vertically. Reduces effectiveness of Anti-Solenoid correction and leads to increased beam aberrations. QD0 SD0 QD0 SD0 SiD ILD

IR Solenoid Field Maps (+ Anti-DID) 3D field maps provided by detector collaborations Transform to beam reference frame (14 mrad horizontal x-ing) Common L*=4.1m Fields superimposed onto QD0 and SD0 fields (not shown) Also use dipole field windings on QD0 to correct IP trajectory (not shown here). ILD has larger impact on beam aberrations due to larger integrated solenoid field overlap with QD0. Using larger field strength option of 4T to assess worse-case scenario SiD ILD QD0 SD0 QD0 SD0 QD0 SD0 QD0 SD0

Beam Tracking with/without Optimized Anti- Solenoid & Dipole Corrections QD0 SD0 QD0 SD0 QD0 SD0 QD0 SD0 SiD ILD

Optimization of Anti-Solenoid SiD TDR 500 GeV baseline: –σ x = 475nm σ y =5.9nm Figures show minimum beam sizes for given anti-solenoid lengths (beam collision maintained with QD0 dipole fields) –Max length restricted to 1.1m (Overlap with QD0A) –Optimizer has set solenoid strength in each case based on (1/σ x /σ y ) ILD

Optimal Anti-Solenoid and QD0 Dipole Fields QD0 SD0 QD0 SD0 QD0 SD0 QD0 SD0

Correction of Remaining Aberrations Remaining aberrations are,, η y, η x Correct using FFS sextupole mover knobs & BDS skew-quads. Compare magnitude of remaining aberrations with those present from expected alignment errors and magnet field errors (100 simulated seeds shown above) Tuning system designed to correct to design beam sizes given above initial state Expect no additional problems if solenoid related errors are small in comparison SiD ILD SiD (+ Anti-DID) ILD (+ Anti-DID)

Summary The addition of an Anti-Solenoid field winding inside the QD0 cryostat improves aberrations due to coupling and dispersive effects of the overlapped quad and detector solenoids. Factor reduction Remaining aberrations can be cancelled using FFS correction knobs required for beam tuning. Need to confirm with tuning simulation including IR fields. Iterate with FD magnet package design More parameters for optimization : independent anti-solenoid lengths, QD0 solenoid winding tweak, solenoid position. Measured QD0/SD0 and dipole field profiles Updated anti-DID fields Check all ILC baseline parameters Tracking model of IR region including all fields will be of further use for calculation and optimisation of backgrounds.