Local transverse impedance measurements atALBA from turn-by-turn acquisition

Michele Carla, Gabriele Benedetti, Thomas Gunzel,Ubaldo Iriso and Zeus Martı

27 October 2016

Transverse beam coupling impedance:

...interaction of a charged particle beam with a self-induced field,mediated by the surrounding environment

Force exerted over an e−

I Bunch induces a field in the vacuum chamber

I Each particle interacts with the fieldI The overall effect is a defocusing kick similar to the one

produced by a quadrupole though with some difference:I Proportional the bunch chargeI Defocus in both planesI Depend on the geometry of the chamber

Transverse impedance from electro-magnetic simulation

Is the reference tool and the only option during the design phase ofa new device. From the geometry of a device we get a full pictureof the EM behavior...

1

...Furthermore computers never lie

1Kindly provided by Andriy Nosych

On the other hand computer simulations offer a vastselection of traps:

I Big devices with complex geometry are computationallychallenging (e.g. IVU)

I New materials with doubt EM properties (e.g. Getter coating)

I Hard tolerance to meet in production (e.g. Coating thickness)

The motivation of this work is toverify simulation results

ALBA impedance budget:

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IV

III

II

I

β

x,y

[m]

Longitudinal Position [m]

Previous Quadrant One Machine Quadrant Next Quadrant

βxβy

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30

40

IV

III

II

I

β

x,y

[m]

Longitudinal Position [m]

InjectionScraper

IVUNEG

SC Wiggler

260 0 10 20 30 40 50 60 70 80

Mac

hine

Qua

dran

ts

260 0 10 20 30 40 50 60 70 80

Mac

hine

Qua

dran

ts

60 70 80 90 100 110 120 130 140

Mac

hine

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dran

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60 70 80 90 100 110 120 130 140

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hine

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dran

ts

130 140 150 160 170 180 190 200 210

Mac

hine

Qua

dran

ts

130 140 150 160 170 180 190 200 210

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hine

Qua

dran

ts

190 200 210 220 230 240 250 260 0 10

Mac

hine

Qua

dran

ts

190 200 210 220 230 240 250 260 0 10

Mac

hine

Qua

dran

ts

kΩ/m (Am)−1

Injection 25.3 0.098IVU 38.2 0.147NEG-chamber 31.2 0.120SCW 14.6 0.056Beam-pipe 105.6 0.404

I All numbers come from GdFidl simulation

I Only vertical impedances are relevant in ALBA

I Impedance of ID do not affect much because ofthe low βy

Measuring focusing/defocusing forces in a storage ring:

A quadrupolar field vanishes on axis, to observe a trajectory/orbit change thebeam must be displaced at the impedance location

Bump method / Closed orbitI An orbit bump is created at the

impedance location.

I Measure orbit change.

Turn by turnI Excite betatron motion with a pinger.

I Measure beam position turn after turn.

With a 0.1 (Am)−1 kick, a bunch current of 5 mA and a bump of 1 mm:

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-1

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0 20 40 60 80 100 120

Orb

it [µ

m]

BPM #

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Pha

se-b

eat [

mra

d]

BPM #

I Turn by turn measurements are technically more challenging.

I During the past years we found that measuring 1 mrad is doable.

Multiple impedance sources through optical measurements

y

s

x

I Measure phase-advance for different charges

I Beating is the signature of impedance sources

I The strength of sources located at differentpositions is obtained by fit

In simulation:

1. Calculate the phase-beat toimpedance-source responsematrix:

M × ~Z = ∆~ψ

2. Calculate M−1 with an SVD

On the machine:

1. Measure the phase-advance

2. Change the per-bunch charge

3. Measure again...

4. Build phase-beat vector: ∆~ψ

~Z0 = M−1 ×∆~ψ

ALBA Beam position monitor (Libera Brilliance):

A

D

B

C

ADC

ADC

Va - VbVa + Vb

Numerical Oscillator

RF master clock

BW ~10 MHz BW < 1 MHz !!!

RF: 500 MHzPeriod: 0.9 us

One Revolution 0.9us

Is this a reflection?

I Preserve bandwidth along thechain!

I What happens in the digitaldomain is fixable ...if HDL isavailable

I Do not underestimate theanalog front-end.

Machine stability & power supply noise:

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0.3628 0.363 0.3632 0.3634 0.3636

Cou

nt

Vertical Tune

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250

300

0.3628 0.363 0.3632 0.3634 0.3636

Cou

nt

Vertical Tune

10-5 0 105 0

20

40

Single Acquisition

We measured Qy 100 times for eachBPM and calculated the RMS...

I BPMs agree within 2.1 · 10−6

during the same excitation

I Tune spread increases to 1.1 · 10−4

between different excitations

Surprised? (We were...)

Quadrupoles induced tune noise:

I Quadrupoles induced detuning:

σQ =1

4π

∮β(s)∆K (s)ds ' β · σK ·

√# of quads

4π

I Magnet power supply stability is ' 10ppm

I We have 112 magnets ...noise is uncorrelated → √...I Average βy is 9 m

σQy =9m · 1.9 · 10ppm ·

√112

4π' 1.5 · 10−4

Faking an impedance source by detuning a quadrupole:

I Proof that the whole measurement + analysis chain isworking.

I Characterize measurement’s noise → define # ofacquisitions

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∆QH01 = -1% ∆QH01 = -0.5% ∆QH01 = -0.2% ∆QH01 = -0.1%

Def

ocus

ing

Kic

k S

tren

gth

[10-3

/(m

)]

QH01 Error

MeasurementsModel

I ∆ψ as small as the one expectedby impedance was measured.

I Dealing with optics fluctuationsrequires > 500 acquisitions.

Looks promising!

Verifying the impedance of an element: the scraper

A scraper can be moved → we can “switch on & off ”itsimpedance

I This time we use high charge bunches.

I 500 acquisitions for each scraper position.

I Plot kick change with respect to the nominal position.

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Bun

ch C

urre

nt [m

A]

Bucket Number

High Current TrainKicker Pulse

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0.1

0.15

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0.25

6 mm 5 mm 4 mm

∆ D

efoc

usin

g K

ick

/ Cur

rent

[(A

m)-1

]

Scraper Gap

MeasurementsModel

Fitting multiple sources by varying the charge per bunch

I We use a high and a low bunch charge filling pattern.(But with the same stored current)

I 500 acquisitions for each filling pattern.

I Fit parameters are the beam-pipe and the injection section...

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100 150 200 250 300 350 400

Bun

ch C

urre

nt [µ

A] Low Current Train

Kicker Pulse

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ch C

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A]

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High Current TrainKicker Pulse

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Beam Pipe Injection Section

Def

ocus

ing

Kic

k / C

urre

nt [(

Am

)-1]

MeasurementsModel

Fitting multiple sources, are we doing it right?

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Beam Pipe Injection Section

Def

ocus

ing

Kic

k / C

urre

nt [(

Am

)-1]

MeasurementsModel

I Add up the tune shift from the fitted sources → ∆Q = 1.8 · 10−3

I Measured tune shift → ∆Q = 2.3 · 10−3

I Discrepancy is ' 20%, accounting for non-fitted sources (IDs) dropsto 4%

Increasing the number of sources in the fit:

I Qy measurement shows a 20% missing impedance

I Error bars are around 10% → What’s left is buried in the noise

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Beam Pipe Injection Section NEG Chamber

Def

ocus

ing

Kic

k / C

urre

nt [(

Am

)-1]

MeasurementsModel

Two options =⇒ 1. Decrease the noise

2. Increase the signal

Magnifying the contribution of an ID by increasing β

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β

x,y

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Longitudinal Position [m]

One Machine Quadrant

In-Vacuum ID

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β

x,y

[m]

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One Machine Quadrant

In-Vacuum ID Nominal βyModified βy

I Optic distortion scales linearlywith βy

I βy at an ID was increased from1.2 m to 6.5 m

Magnifying the contribution of an ID by changing β

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Beam Pipe Injection Section IVU

Def

ocus

ing

Kic

k / C

urre

nt [(

Am

)-1]

High βv Lattice MeasurementsModel

Nominal Lattice Measurements

I 5 times magnification is enough to get a very precise estimation.

I New measurements (blue) are compatible with the previous ones(red).

I Some discrepancy with respect to the model is found.

Looking for future improvements:

I Thermal load influences measurements.

I Each filling pattern has a different thermal load.

I Fast machine fluctuations.

Dealing with thermal loads: hybrid filling pattern

I Our BPMs do not have sub-turn resolution.

I Instead they allow for synchronous measurement:acquire the signal only in a fixed time window (yellow or blue)synchronized with one train (MAF).

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ch C

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A]

Bucket Number

Low Current Train High Current Train

One Revolution 0.9us

Is this a reflection?

Unluckily the analog front-end does not have the required bandwidth

New BPM design (NSLS-II, Sirius2...) are closing the gap

I Multi-GB memory allows forsustained ADC rate acquisition

I High bandwidth fron-end toachieve sub-turn reslution

2”http://www.ohwr.org/projects/bpm/wiki”

Disentangling the two signals by detuning:

I High and low charge bunches oscillates with different tune

I If BPMs are linear we should be able to disentangle the two signals

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Ver

tical

Bea

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ositi

on [m

m]

Turn Number

Turn by turn positionEnvelop

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0.360 0.365 0.370 0.375 0.380A

mpl

itude

[A.U

.]

Vertical Tune

Spectrum

Even if the two signals are clearly distinguishable, phases are notproperly measured...

Conclusions:

I Multiple local impedance sources typical of a light-source have beenmeasured using turn-by-turn technique.

I Results are consistent with GdFidl simulations.

I Optics manipulation has been used to magnify the contribution of a weaksource. (We plan to do the same to measure impedance of the CLIC damping-ring kicker)

I Machine stability, power supply noise and thermal drifts have beenidentified as the main limiting factors.

I Different schemes to work around those limitations have been proposedbut not applied because of BPMs shortcomings (bandwidth and memory).

I A paper has been accepted by PRAB 3

3”Local transverse coupling impedance measurements in a synchrotron light source from turn-by-turn acquisitions”

Acknowledgments:

I A. Olmos and J. Moldes for helping with the BPM set-up

I The ALBA operations group.

I A. Nosych for providing the BPM fields simulation picture

Fit: High-β & nominal lattice

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se B

eat [

mra

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se B

eat [

mra

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Injection

Scraper

In-Vacuum ID

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se B

eat [

mra

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Injection

Scraper

In-Vacuum IDMeasurement

Fit

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se B

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mra

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Longitudinal Position [m]

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se B

eat [

mra

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Injection

Scraper

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se B

eat [

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Longitudinal Position [m]

Injection

ScraperMeasurement

Fit

Kicker & chromaticity

Kick coherently:

I Kick pulse has to be less than 1 turn.

I Kick pulse should be flat.

I Preserve the coherent motion:

Chromaticity & Tune shift withamplitude reduce strongly theobservable number of turns

⇓Special sextupole settings with low

Chromaticity and small Tune shift withamplitude 0 100 200 300 400 500

Turn #

Tran

sver

se P

ositi

on

Nominal SextupolesTbT Sextupoles

Smearing work around

I One train is injected and dumped after one turn.

I BPM are synchronized with the beam.

I The single turn response of each BPM is measured.

I The output signal is deconvoluted with the measured singleturn response (for phases only is not needed).

Moving average filter (MAF):

Replace the low pass filter with an averaging filter synchronizedwith the beam.

I Avoids turn mixing.

I Reduce the integrated noise: most of the turn-time contain nosignal.

Tune noise...

I Every BPM sees the sametune! (Good)

I Every kick has a differenttune! (Bad)

I The Machine is Changing!

0 20 40 60 80 100 1200.1529

0.153

0.1531

0.1532

0.1533

0.1534

0.1535

Hor

izon

tal T

une

BPM #

Tune nois spectrum

0 100 200 300 400 500 60010−4

10−3

10−2

10−1

100

101

102

Frequency [Hz]

Inte

nsity

[A.U

]

100 Hz 300 Hz

I A kick do not last enough!

I Once in a while instabilites are ourfriends → tuning the chromaticityclose to 0 betatron motion get steadilyexcited

I Enough to get a spectrum

I 100 & 300 Hz looks very suspicious...