new progress of the nonlinear collimation system for a. faus-golfe j. resta lópez d. schulte f....

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



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:



4

The nonlinear system for CLIC:

12

2flat

Increase y at spoiler Cancellation of geometric aberrations

02,116 SSR



5

The

opt

ics

solu

tion:



6

The

opt

ics

solu

tion

in th

e B

DS

:



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:



8

Tracking studies:

Optics lattice

MADPlacetSAD

…

Entrance:

Multiparticle tracking

Beam-beaminteraction

Guinea-Pig

performancetransport

Lie

Importance of the benchmarking of codes

IP:



9

Luminosity vs skew sextupole strength:

10.714

7.441



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)]



11


• 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 !



12

beam sizes order by order:

Second order

Fourth order

Third order



13


For an integrated skew sextupole strength Ks=20.86 m-2



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

Vertical plane:

δ0=1%

Collimation cut

ay=1.669 mm

Particles distribution at the spoiler:



16



17



18



19



20



21



22



23



24



25



26



27



28



29



30



31

Collimation gap

For a beam with 3% full width energy spread

ay=1.669 mm

ax=1.103 mm



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



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



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



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.



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)



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:



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:




39


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:



40

yRyy

xRxxspos

spospo

sposspospo

,

34,0

,12,0


spospo

spoxspospo

yy

Dxx

,,0

,,,0





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


-Gaussian distribution for transverse-Uniform flat momentum distribution for longitudinal



42


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:



43


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:



44

yRyy

xRxxspos

spospo

sposspospo

,

34,0

,12,0


spospo

spoxspospo

yy

Dxx

,,0

,,,0





45

22

22

spospoy

spospox

yy

xx

0

00

0

20

22

12

0

)(

flat

flatflat

flat

flat

P

Beam size at the spoiler:



-Gaussian distribution for transverse-Uniform flat momentum distribution for longitudinal



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




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)]




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




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%




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,



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


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



52

-I transformation between the pair of skew sextupoles:


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



53


0

00

0

20

22

12

0

)(

flat

flatflat

flat

flat

P

Beam size at the second skew sextupole:


uniform flat momentum distribution:

2

22

22 SSx xxS



54


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+



55


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+



56

Computation of the beam sizes:

new progress of the nonlinear collimation system for a. faus-golfe j. resta lópez d. schulte f....

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