1. Parameter Optimization in Higgs Factories Beam intensity, beam-beam parameters, by*, bunch length, number of bunches, bunch charge and emittance C.Zhang
HF2014, Beijing
October 10, 2014

2. Discovery of Higgs
A new fundamental particle: light, weakly coupling H
Mh= GeV, G<1 GeV, Spin=0 July 4, 2012
4.9σ 5σ
“Low Higgs mass makes the circular e+e- collider as a viable option”

3. Proposed circular Higgs Factories
LEP3
Super TRISTAN
C=40km, S.R.
C=27km, S.R.
C=50 (~100 ) km, S.R.
FCC
C=100km, D.R.
CEPC
SPPC

4. HF Design Optimization
Energy and luminosity
Beam-beam parameter
Beam intensity
by*and bunch length
Bunch number, charge and
emittance
Summary

5. Energy and luminosity L~1035cm-2s-1
Optimal energy
EHiggs=125 GeV H
Ee=120 (H); (Z), 80 (W), 175(tt) GeV
L=11034cm-2s-1  100fb-1/year, 2104 Higgs/year
(y=3000hrs./year)
Hadron collider in future Ep=50-100TeV,
L~1035cm-2s-1

6. The Parameters need to be optimized !
Cost
The Parameters need to be optimized !
Prf
r , R
kb Ib
ex0 sE L ey sz xy BS
by* DA
tblife

7. Beam-beam parameter
The beam-beam parameter characterizes the strength of the beam-beam force.
The maximum beam-beam parameter strongly depends on the radiation damping in storage rings: e- e+
The scaling of xymax for LEP (NIP=4 ) gives
Crab-waist scheme may reach higher beam-beam parameters.
R. Assmann et al, Proc. EPAC2000

8. Beam-beam parameter (NIP=4) NIP=2 NIP=4 FCC-tt FCC-H CEPC FCC-W FCC-Z
* Data taken from FCC-ACC-SPC-0003
(NIP=4)
FCC-tt
FCC-H
CEPC
NIP=2
FCC-W
NIP=4
FCC-Z

9. Beam intensity Beam intensity is limited by total SR power:
The luminosity is related to the RF power and bending radius as:

10. Bam intensity FCC, r =11km CEPC, r =6.1km FCC-Z FCC-W FCC-H FCC-tt
Hg=0.64
FCC, r =11km
Hg=0.77
FCC-W
CEPC, r =6.1km
FCC-H
Hg=0.83
FCC-tt
CEPC
by*=1mm, Prf=50 MW
Hg=0.78
xy=0.092
xy=0.083, by*=1.2mm, Hg=0.68

11. by*and bunch length sz CEPC FCC-H FCC-W, tt FCC-Z sz=1.17 mm by*=1 mm
Hg=0.83
CEPC
sz=1.49mm
by*=1 mm
Hg=0.78
FCC-Z
sz=2.65mm
by*=1.2mm
Hg=0.68
sz=2.56 mm
by*=1 mm
Hg=0.64

12. Why not smaller by*? Issues other than hour glass effect
Maximum bata-function in the final focusing quedopole, by,FFQ=L*2/by*, where the L*, defined as the distance from the FFQ to IP, is restricted by the geometry of the detector.
Large byFFQ requires high strength + large aperture of FFQ;
Large byFFQ also generates larger chromaticity, Dxy= (bykl)FFQ/4p and causes dynamic aperture problem.
The by* is chosen as ~1mm in Higgs factory design (1.2 mm for CEPC, and 1mm for FFC).

13. Why not larger Hg? Bunch length issue
Bunch length in electron storage rings is determined by synchrotron radiation and collective bunch lengthening effects.
The natural bunch length is expressed as:
Small ap and high Vrf (this is a case in HF) give large ns and short bunch, while the high beam energy causes large sE. The typical value of sz0 in HF’s is 1-2 mm.
Potential and microwave instability, as well as beamstrahlung effects may cause bunch lengthening;
Beamstrahlung fractional energy spread dbs  sz-2.
Maximize the Hg/by*! Hg=0.6~0.7 is too small!
Crab waist scheme may help to solve the problem.

14. BS simulation for TLEP-H
Beamstrahlung
An incoming electron undergo the electromagnetic field of the opposite positron bunch at IP emits hard photos  “beamstrahlung”.
Marco Zanetti, HF2012
BS simulation for TLEP-H
Beamstrahlung adds energy spread to beam:
Where sd,B is standard deviation of the energy loss:
Average emitted photon number per collision:
Beamstrahlung strength:
Beam lifetime is effected:
K. Yokoya, NIMA251(1986)
with
V. I. Telnov, PRL 110, (2013)

15. Beamstrahlung
Beamstrahlung effects beam energy spread and life time in circular colliders, limiting energy and luminosity reach;
To mitigate the beamstrahlung effect:
Use very flat beams (r=sy*/sx*<<1%) for collision
Large energy acceptance (1.5%-2%)
Optimize bunch length together with hour glass effect
Top-up injection to keep peak beam current.
* Obtained with beam-beam-simulation

16. Bunch number, current and emittance
Total beam current kbIb is limited by RF power;
Giving xymax, energy spread due to beamstrahlung is proportional to bunch current Ib=ef0Ne, so small Ib and large kb are preferred;
In the case of small Ib, horizontal emittance ex0 should be small to reach xymax, while the vertical emittance ey must be further smaller for very flat beam;
Double ring structure is superior to single ring of pretzel scheme in holding large number of bunches, especially in the W and Z cases.

17. Luminosity optimization
High luminosity in Higgs factories call for large rings with high RF power, large xymax, large DA, small r=sy/sy and optimized by*, sz , Ib, kb, ex0 and other parameters.
Limited by beam power
r  cost 
by*/sz  L/L0
Limited by beam-beam
Crab waist !
Limited by b FFQ ,
L*, DA, sz, Hg
xy , Ne, sz , r  dBS   tlife for same DA
LEP data
xymax  tE -0.4
B-B simulation

18. CEPC and FCC baseline parameters

19. Summary
Low Higgs mass makes the circular e+e- collider as a viable option.
High luminosity in Higgs factories call for large rings with high RF power, large xymax, large dynamic aperture, small r=sy/sy and optimized by*, sz , ex0 and other parameters.
xymax is chosen based on the LEP data and beam-beam simulation;
1 mm scale by* can be obtained with optimized L*, sz , DA, but very challenging;
Beamstrahlung limiting beam life time preferes low bunch charge，more bunches and smaller emittance.
Design of proposed Higgs factories is in an active progress, and their parameters have been being optimized.