Impedance Estimate for SOLEIL

11th ESLS Workshop, 17 ~ 18 November 2003, ESRF, Grenoble, France

Ryutaro Nagaoka Synchrotron SOLEIL

List of Contents -----------------------------------------------------------------

1. GdfidL results 2. Resistive-wall impedance related

-----------------------------------------------------------------

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 2/16

1 GdfidL Results 1.1 Introduction

◊ Impedance calculations made with GdfidL using the computer cluster developed at SOLEIL (composed of 12 processors).

◊ So far bellows, tapers, BPMs, pumping holes, absorbers, slots and

flanges have been evaluated. Details are reported on the latter two. 1.2 Dipole chamber slot

◊ Can we enlarge the slot size of originally 9 mm?

◊ Numerical study with a simplified model - |ZH| >> |ZV| - Qualitative agreement with theory • No dependence on the longitudinal slot length • Steep (exponential) growth of |Z| with increasing slot size • Presence of narrow bands (at chamber cutoffs)

◊ Theory for the slot impedance - Based on Bethe’s theory (EM dipole radiation at a hole) - Important extension made by G. Stupakov to long slots.

(Phys. Rev. E 51, 3515 (1995))

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 3/16

◊ Evaluation of the total impedance of a dipole chamber

- |Z|total >> |Z|slot at 9 mm slot - Transition occurs around 18 mm slot - Anyway, |Z|total is sufficiently small w.r.t. other components

1,E-06

1,E-05

1,E-04

1,E-03

6 9 12 15 18 21 24 27Slot size [mm]

Los

s fac

tor

[V/p

C]

Slot aloneTotal

0,0001

0,001

0,01

0,1

6 9 12 15 18 21 24 27Slot size [mm]

(Im

ZL

/n)e

ff [m

Ω]

Slot alone

Total

0,01

0,1

1

10

100

6 9 12 15 18 21 24 27Slot size [mm]

(ReZ

H)e

ff [ Ω

/m]

Slot aloneTotal

1

10

100

1000

6 9 12 15 18 21 24 27Slot size [mm]

(Im

ZH

)eff

[ Ω/m

]

Slot aloneTotal

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 4/16

◊ Comparison of slots in several existing machines

Machine Slot size

[mm] Beam chamber

H×V [mm] Courtesy

ESRF

9 (Normal B)

75×33 (Standard)

T. Guenzel

ELETTRA 10 (Normal B) 20 (FEL) 30 (IR)

82×54 (Standard)

E. Karantzoulis

SLS

10 (Standard)

65×32 (Standard)

M. Dehler/

A. Streun

BESSY

15 (Normal B)

8 5 35 (InfraRed)

65×35 (Normal B)

60×16 60×11 65×35 (Normal B)

S. Khan/ P. Kuske

ALS

10 (Standard)

64×38 (Standard)

J. Byrd/J. Corlett

APS

10.8 (Standard) 5.7 4.5 4.5

85×48 (Standard) 40×16 36×15 30×10

L. Emery/ K. Harkay

Spring-8

10 (Standard) 12

70×40 (Standard)

T. Nakamura

NSLS

No slot to

ante-chamber

80×40 (Standard) (4 mm thick)

B. Podobedov

KEKB

14 (HER) 14 (LER)

98×50 (HER) φ 90 (LER)

K. Ohmi/

Y. Suetsugu

NB Machines with “Standard” indicated for the slot size have ante-chambers in their standard vacuum chambers. “Normal B” instead stands for the slot size of normal dipole chambers for those other machines.

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 5/16

1.3 Flanges

◊ So-called “non short circuited” ESRF type is considered, with the slit

size of 0.4 mm.

◊ Primary nature of the wake field found: • Presence of strong trapped modes • Good overlap with the bunch spectrum

⇒ Raise risk of multibunch instabilities ⇒ Need to integrate the wake to a large value of s

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30

f [GHz ]

ZL

[ohm

]

Real

Imaginary

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 6/16

◊ Dependence on the longitudinal gap (slit size)

012345678

0 10 20f [GHz ]

ZV

[koh

m/m

]

30

Real

Imaginary

0.6 mm

012345678

0 10 20f [GHz ]

ZV

[koh

m/m

]

30

Real

Imaginary

0.4 mm

012345678

0 10 20f [GHz ]

ZV

[koh

m/m

]

30

Real

Imaginary

0.2 mm

012345678

0 10 20 30012345678

0 10 20f [GHz ]

ZV

[koh

m/m

]

30

Real

Imaginary

ESRF 0.1 mm

f [GHz ]

ZV

[koh

m/m

]

Real

Imaginary

0.1 mm

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 7/16

◊ Estimate of multibunch instability thresholds

- Total number of flanges counted: 332 = 4×(19 + 2 × 22 + 20) - <βH> ~ < βV > ~ 10 m

- Employed formulae

Longitudinal

)(Re/4

1//

)(0

//

2

∑ −⋅⋅=k

knknfsn

ZeNeEQ

I kn ωωπ

ατ

τσω

( 0)( ωω ⋅++⋅= skn QnkM )

Transverse

)(Re/2

1 2)(00 ∑ ⊥−

⊥⊥

⋅⋅−=k

knfn

ZeNeE

If kn ωβτ

τσω

( 0)( ωω β ⋅++⋅= QnkMkn )

- Equilibrium with radiation damping

0

100

200

300

400

500

600

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7Slit size [mm]

Ith

[mA

]

LongitudinalVerticalHorizontal

-400-300-200-100

0100200300400

0 50 100 150 200 250 300 350 400CBM n

Ith

[mA

]

0.4 mm

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 8/16

◊ Some numerical verifications - Dependence on Smax:

• No convergence on Z itself, but area ∫ ωω dZ )( is preserved

⇒ Ith, kloss … converge

01

23

45

67

8

0 2 4 6smax [m]

ReZ

Y [k

Ω/m

]

8

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8smax [m]

Ver

tical

thre

shol

d [m

A] GdfidL

Fit

Fitted function:y = 16.4 + 41.4/(x - 1.004)

0

0,01

0,02

0,03

0,04

0 2 4 6 8

smax [m]

klos

s [V

/pC

]

- Comparison with the ESRF in the vertical case: • The same computation applied to the ESRF gives (Ith)V = 201 mA

(201 mA)ESRF = (46 mA)SOLEIL × 1.43 × 3.13

Machine parameters

⇒ ZSOLEIL is more responsible for low ( • If ZESRF is applied to SOLEIL, (Ith)SOLEI• If ZSOLEIL is applied to the ESRF, (Ith)ESRF

Impedance & bunch

Ith)SOLEIL

L = 139 mA = 65 mA

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 9/16

◊ Broadband aspect of the flange impedance

• Longitudinal

• Vertical

⇒ Flanges make a significant contribution to Zbb as well

Impedance estimate for SOLEIL 1

1th ESLS, ESRF 17~18 November 2003 10/16

2 Resistive-Wall Impedance Related Effects 2.1 Impedance and machine inputs

◊ Creation of a detailed machine structure input - A big file representing the entire machine - Use of data bush (M. Plesko) - a0, b0, d0, ρ,… are entered piecewise - ∫ dsβ evaluated locally for a given optics

⇒ Evolution of ZRW can be followed systematically

◊ Three numerical codes developed to calculate

- RW instability (rwmbi.f) - Incoherent tune shift (Mdetuning.c) - Effective impedance and loss factors (effectiveZ.f) read the same machine structure input

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 11/16

◊ Calculated effective impedance

Real part Imaginary part [Σ β*ZH (ω)]eff [MΩ] 0.191 (0.307) 0.376 (0.490) [Σ β*ZV (ω)]eff [MΩ] 0.467 (0.492) 0.744 (0.769)

[Σ ZL (ω)/n]eff [Ω] 0.055 (0.056) 0.086 (0.086) Numbers in parenthesis are with the three U20s closed to 5.5 mm

- Imaginary part > Real part due to NEG coating - Closure of in-vacuum IDs enhance the horizontal impedance - 50 µm Cu coating is not fully sufficient for the RW instability

0

1

2

3

4

5

6

7

0 200 400 600 800

f [kHz]

ReZ

T [M

Ω/m

]

Cu + NdFeB (50 microns Cu)Cu aloneCu + NdFeB (60 microns Cu)

Circular

0.3*f0

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 12/16

2.2 Resistive-wall instability and incoherent tune shifts

◊ Threshold calculation - Solution of Sacherer’s equation - (τ-1)coherent = (τ-1)radiation damping (i.e. no Landau effects)

- Number of unstable modes at ξ = 0 At 500 mA, ~90 vertical and ~30 horizontal

0

100

200

300

400

500

0 20 40 60 80 100Coupled-bunch modes

Thr

esho

ld c

urre

nt [m

A]

VerticalHorizontal

Zero chromaticityRW only

No in-vacuum

◊ Dependence of threshold on chromaticity - Importance of assuming a plausible ZBB

0

100

200

300

400

500

0 0,2 0,4 0,6 0,8 1 1,2

Normalised vertical chromaticity

Ith

[mA

]

m=0

m=2

m=1

RW + BBR (RT*β = 1.43 MΩ, fres = 22 GHz, Q=1)

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 13/16

0

100

200

300

400

0 0,1 0,2 0,3 0,4 0,5 0,6

Normalised vertical chromaticity

Num

ber

of U

nsta

ble

CB

Ms

RW aloneRW+BBR

RW + BBR (RT*β = 1.43 MΩ, fres = 22 GHz, Q=1)

- In the case studied, • Ith does not rise monotonously with increasing ξ • A “dip” on the # of unstable CBMs at a slightly posive ξ (~0.1) • When Ith is dominated by ZBB, # of unstable CBMs ~ h

⇒ If one could always rely on the “dip” at which, #CBMs < 5, the mode/mode feedback may be an adequate solution

◊ Improved calculation of incoherent tune shifts

- Effects evaluated piecewise and bunch wise - Quad strength according to K. Yokoya (Part. Acc. 41 (1993) 221) - Time dependence according to A. Chao et al. (PRST AB 5 (2002) 1)

Field diffusion = f(b0, d0, ρ, t )

- Take into account the beam structure and multi-turns

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 14/16

- Multibunch (uniform filling)

-0,03

-0,02

-0,01

0

0,01

0,02

0,03

0 100 200 300 400 500

I [mA]

Inco

here

nt tu

ne sh

ift

• Tune shifts are comparable in H/V (~0.025 at 500 mA)

- Single bunch

• Non-negligible effect of NEG coating taken into account, thanks to the relation (ZH)incoherent = -(ZH)coherent in flat chambers

)(Im)(~ /14 2

0ωωρωπ

xeffs ZdeEQ

k ⋅⋅=>< ∫∞

-0,008

-0,004

0

0,004

0,008

0 4 8 12 16 20

Isingle [mA]

Inco

here

nt tu

ne sh

ift

With NEG

Without NEG

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 15/16

◊ Collaboration with existing ESLS’s

- Application of the same calculation to measurable cases ⇒ Helps examine the validity of methods and results obtained.

People involved so far:

BESSY (P. Kuske, ...) SLS (A. Streun, M. Dehler, L. Rivkin, M. Munoz, ...) ESRF (J.L. Revol, P. Elleaume, ...)

In particular, SLS (A. Streun) kindly provided a complete list of the vacuum chamber structure along with the optics in the ring.

- Calculated resistive-wall instability thresholds (vertical @ ξ = 0)

ESRF 16 mA SLS < 26 mA

BESSY 9 mA SOLEIL 33 mA

Impedance estimate for SOLEIL 11th ESLS, ESRF 17~18 November 2003 16/16

- Incoherent tune shifts

ESRF

-0,015

-0,010

-0,005

0,000

0,005

0,010

0,015

0,020

0,025

0 50 100 150 200

Total current [mA]

Tune

shi

ft

Measured HMeasured VCalcul HCalcul V

BESSY

-0,006

-0,004

-0,002

0,000

0,002

0,004

0,006

0 50 100 1

Total current [mA]Tu

ne s

hift

50

M easured HM easured VCalcul HCalcul V

SLS

SLS

-0,015

-0,010

-0,005

0,000

0,005

0,010

0,015

0 100 200 300 400

Total current [mA]

Tune

shi

ft

Meas f itted V Calc H Calc V

(Measured by A. Streun on 5 Nov 03) (Current interpretation, to be confirmed)

Acknowledgement The author thanks C. Herbeaux, J.C. Denard, J.M. Filhol, P. Marchand, M.P. Level, for useful discussions. Thanks are also to A. Streun (SLS), P. Kuske (BESSY), T. Guenzel (ESRF) and other external colleagues, who gave precious help to the present work.