Influence of Insertion Devices on Dynamic Aperture and ... · † RADIA kick map (P. Elleaume,...

BROOKHAVEN SCIENCE ASSOCIATESBROOKHAVEN SCIENCE ASSOCIATES

S ry Committee

am

es onifetime

1 of 30

II Accelerator Systems Adviso

October 8 – 9, 2007

Johan Bengtsson

for the NSLS-II Design Te

Influence of Insertion DevicDynamic Aperture and Beam L

NSL


i

olSyImFi FMo

iImImTh

n

t

ol

lusFu

2 of 30

c Aperture (DA): Analysis ..........................................3

of Insertion Devices (IDs): Guidelines .....................4mplectic Integrators: Overview.................................5pact of the Length of a CPMU on the DA .................6eld Harmonics of Damping Wigglers: DW100...........7ield Deviations: DW100 ...............................................8

del Validation: DW80 .................................................9

c Aperture with 3 DW90............................................10pact on the DA from CPMUs and DWs ................... 11pact on the DA from EPUs.......................................12e Driving Terms ........................................................13

of Linear IDs: From First Principles ........................14

of IDs on Momentum Aperture .................................15

of the Driving Terms (SLS) ......................................16

ions ...........................................................................17ture Work...................................................................18

Overview

1.0 Dynam

2.0 Contr2.12.22.32.42.5

3.0 Dynam3.13.23.3

4.0 Desig

5.0 Impac

6.0 Contr

7.0 Conc7.1


Normalized Dynamic Aperture

100 90 80 70 60 50 40 30 20 10

32.2 32.4 32.6 32.8 33 33.2 33.4 33.6 33.8

νx

15.5

16

16.5

17

17.5

18

18.5

19

νy

pd

-20

Dynam

δ33.5

4×10 δ49.7

5×10 δ5 …,+–+

δ27.2

3×10 δ41.2

5×10 δ5 …,+––

.02 …+

0.003 …+

ith Misalignments

0

nalysis

3 of 30

erture by injection beam pipe.

-10 0 10 20 30

x [mm]

ic Aperture (bare lattice, 2.5 DOF)

δ=0.0%δ=3.0%

δ=-3.0%

Residual chromaticity (analytic model)

νx δ( ) 33.36 2.0δ 1.32×10 δ2

– 3.22×10–+=

νy δ( ) 16.28 1.0δ 7.31×10 δ2

– 1.23×10+ +=

νx 3%( ) 33.36 0.06 0.12– 0.09– 0.03 0–+ +=

νy 3%( ) 16.28 0.03 0.07– 0.03 0.005– –+ +=

Bare Lattice W

Normalized Dynamic Aperture

160150140130120110100 90 80 70 60 50 40 30 20 10 32.2 32.4 32.6 32.8 33 33.2 33.4 33.6 33.8

νx

15.5

16

16.5

17

17.5

18

18.5

19

νy

0.14 0.16 0.18 0.2ν

x

−10

−8

−6

−4

−2

−10 0 10 20 30 40x(mm)

1.0 Dynamic Aperture (DA): A

Physical aseptum an

0

2

4

6

8

10

12

14

-40 -30

y [m

m]

0.1 0.12

0.3

0.4

0.5

ν z

−30 −2

2

4

6

8

10

12

14

z(m

m)

06−Oct−2007 13:29:04


ea

iv inear resonances, and e

a .

e:

l

o

o

O px y,( )4

β0 1 s β0⁄( )2+[ ]=

C s): Guidelines

4 of 30

ding order impact of a planar IDs is given by

e beta and phase advance beat, tune shift, nonl dependent tune shift.

gation of the beta function in free space is:

ear => ,

l of IDs: linear optics => ,

l of IDs: nonlinear dynamics => .

H⟨ ⟩λu

px2

py2

+

2 1 δ+( )--------------------

Bu2y

2

4 Bρ( )21 δ+( )

------------------------------------π2Bu

2y4

3λu2

Bρ( )21 δ+( )

-------------------------------------------– δ–+ +=

β s( )

β0 L 2⁄=

β0 L 2 34⁄=

β0 L 2 54⁄=

ontrol of Insertion Devices (ID

The the l

which dramplitud

The prop

Therefor

• stay c

• contr

• contr

2.0


ti lytic basis:

ra 991),

rd

r

ra 006),

n etry (C. Mitchel, A. t,

ti ield maps:

A

n iggler, aperiodic, di

rview

5 of 30

c integrators based on fit of 3D field map to ana

ting function, implicit (G. Wüstefeld, J. Bahrdt, 1

er, explicit (E. Forest, K. Ohmi, 1992),

der explicit (Y. Wu, E. Forest, D. Robin, 2001),

ting function, explicit (G. Wüstefeld, J. Bahrdt, 2

vector potential by fit 3D field for elliptical geom2006).

c integrators based on direct integration of 3D f

kick map (P. Elleaume, 1992),

vector potential from 3D field map (three-pole-wng radiation effects, J. Bengtsson, 2007).

2.1 Symplectic Integrators: Ove

Symplec

• gene

• 1st o

• 2nd o

• gene

• obtaiDrag

Symplec

• RADI

• obtaiinclu


Ught)

SCU(S. Strght)

1 1,260

40

11

T. Shaftan

CDRLattice

2 on the DA

6 of 30

DrivingTerms Effect Sextupole

SchemeDW

(L. Strght)CPMU

(S Strght)CPM

(L. Str

607 1,089 1,103 3,68

76 52 7 379

47 59 14 228

h00220 ∂νy ∂Jy⁄

h00310 2νy

h00400 4νy

-40 -30 -20 -10 0 10 20 30 400

2

4

6

8

10

12

14

16

18

20DA for DBA-30

Bare1m2m3m4m5m

by

.2 Impact of the Length of a CPMU


-10

DW

fit

ld: By(y)

La

a(

10 15

-15 -10 -5 0 5 10 15-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0

0.005DW field: By(x)

By(x), T

1->13th harm. fit

absolute error

10 15

Dependence of the field roll-off versuspole width (same scale) 80 52 45 mm.Red: RADIA field map, Blue: fit

Pole width 52 mm

ntal Field Roll-Off

.3 lers: DW100

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100 mm DW, B=1.8001 T, ky=0.0627 1/m, kx=0.0048 1/m

0 10 00 2 00 0 3 0 00 4 00 0 50 00 6 00 010

1

102

103

104

105

106

0 1 0 20 3 0 4 0 5 0

fie ld : B y (z )

-15 -10 -5 0 5 10 15-3

-2.5

-2

-1.5

-1

-0.5

0

0.5x 10

-3 DW field: By(x) on the positive pole

by(x), T

1st harm. fit

error, x10%

0 1 2 3

on the positive pole

place

Spectrum of harmonics

z, mm

y, mm x, mm

By, T

f, arb. units

Spectral amplitude

lbach Basis from Radia Model for DWwith T. Shaftan and T. Tanabe)

-15 -10 -5 0 5-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0


By(x), T

1->13th harm. fitabsolute error

-15 -10 -5 0 5-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005

0


By(x), T

1->13th harm. fit

absolute error

Pole width 80 mm

Pole width 45 mm

Horizo

Field Harmonics of Damping Wigg(with T. Shaftan and T. Tanabe)

-50 -40 -30 -20-2

-1.5

-1

-0.5

0

0. 5

1

1. 5

2

b y (z ), T

1 -> 11 th ha rm . e rror, 1 0 x %

-3 -2 -1-0.005

0

0.005

0.01

0.015

0.02

0.025DW fie

by(y), T

1st harm. fit

error, 10x%

Does comply with

Bz, T

By, T

Fitted H

2


-50

050

-10

d) and Fit (blue,mag,green)

-50

050

-10

0

8 of 30

-50

050

-10

0

10-5

0

5

By(y,z) Bx(y,z) Bz(y,z) at x=13 mm from axis.

-50

050

-10

0

10-0.01

0

0.01

Fits are computed at x=-10 mm from axis.

0

10-2

0

2

RADIA field (re

-50

050

-10

0

10-0.1

0

0.1

Differences, T

-50

050

-10

0

10-2

0

2

x 10-3

0

10-0.1

0

0.1

5 harmonics

2.4 Field Deviations: DW10(with T. Shaftan and T. Tanabe)


22:21:17 22:21:58 22:22:50

0.28 0.3 0.32 0.34 0.36 0.38ν

x

−10

−8

−6

−4

−2

−20 −10 0 10 20 30x(mm) 22:23:52

0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39

3

4

5

νx

−10

−8

−6

−4

−2

−20 −10 0 10 20 30

1

2

3

4

5

x(mm)07 22:32:58

3 0

luding Harmonics up to 9th

ic

B

0

9 of 30

06−Oct−2007 22:21:1706−Oct−2007 22:21:58

0.3 0.32 0.34 0.36 0.380.03

0.04

0.05

0.06

νx

ν z

−10

−8

−6

−4

−2

−20 −10 0 10 20 30

1

2

3

4

5

x(mm)

z(m

m)

06−Oct−2007 22:22:50 06−Oct−200706−Oct−200706−Oct−2007

0.02

0.04

0.06

ν z

1

2

3

4

5

z(m

m)

06−Oct−2007

0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39

0.03

0.04

0.05

0.06

νx

ν z

−10

−8

−6

−4

−2

−20 −10 0 10 20 30

1

2

3

4

5

x(mm)

z(m

m)

06−Oct−2007 22:34:47

0.0

0.0

0.0

ν z

z(m

m)

06−Oct−20

.34 0.35 0.36 0.37 0.38 0.39ν

x

−10

−8

−6

−4

−2

−10 0 10 20 30x(mm)

IncImpact of 5 Ideal Damping Wigglers

with Radia KickMap (full gap)

k

are Lattice

2.5 Model Validation: DW8

0.31 0.32 0.3

0.03

0.04

0.05

ν z

−20

1

2

3

4

5

z(m

m)

07−Oct−2007 08:03:38

Radia KMap


-20 -15 -10 -5 0 5 10 15 20 25

x [mm]

Dynamic Aperture (bare lattice, 2.5 DOF)

δ=0.0%δ=3.0%

δ=-3.0%

0.12 0.125 0.13 0.135ν

x

−10

−8

−6

−4

−2

−10 0 10 20 30x(mm)

ontly

op

s

DW90

10 of 30

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-10 -8 -6 -4 -2 0 2 4 6 8 10

y [m

m]

x [mm]

Dynamic Aperture (bare lattice, 2.5 DOF)

δ=0.0%δ=3.0%

δ=-3.0%

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-30 -25

y [m

m]

0.115

0.4

0.45

0.5

ν z

−30 −200

1

2

3

4

5

z(m

m)

06−Oct−2007 14:50:22

With locally corrected optics.

e of the quads in the matching section is weaker than the other two. To fix it:

tics by using all non-chromatic quads,

t working point to .νx y, 33.356 16.266,( )=

3.0 Dynamic Aperture with 3

Problem: significan

• Correct

• and adju


33 0.34 0.35 0.36 0.37 0.38 0.39 0.4ν

x

−10

−8

−6

−4

−2

0 −20 −10 0 10 20 30x(mm):47

:23:35

0.35 0.4 0.45 0.5ν

x

−10

−8

−6

−4

−2

−30 −20 −10 0 10 20 30 40x(mm):21

and DWs

11 of 30

0.

0.3

0.4

0.5

ν z−3

0

1

2

3

z(m

m)

06−Oct−2007 20:14

0.35 0.4 0.45 0.50.2

0.3

0.4

0.5

νx

ν z

−10

−8

−6

−4

−2

−30 −20 −10 0 10 20 30 40

1

2

3

4

5

6

x(mm)

z(m

m)

06−Oct−2007 19:50:23

06−Oct−2007 19:50:23

0.35 0.4 0.45 0.5

0.3

0.4

0.5

νx

ν z

−10

−8

−6

−4

−2

−30 −20 −10 0 10 20 30 40

1

2

3

4

5

6

x(mm)

z(m

m)

06−Oct−2007 20:10:35

06−Oct−2007 19:5006−Oct−2007 20:10

0.2

0.3

0.4

0.5

ν z

1

2

3

4

5

6

z(m

m)

06−Oct−2007 20:11

15 CPMUs

5 DWs and15 CPMUs

3.1 Impact on the DA from CPMUs

1 CPMU

5 CPMUs


.2 0.3 0.4 0.5ν

x

−10

−8

−6

−4

−2

0 10 20 30x(mm)

−

iSOR type

Us

12 of 30

0 0.1 00

0.1

0.2

0.3

0.4

ν z

−20 −10

2

4

6

8

z(m

m)

06−Oct−2007 21:15:12

0.1 0.2 0.3 0.4 0.5ν

x

−10

−8

−6

−4

−2

20 −10 0 10 20 30x(mm)

Apple-II type H

3.2 Impact on the DA from EP

00

0.1

0.2

0.3

0.4

ν z

2

4

6

8

z(m

m)

06−Oct−2007 21:19:11

13 of 30
3.3 The Driving Terms


a

le ted along a straight line an ds, while the linear and r force), it can be cor-c by minimizing the rele-g and BESSY-II.

' sd x∼

st Principles

14 of 30

nd second integrals are given by

m is that these integrals are traditionally evalua the path followed by the electron. In other wor

focusing are of dynamic origin (like the coriolis ally by using L-shims between the magnets andral. Pioneering work has been done at the ESRF

I1 By s( ) sd0

L

∫= x',∼ I2 By s'( ) sd0

s

∫0

L

∫=

Design of Linear IDs: From Fir

The first

The probrather thnonlinearected lovant inte

4.0


3

2

1

0

1

2

3

0 100 200 300 400 500 600 700 800

s [m]

Momentum Aperture

3

2

1

0

1

2

3

0 100 200 300 400 500 600 700 800

s [m]

Momentum Aperture

5 Aperture

15 of 30

-

-

-

δ [%

]

-6

-4

-2

0

2

4

6

0 100 200 300 400 500 600 700 800

δ [%

]

s [m]

Momentum Aperture

-6

-4

-2

0

2

4

6

0 100 200 300 400 500 600 700 800

δ [%

]

s [m]

Momentum Aperture

-

-

-

δ [%

]

gap = 5 mm

δRF 3%=

with 15CPMUs

.0 Impact of IDs on Momentum

δRF 5%=

with 3 DWs


gt ): An Analytic Approach”ot, M t, T. Satogataur RHIC” PAC07.

s (SLS)

16 of 30

sson “The Sextupole Scheme for the Swiss Light Source (SLSe 9/97.. Bai, R. Calaga, J. Bengtsson, W. Fischer, N. Malitsky, F. Pila

ement and Correction of Third Resonance Driving Term in the

A. Streun

6.0 Control of the Driving Term

• J. BenSLS N

• Y. Luo“Meas


p

ro ular, distributed (non-) c fine tuning of the in

P r study and guidelines w

g ple-II devices.

t based on the first and nd straight lines, and con-e ng work has been done E

r tor with BPM turn-by-a given a sufficient num-

f

17 of 30

arent show stoppers.

lling the optics with DWs requires care. In particorrection with the achromatic quadrupoles, andg point.

Us are challenging devices that requires furthe to control their nonlinear effects.

nificant advantage of HiSOR type EPUs over Ap

principles approach is to design linear devices integrals evaluated along the orbit, rather than nonlinear effects locally by shimming. PioneeriSRF and BESSY-II.

iving terms can be controlled for a real accelerata and the inverted sextupole response matrix;

knobs.

7.0 Conclusions

• No ap

• Contlocalwork

• The Efor ho

• No si

• A firssecotrol that the

• The dturn dber o


t new baseline lattice a ces, and corrections.

a the residual horizontal

el nonlinear effects from ,

18 of 30

o evaluate the DA and Touschek lifetime for the full set of insertion devices, engineering toleran

te the merits/feasibility to improve the control ofaticity by introducing octupoles/decapoles.

ines needs to be worked out for local control thei.e., with L-shims.

7.1 Future Work

• Needwith

• Evaluchrom

• GuidEPUs

19 of 30
Back-Up Slides


4.0

000

050

100

150

200

250

300

.0 0.0 1.0 2.0 3.0 4.0

δ [%]

20 of 30

Fit Fit0 33.36 33.36 ±5.87e-07 16.28 16.28 ±1.86e-071 2.00E+00 2.01E+00 ±5.81e-05 9.66E-01 9.95E-01 ±1.85e-052 -1.51E+02 -1.34E+02 ±2.20e-03 -8.01E+01 -7.28E+01 ±6.98e-043 -2.55E+02 -3.23E+02 ±1.37e-01 1.31E+03 1.15E+03 ±4.34e-024 6.78E+04 3.49E+04 ±1.46e+00 4.89E+03 -7.21E+03 ±4.65e-015 -1.19E+06 -9.73E+05 ±7.16e+01 -3.31E+05 -1.17E+05 ±2.28e+01

υx υy

Analytic AnalyticOrder

33.150

33.200

33.250

33.300

33.350

33.400

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0

δ [%]

16.

16.

16.

16.

16.

16.

16.

-4.0 -3.0 -2.0 -1

υ y

Residual Chromaticity

-

υ x

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Influence of Insertion Devices on Dynamic Aperture and ... · † RADIA kick map (P. Elleaume,...

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Transcript of Influence of Insertion Devices on Dynamic Aperture and ... · † RADIA kick map (P. Elleaume,...