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Optimization of Solenoid Configuration for FCC-ee Collider Emittance Control

This study explores the effect of compensating and screening solenoids on the solenoid fringe field in the FCC-ee collider using various models and lengths. Key findings include optimized solenoid positions and verified emittance calculations. The results provide valuable insights for designing the solenoid system to minimize fringe field effects.

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Optimization of Solenoid Configuration for FCC-ee Collider Emittance Control

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  1. IR with compensating and screening solenoids in FCC-ee S. Sinyatkin Budker Institute of Nuclear Physics 30 October 2015, CERN

  2. What was done • The solenoid fringe field effect is estimated for various solenoid models: • - compensating and main solenoid lengths are varied, the sum is kept unchanged; • - compensating solenoid length is varied, the main solenoid length is kept unchanged. • Optimized positions of compensating and screening solenoids. • Checked MAD calculations (EMIT module) of emittance.

  3. L_main/2 L_comp Compensating solenoid is located between IP and QD0 Radius of: - compensating solenoid R = 0.1 m - screening solenoid R = 0.2 m

  4. Variation of main and compensating solenoids lengths Geom. length: 1 – L_comp = 0.5 m 2 – L_comp = 0.6 m 3 – L_comp = 0.7 m 4 – L_comp = 0.8 m 5 – L_comp = 0.9 m 6 – L_comp = 1 m Area of residual field ~ 0.5 m B_comp_max ~1/L_comp Conditions: B_main*L_main+2*B_comp*L_comp=0 L_total=L_main+2*L_comp=const=4 m(geometric length)

  5. Variation of main and compensating solenoids lengths Geom. length: 1 – L_comp = 0.5 m 2 – L_comp = 0.6 m 3 – L_comp = 0.7 m 4 – L_comp = 0.8 m 5 – L_comp = 0.9 m 6 – L_comp = 1 m Bx ~ (L_total_h-L_comp)2/L_comp Conditions: B_sol*L_main+2*B_comp*L_comp=0 L_main+L_comp=const=2 m (geometric length) Bx~ (L_total_h-L_comp)2/L_comp

  6. Estimation of vertical emittance dependence on compensating solenoid length*. Conditions: B_sol*L_main+2*B_comp*L_comp=0 L_main+L_comp=const=2 m (geometric length) I5,y ~ hy5 ~ Bx5 *-Equivalent model is used for MAD simulation

  7. Variation of main and compensating solenoids lengths* *-Equivalent model is used for MAD simulation

  8. Variation of compensating solenoids length Geom. length: 1 – L_comp = 0.5 m 2 – L_comp = 0.6 m 3 – L_comp = 0.7 m 4 – L_comp = 0.8 m 5 – L_comp = 0.9 m 6 – L_comp = 1 m B_comp_max ~1/L_comp Conditions: B_sol*L_main+2*B_comp*L_comp=0 L_main+L_comp is variable L_main=±1 m (geometric length)

  9. Variation of compensating solenoids length Geom. length: 1 – L_comp = 0.5 m 2 – L_comp = 0.6 m 3 – L_comp = 0.7 m 4 – L_comp = 0.8 m 5 – L_comp = 0.9 m 6 – L_comp = 1 m Conditions: B_sol*L_main+2*B_comp*L_comp=0 L_main+L_comp=var. L_main=2 m (geometric length)

  10. Variation of compensating solenoids length* Conditions: B_sol*L_main+2*B_comp*L_comp=0 L_main/2+L_comp=const=2 m I5,y ~ hy5 ~ Bx5 *-Equivalent model is used for MAD simulation

  11. Variation of compensating solenoid length* *-Equivalent model is used for MAD simulation

  12. Optimisation of edge field area Final quads Main detector solenoid 2 Quad screening solenoid 1 4 3 Compensating solenoid 1 – Half of main solenoid length ( 1 m) 2 – Length of compensating solenoid (0.7 m) 3 – Overlap of compensating and screening solenoids (5 cm) 4 – Length of screening solenoid ( 3.95 m) Transverse half size: - compensating solenoid - R = 0.1 m - screening solenoid - R = 0.15 m

  13. Field distribution versus overlap length Overlap length: 1 – 0 cm 2 – 5 cm 3 – 15 cm 4 – 20 cm With overlap length of 5 – 10 cm Edge field Bs<0.01 T in the 10 cm area after end of compensating solenoid Transverse half size: - main solenoidfield - Lgeom = 1 m, Bs = 2 T - compensating solenoid - R = 0.1 m, Lgeom = 0.7 m, Bs~ 2.8 T - screening solenoid - R = 0.15 m , Lgeom = 3.95 m

  14. Beam parameters (E = 45 GeV)

  15. Optic model of solenoids • Piecewise elements have been inserted into 2 m (distance from IP to QD0) • Solenoids are presented by thick elements. • Skew components are thin elements. • Radial and vertical fields are presented by thin elements with nonzero length to carry out emittance calculation by EMIT module (Lrad = 2/N, N – slices number).

  16. Beam Orbit at IR Critical photon energy (E=175 GeV): εc up to 4.9 MeV Radiation angle ~ ± 0.2 mrad Bx_max = 0.24 T

  17. Check of emittance calculation • Formula I2 = 6.07*10-4 m-1 • MAD calculation (EMIT module) Ey = 0.259 pm*rad • Deviation between MAD calculation and formulas increases at short comp. solenoid (strongcomp. field)

  18. Tilt of eigen oscillation modes degree

  19. Summary • Vertical emittancelightly increases when compensating solenoid length decreases with unchanged main solenoid length(2 m). • Slicing allows to take into account fringe fields of the solenoids more precisely. • To exclude leakage of the edge magnetic field into the quadrupole area the length of the compensating solenoid must be reduced to 0.7 m. • For design luminosity the length of the main solenoid should be 1 m, compensating – 0.7 m, the screening solenoid should be overlapped with the compensating solenoid by 5 -10 cm. • The distance between the compensating solenoid end and QD0 quadrupole should be more than 30 cm.

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