Les Effets Collectifs Rencontres LAL/SOLEIL, le 17 avril 2008 R. Nagaoka, au nom de léquipe des études collectives à SOLEIL

Les Effets Collectifs

Rencontres LAL/SOLEIL, le 17 avril 2008R. Nagaoka, au nom de l’équipe des études collectives à SOLEIL

Les gens qui ont specialement contribué à cette étude:

M.P. Level, C. Mariette, R. Sreedharan, F. Ribeiro, J. Labelle, T. Nakamura (SPring-8), K. Kobayashi (SPring-8)

Mesures des instabilités:

M.P. Level, M. Labat, M.E. Couprie, L. Cassinari, A. Loulergue, A. Nadji, J.M. Filhol et les autres membres de l’équipe de SOLEIL commissioning

Calculs des impédance et le développement d’un code de tracking multi-paquets:

A. Rodriguez (Supelec), V. Krakowski (Supelec), Ph. Martinez, W. Bruns (GdfidL)

Développement du système de feedback transverse:

R. Nagaoka et al. Les Effets Collectifs Rencontres LAL/SOLEIL le 17 avril 2008: 2/20


1. Études des impédances coupléesUn des objectifs majeurs de SOLEIL :

Haut courant (500 mA multipaquet et >10 mA en monopaquet) pour des utilisateurs.

Effets collectifs dus aux impédances deviennent un point critique.

Effects are further enhanced by small chamber openings b0, since wake fields scale ~ b0

-1 longitudinally, and ~ b0-2, b0

-3 transversally.

With b0 = 12.5 mm (standard SOLEIL chamber), the wake sensitivity is enhanced for SOLEIL.

0

5

10

15

20

25

30

0 2 4 6 8 10

E [GeV]

b0

[m

m]

SOLEIL

SLSBESSY

ALS

ELETTRA

NSLS

ESRF

APS

SPring8

E*b0^3 = const2 sources principaux des « wakes »

Difficulty to include resistive-wall (skin) effects into 3-dim wake field codes.

Resistive-wall (RW) effects were treated semi-analytically.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-30 -20 -10 0 10 20 30

x [mm]P

s(x

)/(P

s)c

irc

le

b = 12.5 mm

Air (or Ferrite)

Ceramic

Metal d

dc

VacuumbBeam

Wakes dus à des parois résistives

Modification to standard treatment (non-circular cross section, finite wall thickness) were introduced.

In particular, field matching due to different metallic and non metallic layers were made.

Copper, NEG, titanium coating etc.

Machine files following local RW changes were created including - variations, which is important for light sources.

Azimuthal dependence of power dissipation was followed to study the ceramic chamber heating.

Evaluation of incoherent tune shifts.


-0,004

0,000

0,004

0,008

0,012

0,016

0,00 0,02 0,04 0,06

s [m]

Wx

[V/p

C]

Ws1w0

Ws0.5w0/0.5

(Ws1w1 - Ws0.5w1)/0.5

Ws1w1

Ws0.5w0.5/0.5

Wakes géométriques

Many vacuum components possess non-axis symmetric (3D) & sub-millimeter structures.

Often they excite resonant modes that interact with beam.

- Necessity to reduce the mesh size (~0.1 mm) & integrate over a long distance (meters). - Enormous memory (tens of Gbytes) and cpu time required.- GdfidL that runs on a cluster of cpu’s (parallel processing) was employed.

L’impédance d’un taper est généralement difficile à converger

Soufflet blindé type SOLEIL

Une grande contribution au budget totale à cause de leur grand nombre

Sections non circulaire créent des champs “monopôle”

Monopôles soustraits


0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.2 0.4 0.6 0.8

Mesh size [mm]

(Im

ZL

/n)e

ff [

mo

hm

]

cf) Le cluster des ordinateurs à SOLEIL aujourd’hui:

232 core AMD Opteron of 2.2 to 2.6 GHz with 500 Gbyte of distributed memory.

0.000

0.002

0.004

0.006

0.008

0.010

0 2 4 6 8 10 12

Button Diameter [mm]

Lo

ss F

acto

r [V

/pC

]

thickness 2 mm

Fit of thickness 2 mm

thickness 5 mm

Fit of thickness 5 mm

Initial Model

Final Model

Quelques exemples qui ont influencés les dessins des composants vide:

- La fente des chambres dipôles

Increase of slot height was confirmed not dangerous for the beam and the system.

- Les brides

0

10

20

30

40

50

60

70

0 5 10 15 20 25 30

f [GHz ]

ZL

[oh

m]

Real

Imaginary

- BPMsTo reduce the heat deposited, the button thickness was increased, instead of reducing its diameter.

Trapped modes strongly excited in a cavity-like structure were estimated to induce severe coupled-bunch instabilities.

RF shielding foil was inserted.


Flat

0

1

2

3

4

0 2 4 6 8 10

f [GHz]

Ver

tica

l Z

T [

ko

hm

/m]

With coating ImZT

With coating ReZT

No coating

Étude des effets de la couche NEG

- À SOLEIL, à peu près la moitié des chambres ont la couche NEG.

- À Elettra, une augmentation anomale de l’impédance mesurée avec des chambres NEG.

(Courtesy E. Karantzoulis (Elettra))

Field matching shows that ImZT nearly doubles, but was not enough to explain the Elettra results.

(Courtesy T. Perron (ESRF))

Measurements elsewhere showed granular surface on NEG coated chambers, which could explain the Elettra results.

L’épaisseur de la couche a été réduite de 1 à 0.5 m à la proximité de faisceau.


-9

-6

-3

0

3

6

9

0.00 0.04 0.08 0.12 0.16 0.20

s [m]

WL

[V

/pC

]

OrgFitCharge

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

1.6

0 2 4 6 8 10

u = s/s0

RW

gre

ens

fun

ctio

n Henry/Napoly

Standard Formula

Utilisation des impédances obtenues dans les simulations des instabilités

Impédance géométrique:- Wake potentials need be processed to get Green’s functions for tracking codes.- Impedance was decomposed into purely inductive and resistive components.

Un exemple de la décomposition d’impédance et la reconstruction d’un potentiel wake.

plus BBRs, whose wake functions are known.

Impédance d’une paroi résistive:

- Form factors used to treat non-circular chambers.

- Longitudinal short-range singularity is overcomewith the Henry & Napoly functions.


2. Simulations des dynamiques faisceau collectives

Développement d’un code de tracking multipaquet traité en mode parallèle

- To analyze RW & Ions driven transverse multibunch instability.- To able to treat different beam fillings, incoherent tune spread, beam-ions interactions.

- Master-children structure using pvm. Each child performs single bunch tracking.- Master stores CM motions of all bunches. Each child then takes into account long-range (RW) forces of all bunches over multiple turns.

Effets multi-tours Mouvement interne d’un paquet Spectre faisceau

At SOLEIL, 1000 turn tracking of 138 bunches (1/3 filling) with 2000 particles/bunch:

Takes ~ ¼ hour with 16 processors

(A. Rodriguez, R. Nagaoka)


In the summer 2007, the code was extended to include fast beam-ion interactions, following the scheme of Raubenheimer/Zimmermann (Phys. Rev. E 52, 5487 (1995))

To conserve the parallel-processed structure;

- In the 1st step, each child simulates the ionisation and interaction of ions with a single bunch (parallel-process).

- In the 2nd step, the sequential passage of electron bunches is simulated and the growing ion distribution interacts with the electron beam. (sequential-process).

The code is nearly debugged and ready to produce results.

(V. Krakowski, R. Nagaoka)


0

20

40

60

80

100

120

140

160

180

200

0.00 0.10 0.20 0.30 0.40

Vertical normalised chromaticity

Inst

abili

ty t

hre

sho

ld [

mA

]

3/4 filling2/4 fillinguniform fillingSimulation

Signature of ions

0

10

20

30

40

50

60

70

80

90

0.00 0.05 0.10 0.15 0.20 0.25

Horizontal normalised chromaticity

Inst

abili

ty t

hre

sho

ld [

mA

]

3/4 filling

uniform fillingions

ions + RW

3. Observations Expérimentaux

Instabilités multipaquet- Apparently, mixture of RW and ions induced instabilities in both V & H planes.- No instability observed in the longitudinal plane (HOM free SOLEIL SC cavities).

(Mesurés lorsque la dose faisceau était ~20 A.h)

- Ion-induced instability depends much on the beam filling

- (Ith)V at low chromaticity in rather good agreement with prediction

- (Ith)H much lower than expected


- Distinction between the RW and ions-induced instabilities made by beam spectra observations

Dominé par RW Mélange de RW & des ions Dominé par des ions

- Influence of ions on “RW dominated” cases not yet clear- Stabilisation of m=0 mode occurs at chromaticity of ~0.2 in vertical- Not yet clear if the beam shall be stable at 500 mA by increasing the chromaticity

(i.e. Influence of |m|>0 modes)

Excitation du mode m=-1 à 250 mA, v=0.3

en remplissage ¾

(Observations en remplissage ¾ )


effZeEdI

df Im

/8

2/3

Mode detuning and TMCI threshold

Vertical detuning

Cancellation between the coherent and incoherent tune shifts seen in H.

Comparison of impedance using

(Horizontally, df/dI is deduced as -f0Qs/Ith. )

Horizontal detuning

: Measured threshold

(df /dI )meas *Im(Z )eff [ *Im(Z )eff ]budget * ratio (I TMCI)meas * (I TMCI)calc *** ratio[kHz/mA] [MW] [MW] (meas/calc) [mA] [mA] (calc/meas)

Vertical -1.34 2.45 1.35 1.8 2.8 5.0 1.8Horizontal -0.44 1.05 0.63 1.7 8.4 14.0 1.7

0.312

0.313

0.314

0.315

0.316

0.317

0.318

0.319

0.320

0 1 2 3

Bunch current [mA]

QV

0.203

0.204

0.205

0.206

0.207

0.208

0.209

0.210

0 2 4 6 8 10 12

Bunch current [mA]

QH

Effets monopaquet


Bunch lengthening (streak camera) Synchronous phase shift (streak camera)

- Measured data seem to indicate that ImZ is larger than expected by a factor of ~2 in all

Both measurement and simulation show no substantial widening up to 20 mA

Energy spread widening

0

10

20

30

40

50

60

0 5 10 15 20

Ib [mA]

CM

sh

ift

[ps

]

MeasuredNo bunch lengtheningWith measured bunch lengthening

Vrf = 1.2 MV

10

20

30

40

50

60

0 5 10 15 20

I [mA]

Bu

nc

h l

en

gth

[p

s]

Blue : MeasuredBlack : Tracking (RW+BB)Red : Inductive 0.45 ohmGreen: Inductive 0.20 ohm

Vrf = 2 MV

- Measured |Z/n|eff is still less than 0.5 W.

H, V and L planes.


Est-ce que l’écart sur ImZ pourrait venir de la rugosité de la couche NEG?

SOLEIL extruded Al chamber (rms ~0.3 m, peak to peak ~1 m)

Courtesy SOLEIL’s Metrology Lab.

NEG coated SOLEIL extruded Al chamber

Courtesy SAES Getters

Estimation avec les modèles de l’impédance de la rugosité: (rugosité de ~1 m supposée)

beam

beam

- G. Stupakov’s “small angle approximation” model.

- K. Bane et al.’s “(non-smooth) bump” model.

However, inspection made so far indicates that, unlike elsewhere, NEG coating for SOLEIL chambers did not degrade the original roughness

L’écart observé ne semble pas être attribué à la rugosité

…since the roughness impedance is inductive, it goes in the right direction.

Could explain the factor 2 discrepancy

Too small to explain the factor 2 discrepancy

fb

d

c

ZiZ

22

30

//6

)(

k

kl

kkdldkdk

cb

ZiZ z

czxc

xz

22

22220

// )2

exp(22

)(


Mesure des instabilités transverses paquet par paquet avec le FBT:

0

200

400

600

800

1000

1200

0 100 200 300 400

Bunch No.

Be

tatr

on

Ph

as

e [

de

g]

50 mA100 mA250 mA

~40 /bunch

~0.9 /bunch(360 /416 = 0.87

fA=28(CO)

Afin de comprendre la nature de l’instabilité multipaquet, la dynamique du faisceau mesurée paquet par paquet, en coupant FBT typiquement sur ~ms.

- A bas courant, le comportement de l’instabilité est plutôt du type RW.

- A partir de ~200 mA, il y a une transition au type Fast Ions (FBII).

Il faut suivre l’évolution de l’instabilité en fonction de niveau du vide.

Amplitude d’oscillation en fonction des paquets.

Phase d’oscillation betatron en fonction des paquets.

Spectre du faisceau mesuré à 250 mA en remplissage 3/4.


4. Développement d’un système de feedback transverse

Motivation: - Envisaged 2 operation modes at SOLEIL (500 mA multibunch, 8x10 mA single bunch) - Vertically narrow vacuum chambers around the machine

Low transverse multi and single bunch instability thresholds predicted.Chromaticity shifting predicted not to fully stabilise the beam.

Décision faite pour avoir un FBT disponible depuis le début de l’opération de l’anneau.

Performance demandée: - Capable of suppressing different transverse multibunch and single bunch instabilities - Not spoil the small transverse beam size ( < /10)

Strategie adoptée: Make use of the technologies and devices already developed elsewhere. - SPring-8 digital processor chosen for its proven performance in different machines. - BPM, RF frontend, stripline kicker developed in house


-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

0 1 2 3 4 5 6 7 8 9 10

Frequency [GHz]

Sig

na

l le

ve

l [d

Bm

]

Electrode

with 22 m of CNT195

with 22 m of CNT 400

with 22 m of CNT 600

Chaîne du feedback transverse développé

Four 12-bit ADCs working at 88 MHz (352.2 MHz/4)

All FIR filters and multiplexers integrated into one FPGA board (latency < 1 turn)

Two 20-tap or one 50-tap FIR filter

Five 12-bit DACs

Caractéristiques du processeur numérique:

Sensibilité du BPM SOLEIL

à 1.2 mA/paquet

RF frontend:

Creates a -signal and extract a band of frf/2 at 4th harmonic of frf, then down coverts to the base band.

Kicker:

A 4-electrode stripline developed for diagnostic purposes is currently used for feedback in the two transverse planes. peak ~47 V/mA/m


0

10

20

30

40

50

60

70

80

90

0 50 100 150 200 250 300

Frequency [MHz]

Sh

un

t Im

ped

an

ce [

ko

hm

] GdfidL

Semi-analytical (2D)

2-electrode solution 4-electrode solution(Courtesy C. Mariette)

Développement des striplines dédiés:A 2-electrode stripline with high shunt (~60 kW) and low coupling impedance was developed and recently installed in the ring (Feb. 08).

Modes de fonctionnement et des filtres numériques:

Following the success at SPring-8, the system is used either in a single plane (H or V), or in both planes (H and V) by working in the diagonal mode.

16-tap FIRs with 2 turn delay are currently applied.

Le gain et la phase d’un filtre FIR 16-tap vertical


La performance atteinte:

Stable 300 mA beam with zero chromaticity in both transverse planes.

Feedback damping time of 0.3 ms measured at 250 mA.

Prochains buts:

Absence des raies instables à 300 mA Performance atteinte en monopaquet

Suppression of vertical beam size increase in multibunch, extension to 500 mA.

Increase of single bunch instability threshold current.

Feedback is routinely applied in both transverse planes for user operation with reduced chromaticity.


0

2

4

6

8

10

12

14

16

18

20

0 1 2 3 4 5 6Vertical chromaticity

Th

resh

old

cu

rren

t [m

A]

15 Dec 06

No TFB

With TFB (Sep07)

With TFB (Apr08)

TMCI

m=-1

m=-2

TFB

TFB

TFB

Documents

Les Effets Collectifs Rencontres LAL/SOLEIL, le 17 avril 2008 R. Nagaoka, au nom de léquipe des études collectives à SOLEIL