Impedance Modeling of the APS Storage Ring: Current and APS Upgrade

Yong-Chul ChaeAdvanced Photon Source

48th ICFA Advanced Beam Dynamics Workshop on Future Light Sources SLAC National Accelerator Laboratory, March 1-5, 2010

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Outline

Impedance Modeling– Impedance Database I (z = 5 mm)– Impedance Database II (z = 1 mm)– Modeling vs. Experiment

APS Upgrade with Long Straight Section– Impact of Long Straight Section to the Single Bunch Current– Undulator Chamber Optimization

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Impedance Elements

2cm

1cm

4cm

153 mm

8 mm

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,**Element

iiitotal WNW

Wtotal = total wake-potential of the ring,

Ni = number of the element in the ring,

Wi = wake-potential of the element,

i = weight of the element.

GOAL: Total Wake Potential

Impedance Database

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VERTICAL

LONGITUDINAL HORIZONTAL

Total Impedance of the APS Storage Ring (wo lattice function)

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APS Low Emittance Lattice

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What limits the single-bunch current?

Accumulation Limit was 6-8 mA at low chromaticity at 5-7.Chromaticity was limited by sextupole

strength until the pole tip was modified.Higher chromaticity (> 10) achieved with

modified sextupoles.Accumulation Limit is 20 mA at high

chromaticity at 10.

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Vertical TMCI: Simulation

Centroid Kick y=1mm Spectrum Vertical Beam Size

2 mm

3 mm

1. Well known decoherence behavior at low current2. Mode coupling completes 3 mA3. Beam size blow-up above mode coupling Beam Loss due to 5-mm

Insertion Device Chamber

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Injected Beam

Stored Beam

x

y Stored beam

Injected beam

x (mm) 3 4

y (mm) 0 0.2

x (m) 3e-9 1.5e-7

y /x (%) 3 10

x (m) 20 20

y (m) 3 3

s (mm) 7 - 12 24

p (%) 0.1- 0.13 0.1

Coordinates of Initial Beam at the center of ID straight

Initial Condition of Beam Simulating Current Injection Scheme

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Injection Efficiency vs. Current

Accumulation Limit

Measured Accumulation Limit < 8 mA

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Significant amount of stored beam is lost during the injection process

Reduce the Beam Loss Reduce the Separation

Longitudinal Injection

Injected Beam

Stored Beam

x

yInitial Coordinates of Lost Beam

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Prediction of Accumulation Limit: High Chromaticity

Threshold current is 20 mA determined by simulation– Vertical beam size blow-up

Simulation reproduced the accumulation limit at 20 mA observed in the APS storage ring

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Single Bunch: Prediction for the APS

We can now predict the effect of small gap chambers.

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Single Bunch Current of the Future APS RingAdd (%) Total (%) Current

(mA)Note

Reference 0.00 100 20.0 1*5-mm + 29*8-mm + Others

Short pulse sector

1.33 101.33 19.3 1*3-cell + 2*9-cell (r=23.5 mm), T1+T2

8-mm gap 1.54 102.87 18.6 Replacing EMW @ S11

4*8-mm gap

6.16 109.03 15.8 New addition

7-mm gap 0.64(2.18)

109.67 15.6 Replacing 8mm3.5 m long SC ID

6-mm gap 1.71(3.25)

111.38 14.9 Replacing 8mm5 m long ID @ S1

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Impedance Database II: Choice of Bunch Length

The shorter, the better.

But, computer resources are limited.

We choose z =1 mm– quasi-Green Function

We purchased 60-node cluster equipped with 240 GB of memory

We used GdfidL for parallel computation.

Remove “ad-hoc” modification made to IDB-1, which was necessary for the good agreement in microwave instability.Need a broadband impedance!Used a short bunch to calculate wake potential!

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Impedance Database II: Results

Bandwidth increased from 40 to 200 GHz!

200 GHz

500 GHz

50 GHz

Wz (V/pC) | FFT(Wz )|

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Bunch Length Measurement

Simulation results was obtained by a raw impedance.

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Bunch Length Measurement (cont)

1. Profile is not in Gaussian.2. Simulation fits profile well.3. Profile is sensitive to

dynamic range of camera (500-1000).

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Energy Spread Measurement

The difference is only 2% if we include 40 um resolution.

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Plan for the APS Upgrade

Increasing the length of an APS straightFig. 3.1.1. Schematic of the lattice changes for a longer straight section. The proposed increase in length from4.8 to 7.7 m is achieved as shown by removing Q1 and shortening Q2 (Key: dipoles -red; quadrupoles - blue;sextupoles - yellow).

KEEP 16 mA single bunch current in the hybrid fill!

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Effect of LSS to the Single Bunch Current

Impedance (y *Zy ) Breakdown (APS Now)

Geometric Undulator Chamber Transition (0.3 zu) + Bellow (0.2 zu) + Other (0.5 zu) = 1.0 zu

Resistive Undulator Chamber + Regular Chamber = 0.3 zu

Total 1.3 zu

LSS Taper (Geometric) Reduce to 5/8 Taper Optimization (Development)

LSS Undulator Chamber (Resistive) Reduce to 1/2 Silver Coating (R&D)

y *Zy :1.44 zu 10% Increased

Current: 14 mA 6 mA decreased

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Taper Optimization for Long Straight Section

Optimize h(z) nonlinear taperOptimize w narrow horizontal apertureOptimize linear h’(z) long taper

20

3

'( )4 ( )

recty

Z w h zZ j dzh z

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Nonlinear Taper

Optimum profile found by B. Podobedov and I. Zagorodonov*

maxmin

21/ 2 min

( ) , 1 1 /

hhh zhz L

28

(1 ) 1

optimumy

lineary

ZZ

*B. Podobedov, I. Zagorodonov, “Impedance Minimization by Nonlinear Tapering,” Proc. of PAC2007, p. 2006.

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Nonlinear Taper: Confocal Ellipse (1)

APS 8-mm gap chamber:hmax =20 mm, hmin =4 mm ZNL /ZL =0.64

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Nonlinear Taper: Confocal Ellipse (2)

APS 8-mm gap chamber: hmax =20 mm, hmin =4 mm ZNL /ZL =0.64

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Nonlinear Taper: Confocal Ellipse (3)

APS 8-mm gap chamber: hmax =20 mm, hmin =4 mm

Theory

Simulation

ROI

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Nonlinear Taper: APS 8-mm Gap Chamber (1)

APS 8-mm gap chamber is neither flat nor confocal!

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Nonlinear Taper: APS 8-mm Gap Chamber (2)

APS 8-mm gap chamber is neither flat nor confocal!

ROI

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Optimize Width of Undulator Chamber

APS undulator chamber has half width w=18mm

APS regular chamber has half width w=40 mm

IVU

APS(Now)

RHB

20

3

'( )4 ( )

recty

Z w h zZ j dzh z

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Long (Linear) Taper

Nonlinear taper– Effective for flat and confocal chamber– Not effective for the APS 8-mm gap undulator chamber

(a, b)=(20 mm, 4 mm)

Narrow width – Effective in reducing the impedance – May reduce the injection efficiency

Long Taper– Universal reduction (Linear, Nonlinear, Width)– How long it should be to maintain 16 mA single bunch in the

hybrid fill pattern

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Long Linear Taper (2)

Normalized by the current APS 8-mm gap chamber.

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Long Taper for the APS Upgrade (1)

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Long Taper for the APS Upgrade (2)

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Summary

Impedance Database was proved as a useful tool to investigate the single-bunch instability in the APS:– The APS storage ring (operation),– The APS storage ring with crab cavities for short x-ray

pulse (planned),– The 1-nm storage ring with smaller chamber (R&D).

Found that the 8 LSS could decrease the operational single bunch current from 16 mA down to 12 mA (unacceptable!).

We developed a long taper (and propose silver coating on Al chamber) to keep the16 mA single bunch current in the upgraded APS storage ring.

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Acknowledgement

Taking DataM. Borland, L. Emery, K. Harkay, A. Lumpkin, N. Sereno,

V. Sajaev, J. Song, C. Yao, B. Yang, APS OperatorsComputer Software/Hardware

M. Borland, B. Soliday, Y. Wang, A. Xiao, W. Bruns (GdfidL)Drawings

P. Choi, G. Goepner, L. Morris, E. Rossi, S. SharmaSupport

R. Gerig, K. Harkay, K. Kim, S. MiltonDiscussion

S. Krinsky, B. Podobedov, J. Wang (NSLS) R. Nagaoka (SOLEIL), M. Blaskiewicz (BNL)