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New Progress of the Nonlinear Collimation System for
A. Faus-Golfe J. Resta López D. Schulte F. Zimmermann
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
2
Basic Scheme:The purpose of the 1st nonlinear element is to blow up beam sizes and particle amplitudes, so that the collimator jaw can be placed further away form the nominal beam orbit (reducing the wake fields) and the beam density is decreased (for collimation survival). A 2nd nonlinear element downstream of the spoiler, and from the 1st, cancels all the aberrations induces by the former
increase beam size at the spoilers cancel aberrations
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
3
• collimation only in energy
• maximize the overall fraction of the system occupied by bends and decreased the bending angle until SR became reasonably small
• but no bends between the skews to cancel the geometric aberration (R16 s1s2 = 0) avoiding the luminosity degradation
• keep -functions as regular as possible to avoid the need of chromatic correction
The changes respect to the previous:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
4
The nonlinear system for CLIC:
12
2flat
Increase y at spoiler Cancellation of geometric aberrations
02,116 SSR
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
5
The
opt
ics
solu
tion:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
6
The
opt
ics
solu
tion
in th
e B
DS
:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
7
E x y
flat
1.5 2.8 x 10-3
0.23 6.8 0.01
Tev pm fm
Lt ld
b Ksx
s
ys
x,ys,sp
x,ysi,sf
R12s,sp
R34s,sp
I5
2536 220
0.00014 20.9 896.1 266.0
0.25/0.25 0.5/0.5 763.2 131.5
1.64 x 10-21
m m rad m-2
m m 2 2 m m
rsp
ax
sp
aysp
134.27 0.013 1.103 1.669
m mm mm
Performance from analytical studies:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
8
Tracking studies:
Optics lattice
MADPlacetSAD
…
Entrance:
Multiparticle tracking
Beam-beaminteraction
Guinea-Pig
performancetransport
Lie
Importance of the benchmarking of codes
IP:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
9
Luminosity vs skew sextupole strength:
10.714
7.441
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
10
• Generate/reads MADx input/output
• compute beam sigmas from map coefficients
• use SVD or Simplex algorithm to optimize the sigmas
Luminosity optimization:
MAPCLASS (Python code)
Optimization of the beam sizes
[R. Tomás,”MAPCLASS: a code to optimize high order aberrations” CLIC Note (2006)]
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
11
Luminosity optimization:
• Skew sextupoles: K2L =20.86 m-2
• Skew octupole: K3L= -5464.93 m-3
• Normal sextupole: K2L = -0.8 m-2
Two additional multipoles for local cancellation of the higher order aberrations
Thin multipoles have been used for a first test !
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
12
beam sizes order by order:
Second order
Fourth order
Third order
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
13
Luminosity optimization:
For an integrated skew sextupole strength Ks=20.86 m-2
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
14
Particles distribution at the spoiler:
Horizontal plane:
δ0=1%
Collimation cut
ax=1.103 mm
22,34
,
2
1
sextxsy
spoilerxx
DKRa
Da
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
15
Vertical plane:
δ0=1%
Collimation cut
ay=1.669 mm
Particles distribution at the spoiler:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
31
Collimation gap
For a beam with 3% full width energy spread
ay=1.669 mm
ax=1.103 mm
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
32
Ks=20.86 m-2
Average energy offset
Δ=1.3 %
Beam peak density at the spoiler vs skew sextupole strength:
Beam is highly non-gaussian at the spoiler, and then it is the density which matters for the collimator survival, not the rms beam size. The spoiler survival is guarantee for off-momentum beams (>1%) using an integrated skew sextupole strength K2L ≈20 m-2
beryllium spoiler: densitylimit = 46.42 x 109/mm2 per bunch
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
33
Collimation efficiency and loss mapTracking sample by using the code Placet with an input gaussian halo of 5x104
macroparticles: 12.5σx, 100σy (a 25% increase over collimation depth:10σx and 80σy ) and 4% full width energy spread (energy collimation depth: ± 1.3%)
Cleaning efficiency:
ENGYSP
ENGYAB
YSP1; XSP1
YSP2; XSP2
YSP3; XSP3YSP4; XSP4
Energy spoiler
YSP1; XSP1
YSP2; XSP2
YSP3; XSP3
YSP4; XSP4
No
n-l
ine
ar
co
llim
ati
on
Lin
ea
r c
oll
ima
tio
n
Linear collimation system ≈ 5.x10-4
Nonlinear collimation system ≈ 5.5x10-4
# outside collimation depth at FD # total initial halo
Aperture final doublet: 14σx and 83σy
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
34
Collimation efficiency and machine protectionFor failures scenarios mis-steered or errant beams will hit the energy spoiler
Tracking of gaussian beams of 105 macroparticles for different energy offsets and without energy spread. Beams with energy offset ≥ 1.3 % (energy collimation depth) are totally intercepted by the spoiler.
The nonlinear collimation system uses a vertical spoiler. Unlike the linear collimation system, the beam density is
reduced by the nonlinear system as the beam energy
offset increases. This helps to spoiler survival
Linear Nonlinear
Collimation limit
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
35
OutlookA skew sextupole integrated strength of ≈ 20 m-2 has been chosen. For this value the spoiler survival is guaranteed for off-momentum beams (> 1 %).
The chromatic behavior of the optics has been characterized. Good agreement between the simulated horizontal and vertical rms beam sizes at the spoiler as a function of the skew sextupole strength and the analytical expressions has been found.
High chromatic aberrations of second, third and fourth order are found. The luminosity is degraded with the excitation of the skew sextupole.
A local cancellation of higher order aberrations was made using two additional thin multipoles: a skew octupole and a normal sextupole. The luminosity was improved by more than a factor 2.
Tracking studies with Placet show a comparable cleaning efficiency from linear and nonlinear collimation system.
The nonlinear collimation system uses a vertical spoiler. Unlike the linear system, the beam density is reduced by the nonlinear system as the beam energy offset increases. This helps to spoiler survival.
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
36
Some remarks and Ongoing studiesA shorter lattice( 1.5 Km) is being studied
We have only defined apertures for the collimators in the nonlinear collimation system. No aperture is defined for bendings and quadrupoles.
The loss maps for the comparison between linear and nonlinear collimation systems have been created with a new version of Placet (in collaboration with H. Burkhardt and L. Neukermans).
For a first test we have as input halo at the entrance of the BDS a gaussian distribution of particles with dimensions in the transversal planes 25% higher than the collimation depths.
To avoid the dependence of the cleaning efficiency with the halo model it would be better to do a scan for different halo amplitudes as we have used for the cleaning efficiency study of the nonlinear collimation system of the LHC.
More realistic simulations can be made using the incoming halo generated by beam-gas scattering in the Linac (from H. Burkhardt and L. Neukermans)
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
37
Some analytical calculations:
2
2
s
sTs aB
lBK
yDxKx
Hx sxs
s ,
xDDxyKy
Hy sxsxs
s ,22
,22 2
2
1
yDxyK
H sxs
s2
,3 3
!3The Hamiltonian:
The deflection:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
38
yRyy
xRxxspos
spospo
sposspospo
,
34,0
,12,0
Position at the downstream spoiler:
spospo
spoxspospo
yy
Dxx
,,0
,,,0
Position at the downstream spoiler w/o skew sextupole:
Some analytical calculations:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
39
Some analytical calculations:
2
2
s
sTs aB
lBK
yDxKx
Hx sxs
s ,
xDDxyKy
Hy sxsxs
s ,22
,22 2
2
1
yDxyK
H sxs
s2
,3 3
!3The Hamiltonian:
The deflection:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
40
yRyy
xRxxspos
spospo
sposspospo
,
34,0
,12,0
Position at the downstream spoiler:
spospo
spoxspospo
yy
Dxx
,,0
,,,0
Position at the downstream spoiler w/o skew sextupole:
Some analytical calculations:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
41
22
22
spospoy
spospox
yy
xx
0
00
0
20
22
12
0
)(
flat
flatflat
flat
flat
P
Beam size at the spoiler:
0 average momentum offset
Some analytical calculations:
-Gaussian distribution for transverse-Uniform flat momentum distribution for longitudinal
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
42
Some analytical calculations:
2
2
s
sTs aB
lBK
yDxKx
Hx sxs
s ,
xDDxyKy
Hy sxsxs
s ,22
,22 2
2
1
yDxyK
H sxs
s2
,3 3
!3The Hamiltonian:
The deflection:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
43
Some analytical calculations:
2
2
s
sTs aB
lBK
yDxKx
Hx sxs
s ,
xDDxyKy
Hy sxsxs
s ,22
,22 2
2
1
yDxyK
H sxs
s2
,3 3
!3The Hamiltonian:
The deflection:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
44
yRyy
xRxxspos
spospo
sposspospo
,
34,0
,12,0
Position at the downstream spoiler:
spospo
spoxspospo
yy
Dxx
,,0
,,,0
Position at the downstream spoiler w/o skew sextupole:
Some analytical calculations:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
45
22
22
spospoy
spospox
yy
xx
0
00
0
20
22
12
0
)(
flat
flatflat
flat
flat
P
Beam size at the spoiler:
0 average momentum offset
Some analytical calculations:
-Gaussian distribution for transverse-Uniform flat momentum distribution for longitudinal
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
46
20
24
4,
22,34
,20
22,
22,12
22,
3
1
1804
1
1212
flatflat
sxsspos
y
ysyflat
sxssposflat
spoxx
DKR
DKRD
Beam size at the spoiler for uniform flat momentum distribution:
xD
Some analytical calculations:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
47
For spoiler survival:
yxr min,
minimum beam sizem120
[S. Fartoukh et al.,”Heat Deposition by Transient Beam Passage in the Spoilers” CERN SL 2001 012 AP (2001)]
Some analytical calculations:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
48
xsy
sxy
xsx
sxx
Dn
Dn
,
,
,
, ,
yspoy
sxspos
s
yspoy
yy
xspox
spox
xspox
xx
DRKan
Dan
,
22,
,34
,
)2(
,
,
,
)2(
2
1
The sextupolar deflection also yields a weak betatron collimation
for horizontal or vertical amplitudes at collimation depth (units of ) of:
Additionally we can collimate (in the other betatron phase) using the linear optics:
Energy collimation depth (units of
Some analytical calculations:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
49
The achievable value of Dxs is limited by the emittance
growth Δ(γεx) due to SR in the dipole magnets:
xx fIEGeVm 5
6628104
f: fraction of the initial emittance
I5: radiation integral
1.0 x 10-19 m7%
Some analytical calculations:
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
50
r.m.s beam size at the spoiler vs skew sextupole strength:
Taking the analytical formulas:
Spoiler survival is guaranteed for off-momentum beams (>1%) for a
integrated sextupole strength KK22L ~ 20 m L ~ 20 m -2-2
mr 120min,
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
51
-I transformation between the pair of skew sextupoles:
1
565251
26
16
2100000
100
001000
000100
00010
00001
S
y
x
S
y
x
ct
p
y
p
x
RRR
R
R
ct
p
y
p
x
Some analytical calculations:
1
565251
26
16
21
0
100000
100
001000
000100
00010
00001
1
0
S
p
y
p
x
S
p
y
p
x
y
x
y
x
D
D
D
D
RRR
R
R
D
D
D
D
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
52
-I transformation between the pair of skew sextupoles:
Some analytical calculations:
02,116 SSR
2,116
12
2,11612
12
SSxx
SS
SSSS
RDD
yy
Rxx
SS
12
12
12
SS xx
SS
SS
DD
yy
xx
without bends between skews
-I transport + higher dispersion terms between the pair of skew sextupoles
32,11666
22,116612 SSSS
SS UTxx
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
53
Some analytical calculations:
0
00
0
20
22
12
0
)(
flat
flatflat
flat
flat
P
Beam size at the second skew sextupole:
0 average momentum offset
uniform flat momentum distribution:
2
22
22 SSx xxS
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
54
Some analytical calculations:
2
1
20
24
2,11666
02
2,1166
30
204
2,11666
2,1166
40
220
4622,1
1666
20
24
22,1166
22
4
1
802
62
2
1
242
4
3
8448)(
3
1
180)(
12
11
12
flatflat
xSSflat
xSS
flatflatSSSS
flatflatflatSS
flatflatSSflat
xx
SS
SS
DUDT
UT
U
TD
02,116 SSR
1SxDtaking0
02,1
1666
2,1166
SS
SS
U
T+
15-17 May LAL A. Faus-Golfe
Electron Accelerator R&D for the Energy Frontier
55
Some analytical calculations:
2
1
30
204
2,13666
2,1366
40
220
4622,1
3666
20
24
22,1366
2
1
242
4
3
8448)(
3
1
180)(
2
flatflatSSSS
flatflatflatSS
flatflatSS
yyy
UT
U
TS
02,126 SSR 0yDwith
0
02,1
3666
2,1366
SS
SS
U
T+