1. MDI and head-on collision option for electron-positron Higgs factories
S. Sinyatkin
Budker Institute of Nuclear Physics
12 January 2016

2. IR with compensating and screening solenoids
Head-on collision.
Main and compensating solenoids are placed between defocusing lenses of FF. Betatron coupling is corrected by compensating solenoids. Vertical emittance is not excited.
Compensating solenoids are located outside the area of FF quad lenses. Betatron coupling is corrected by compensating solenoids and additional skew quads. Vertical emittance is created by area with non zero vertical dispersion.

3. IR with compensating and screening solenoids
Collision with crossing angle at IP and crab-waist sextupoles.
Main and compensating solenoids are placed between defocusing lenses of FF. Betatron coupling is corrected by compensating solenoids. Vertical emittance is formed by horizontal magnetic field of solenoids.
Compensating solenoids are located outside the area of FF quad lenses. Betatron coupling is corrected by compensating solenoids and additional skew quads. Vertical emittance is created by area with non zero vertical dispersion and horizontal magnetic field of solenoids.

4. Compensating solenoid is located between IP and QD0 Radius of:
L_main/2
L_comp
Для уменьшения влияние краевых полей необходимо иметь максимальные поперечные размеры антисоленоида. Чтобы уменьшить вывал поля в область экранированного поля необходимо иметь наименьшие размеры экранирующего соленоида. Здесь предполагается, что основное поле соленоида однородное в области других соленоидов.
Compensating solenoid is located between IP and QD0
Radius of:
- compensating solenoid R = 0.1 m - crossing angle α = 30 mrad
- screening solenoid R = 0.2 m

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
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)

6. 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/2+L_comp=const=2 m (geometric length)
Bx~ (L_total_h-L_comp)2/L_comp

7. Emittance calculation
Ring:
I2 = 6.07*10-4 m-1
Solenoids: .

8. Vertical emittance vs. compensating solenoid length.
Conditions:
B_sol*L_main+2*B_comp*L_comp=0
L_main/2+L_comp=const=2 m (geometric length)
I5,y ~ hy5 ~ Bx5

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
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=2 m (geometric length)

10. 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)

11. 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

12. Optimisation of edge field area
Final quads
Main detector solenoid 2 1
Quad screening solenoid 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 – 0.15 m
- screening solenoid R = 0.15 m

13. 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).

14. Beam Orbit at IR Critical photon energy (E=175 GeV): εc up to 4.9 MeV
Main detector solenoid
Compensating solenoid
Final quads
Critical photon energy (E=175 GeV):
εc up to 4.9 MeV
Radiation angle
~ ± 0.2 mrad
Bx_max = 0.24 T

15. Check of emittance calculation
Formula
I2 = 6.07*10-4 m-1
MAD calculation (EMIT module) Ey = pm*rad .

16. Tilt of eigen oscillation modes
degree

17. Summary
Vertical emittance is not excited (or is small) for head-on collision scheme.
Vertical emittance is excited by radial magnetic field of edges between main solenoid, compensating solenoid and screening solenoid for crab-waist scheme.
There is a possibility to optimize magnetic field of edges.
Vertical emittance is strongly excited by radial field of solenoids at low energy (Bmain sol = const).
Slicing of solenoids and fringe field areas allows to take into account fringe fields of the solenoids more precisely.

18. Head-on collision lattice

19. IR design
Transverse size of tunnel is small in comparison with crab-waist scheme.
Single aperture of final focus elements. Simple elements are used.
There is limitation of critical energy of synchrotron radiation photons in experimental section (100 keV at beam energy 120 GeV)
The Crab section can be excluded.
Local chromaticity correction to provide maximal energy acceptance (± 2% at 120 GeV).
Maximal number of bunches is limited by area of beam separation.

20. Experimental section layout Head-on collision
CCSX
CCSY
Distance between reference orbits is 1.8 m
Сritical energy of synchrotron radiation photons :
Region: 0 – 500 m, Eγ = 100 keV
Region: 500 – 730 m, Eγ = 200 keV

21. Final focus Quad Q0: K1 = -91 T/m L = 3.6 m Quad Q1: K1 = 84 T/m

22. Experimental section layout Head-on collision
Single aperture lenses: QD0 – QD1
Double aperture lenses:
Quad: Q3-Q8
Sext: MSY1, MSY2
Electrostatic dipoles ( 0 – 100 m):
MB0,MB1, L=30m, E= 15 kV/cm,
Angle= 0.25 mrad
Magnetic dipole (100 – 230 m) ?
MB2, L=30 m, Angle= 0.25 mrad
MB3, L=22 m, Angle= 0.19 mrad

23. Beam size at IR Horizontal size – ±27*σx
Distance between electron and positron bunches is more than 108 m.
Maximal possible number of bunches is ~ 450 (Circumference ~ 50km)

24. Interaction Region optical functions
CCSY
CCSX
Compres.
section
Arc
cells
Ratio of dispersions between CW and head-on lattices is ~ 5.
Maximal dispersion is limited by dipole radius
and dipole length in CCSY and CCSX.
It is difficult to optimize DA and energy acceptance.

25. Interaction Region Montague functions
horizontal
vertical
CCSY
CCSX
Vertical Montague function is reduced by main sextupoles of CCSY section.
Radial Montague function is reduced by main sextupoles of CCSY and CCSX section.
Montague functions at entry to arcs are:
Wx < 0.6, Wy < 50.
Best compensation is possible.
Compres.
section
Arc
cells

26. Interaction Region optical functions
horizontal
vertical
CCSXY
Radial and vertical Montague functions are reduced by main sextupoles of CCSXY section.
IR is short.
Nonlinearities of tunes are difficult for correcting.

27. Interaction Region Montague functions
CCSXY
horizontal
vertical
μx,y
Radial and vertical Montague functions are reduced by main sextupoles of CCSY section.
Montague functions at the end of chromatic section are small.
μx ≈ 0.5, μy ≈ 0.75.

28. Optical functions Beta function: QD0 - βy = 10 km. CCSY – βy = 7 km.
CCSX - βx = 150 m.

29. Montague functions horizontal vertical Montague functions in arcs:
Wx < 5, Wy < 30, |DDx| < 0.3.
Montague functions at IP:
Wx = 0.5, Wy = 58, DDx = 0.02.

30. Montague functions horizontal vertical Montague functions in arcs:
Wx < 5, Wy < 30, |DDx| < 0.3.
Montague functions at IP:
Wx = 0.5, Wy = 58, DDx = 0.02.

31. Energy acceptance Eacc≈ ± 1 % RF is switched off
Damping is switched off
Chromaticity is corrected by 2 sextupole families of arc and main chromatic sextupoles of CCSY and CCSX sections.

32. Energy acceptance
1 – chromaticity is corrected by 2 sextupoles famalies of arc and main sextupoles of CCSY and CCSX sections.
2 – Optimization of vertical nonlinearity of tune by additional sextupoles in CCSX, CCSY sections .
3 – Optimization of energy acceptance (± 1.4 %) by additional sextupoles in CCSX, CCSY sections and sextupoles of matching sections.

33. Parameters of lattice Energy E, GeV 175 Damping time Circumference, m
Circumference, m
99915
tx, sec
1.47E-02
Revolution period, sec
3.33E-04
ty, sec
Betatron tunes
te, sec
7.33E-03 qx
Sigma_s, mm
2.7 qy
RF voltage, MV
9.00E+03
Natural chromaticity
RF harmonic number
133312 Cx
RF frequency, MHz
400 Cy
RF acceptance
3.67E-02
Emittance, nm*rad
1.29
Synchrotron tune
5.89E-02
Betatron coupling
0.20%
Radiation integral
Energy spread
1.47E-03
I1, m
6.81E-01
Momentum compaction
6.81E-06
I2, m^-1
6.03E-04
Energy loss, MeV
7.96E+03
I3, m^-2
5.80E-08
Damping partition number
I4, m^-1
6.19E-09 Jx
1.00
I5, m^-1
1.73E-11 Jy 1
Beta_x_IP, m
0.500 Je
2.00
Beta_y_IP, mm
1.000
Dx_IP, m
0.000

34. Summary Maximal number of bunches is limited by separation sections.
Final focus lenses are simple.
Dispersion of IR is small because there is limitation of magnetic field and length of experimental section.
Main chromatic sextupoles are very strong.
Energy acceptance is ± 1.4 %.