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SR power loss in the FCC-ee quadrupoles
(preliminary)
A. Bogomyagkov, E. Levichev, K. Oide, P. Piminov,
S. Sinyatkin
FCC-ee Optics Meeting, CERN 01/04/2016
Important at high energy.
Quad radiation effects:
•Increase energy loss at high amplitude. A particle goes out of
the momentum acceptance.
•Exchange of damping partition numbers. A particle
experiences atni-damping.
•Increase emittance for large amplitude of particles (larger tails,
detector background, less beam lifetime).
Energy loss I
Energy loss per turn E  U   P dt 
C
2
E4I2
Dipoles:
I 2 d  6  10
4
m-1
Ed  U d  7.96 GeV
C  8.85 105 m / GeV 3
 E 

  4.5%
 E d
Quadrupoles horizontal motion, AB lattice, AB formula:
4 FF doublets
The rest FODO lattice
At 10 x , n  10 and for Lq  1.5 m
 E 

  0.35%  0.8%  1.15%
 E q
Energy loss II
KO formula AB lattice
2
Half of AB formula cos  1 / 2 ?
 E 

  0.5  1.15%  0.58%
 E q
Uq 
C
2
E
4
K
2
1
2
( s) x ds
I 6 x   K12 ( s )  x ( s )ds
At 10 x
x  x
2
2
  xx 2 Uq 
(Jowett definition)
C
4
E  x  K ( s)  x ( s)ds 
4
I 6 x  352 m-1
9
and with  x  1.4  10 m
 E  C 3 2
E n  x I 6 x  0.2%

 
 E  q 4
2
1
C
4
E 4 x I 6 x
Energy loss III
The FCC-ee lattice has been represented by a transfer line multiplied 10 times to
average the betatron phase. Then a particle is launched with nx amplitude and
at this trajectory calculated the radiation integrals. Zero amplitude particle
obviously produced pure dipole integrals which correspond exactly to those
obtained from the closed lattice.
At 10x a quadrupoles correction to the second radiation integral, averaged over
10 turns, gives
I 2 q  
ds
2
2
5 1

K
(
s
)
x
ds

2
.
5

10
m
1
2

 ( s)
 E 

  0.2%
E

q
????
Summary
Main contribution comes from the FODO quadrupoles, the QD0 gradient can
be doubled (as it seems) still without harmful effect.
Additional study is necessary.
Change of Lstar and excitation of
vertical emittance
S. Sinyatkin
Task
• To insert device of detector the distance between defocusing
lenses of final focus must be increased from 2*2 m to 2*3 m.
• Vertical beta function at IP for high energy may be increased
to 2 mm.
• At low energy vertical beta function must be remained 1 mm
or may be reduced to 0.5 mm.
• Due to changing of FF lenses placement the maximal vertical
beta function in QD0 is increased and vertical emittance is
rise.
• To optimize FF lenses with according to new parameters of
lenses the rematching of twiss functions is carried out.
8
Original Final Focus layout
Final quads
Main
detector
solenoid
2
1
4
3
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)
Quad
screening
solenoid
Compensati
ng solenoid
Transverse half size:
- compensating
solenoid - R = 0.1 m
- screening solenoid
- R = 0.15 m
9
Final focus layout
E = 175 GeV
Quads:
GQD0 = - 200 T/m
LQD0 = 1.68 m
GQF1 = 192 T/m
LQD0 = 1.17 m
Main solenoid:
Bs = 2 T
Leff_geom=2*1.56 m
Compensating solenoid:
Bs_max_eff = - 3.2 T Rin = 0.16 m
Lgeom= 1 m
Rout = 0.26 m
10
Twiss function of FF
bx,m
by*103, m
•Original lattice
GQD0 = - 93 T/m
GQF1 = 87 T/m
Lstar =
2m
Natural chromaticity:
Cx = -17
by*103, m
bx,m
Cy = -1160
•Modified lattice
GQD0 = - 200 T/m
GQF1 = 192 T/m
Lstar =
3m
Natural chromaticity:
Cx = -14
Cy = -1290
11
Update of solenoid geometry
4
0.4
L_comp_sol
L_screen_sol
3
0.3
2
0.2
1
0.1
0
0
QD0
-1
Bs
10*Bx
Solenoids
Opening angle 0.1 rad
QD0
-3
-4
0
0.5
1
Bs = 2 T
-0.1
Leff_geom=2*1.56 m
-0.2
Compensating
solenoid:
-0.3
L_free_space
-0.4
1.5
2
s, m
2.5
3
3E-13
3.5
4
dI5y/ds
Em_y
2.5E-13
dI5y/ds, m^-2
Main solenoid:
|B|s_max_eff = 3.2 T
6E-13
Lgeom= 1 m
5E-13
ey = 0.5 pm*rad
2E-13
4E-13
1.5E-13
3E-13
1E-13
2E-13
5E-14
1E-13
0
Em_y, m*rad1
-2
E = 45 GeV
X, m
Bs, 10*Bx,T
L_main_sol / 2
0
0
0.5
1
1.5
2
s, m
2.5
3
3.5
4
12
Vertical emittance vs.
effective length of main solenoid
25
bety_IP= 0.5 mm
bety_IP= 1 mm
bety_IP= 2 mm
Em_y, pm*rad
20
15
10
5
1.06
0.52
0.19
0
1.4
1.5
1.6
1.7
L_main_sol/2, m
1.8
1.9
2
E = 45 GeV
L_star = 3 m
L_main_sol = 1.56 m
bx_IP= 0.5 m
Em_y = 0.5 pm*rad
by_IP = 1 mm
13
βy_IP vs. main solenoid length (free space)
2.5
Em_y =const= 0.5 pm*rad
by_IP, mm
2
1.5
1
0.5
0
1.45
1.5
1.55
1.6
1.65
1.7
1.75
L_main_sol/2, m
E = 45 GeV
 y _ new   y 
 y _ IP
 y _ IP _ new
L_star = 3 m
Em_y = 0.5 pm*rad
14
Ver. Emittance & Change of free space for detector
Parameters
Original*
Geometry Update
E, GeV
Cross angle (tot), rad
45
0.03
0.026
Compensating solenoid
R_in, m
0.100
0.100
0.145
0.157
0.164
0.170
0.186
R_end, m
0.100
0.171
0.256
0.256
0.256
0.256
0.256
0.7
0.7
1.1
0.989
0.915
0.856142
0.7
0.001
0.094
0.134
0.155
0.176
0.184
0.221
0.171
0.180
0.269
0.271
0.274
0.274
0.278
B, T
2.01
2.01
2.00
2.00
2.00
2.00
2.00
L_main/2, m
1.00
1.00
1.450
1.561
1.635
1.694
1.850
bx_IP, m
0.5
0.5
0.5
0.5
0.5
0.5
0.5
by_IP, m
0.001
0.001
0.001
0.001
0.001
0.001
0.001
I2_sol, m^-1
1.94E-06
1.19E-06
1.56E-06
2.11E-06
2.63E-06
3.09E-06
4.97E-06
I5y_sol, m^-1
3.42E-14
8.38E-15
3.82E-14
1.05E-13
2.15E-13
3.70E-13
1.68E-12
Emy_sol, m*rad
1.69E-13
4.14E-14
1.88E-13
5.21E-13
1.06E-12
1.83E-12
8.29E-12
Emy_sol/Emx
1.82E-03
4.48E-04
2.04E-03
5.64E-03
1.15E-02
1.98E-02
8.98E-02
111.8
69.0
89.9
121.7
151.8
178.6
15
287.0
L, m
L_free_space, m
Screening solenoid
R_sc_sol,m
Main solenoid
Optics
Uo_sol, keV
Vertical emittance (E=175 Ge)
Parameters
E, GeV
Cross angle (tot), rad
Original*
Geometry Update
175
175
0.03
0.026
Compensating solenoid
R_in, m
0.100
0.157
R_end, m
0.100
0.256
0.7
0.989
0.000
0.155
0.171
0.271
B, T
2.01
2.00
L_main/2, m
1.00
1.561
bx_IP, m
0.5
0.5
by_IP, m
0.001
0.001
I2_sol, m^-1
1.28E-07
1.39E-07
I5y_sol, m^-1
3.84E-17
1.19E-16
Emy_sol, m*rad
2.87E-15
8.85E-15
Emx, m*rad
1.40E-09
1.40E-09
Emy_sol/Emx
2.05E-06
6.34E-06
16
1840.0
L, m
L_free_space, m
Screening solenoid
R_sc_sol,m
Main solenoid
Optics
Uo_sol, keV
1690.7
Summary
• The increase of Lstar results in growth of
vertical emittance.
• To keep vertical emittance the length of
compensating solenoid must be increased.
• Distance between compensating solenoid and
screening solenoid is used to optimize fringe
magnetic field of solenoids at QD0.
• New parameters of FF lenses allow to avoid
the strong growth of the natural chromaticity
with increasing Lstar.
17