march 20 th 2014 | tu darmstadt | fachbereich 18 | institut theorie elektromagnetischer felder |...

March 20th 2014 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Thibault Ferrand, MSc | 1 Supported by GSI & CERN

Existing bunch-to-bucket transfer schemes

Synchronisation solutions for accelerator facilities

• Introduction• Machine synchronisation

• Energy matching• Batch synchronisation• Fine synchronisation

• Limitations• Beam synchronous transfer timing• Applications

• Booster – PS and LEIR – PS • PS – SPS• SPS – LHC

• Remaining issues


Plan







Introduction – Bunch-to-bucket transfer

Bunch-to-bucket transfers are being considered since particles are being accelerated over several machines successively.

« Bunch-to-bucket » means that a bunch of particle must be deflected from its stable trajectory in a source machine to be injected in the centre of a bucket on its stable trajectory in a target machine.

Source-synchrotron

Target-synchrotron

Ejection septum

Injection septum

Figure : Problem overview


Introduction – Synchronisation

Extraction

InjectionAcceleration in the source-synchrotron

Acceleration in the target-synchrotron

Ene

rgy

Time

Figure : acceleration cycle, overview

Injection

Acceleration ramp

Ejection

Ene

rgy

mat

chin

g

Pha

se m

atch

ing

Loop

cor

rect

ion

Ene

rgy

Time

Figure : acceleration cycle, the source-machine

Extraction energy


Introduction – Bucket, Bunch, Batch

An empty bucket

A bunch in its bucket

4 equally spaced bunches

2 batches of 4 bunches each

Batch spacing

Bunch spacing


Plan

• Introduction

• Machine synchronisation• Energy matching• Batch synchronisation• Fine synchronisation





𝐸𝑒𝑥𝑡𝑟=𝐸𝑖𝑛𝑗

→𝛾𝑒𝑥𝑡𝑟=𝛾 𝑖𝑛𝑗

→ 𝛽𝑒𝑥𝑡𝑟=𝛽𝑖𝑛𝑗

→𝐶𝑠 𝑓 𝑟𝑒𝑣𝑠 =𝛽 𝑐¿𝐶𝑡 𝑓 𝑟𝑒𝑣

𝑡

: Energy of the synchronous particle

With : instant speed of the synchronous particle

Energy matching

Goal of this stage is to ensure that the bunches, which would be sent form the source-machine and the buckets in the target-machine are derived from the same energy level.

𝐶 𝑠 𝑓 𝑟𝑒𝑣𝑠 =𝛽𝑐=𝐶𝑡 𝑓 𝑟𝑒𝑣

𝑡

𝑓 𝑟𝑒𝑣𝑠

𝑓 𝑟𝑒𝑣𝑡 =𝐶𝑡

𝐶𝑠 =𝑁 𝑠

𝑁𝑡

𝑓 𝑅𝐹=h 𝑓 𝑟𝑒𝑣

𝑓 𝑅𝐹𝑠 =𝐶𝑡h𝑡

𝐶𝑠h𝑠𝑓 𝑅𝐹𝑡

Synchrotron’s circumference

Revolution Frequency

𝐶 :𝑓 𝑟𝑒𝑣 :

RF Frequency𝑓 𝑅𝐹 :

Harmonic numberh :

𝑓 𝑅𝐹=h𝑐2𝜋 𝑅0

𝐵

√𝐵2−( 1𝑐 𝜌 𝐸0𝑞 )2

vs. B field relation :

depends on the type of the accelerated particles. Since neutrons have no charge, the frequency sweep for accelerated heavy ions is larger than the one for accelerated protons to the same energy.

MeV

MeV


Batch synchronization (1)

Once the beam energy has been matched, the two-machines-system is periodic of period :

Figure : phase advance

Phase reference

𝜑𝑟𝑒𝑣𝑠

Phase reference

𝜑𝑟𝑒𝑣𝑡

Figure : phase advance

Phase referencePhase advance


Batch synchronization (2)

A frequency bump is produced to correct the phase advance:

∆𝜑=(2𝜋∫𝑡0𝑇

∆ 𝑓 𝑟𝑒𝑣 𝑑𝑡)180°

∆ 𝑓 𝑟𝑒𝑣

Figure : frequency bump

Bump start

Source-synchrotron

Target-synchrotron

Extraction

Transfer

Injection

𝜑𝑒𝑥𝑡𝑟 𝜑𝑖𝑛𝑗

∆ 𝑡 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟


Fine synchronization

V

∆ 𝑡

∆𝐸

This loop can be a simple phase locked loop or a more sophisticated 1st or 2nd order correction function (PSB and LHC case).

Since the frequency () on which the batch rephased is generally not high enough to ensure the required phase accuracy, a second phase matching is performed on a higher frequency () mostly thanks to a feedback loop.

∆ 𝑡 𝑓𝑖𝑛𝑒


Plan







Limitations

𝑑𝑝𝑝

=𝛾 𝑡𝑟2 𝑑𝑅𝑅

+𝑑𝐵𝐵

𝑑𝑝𝑝

=𝛾 2𝑑𝑓𝑓

+𝛾2𝑑𝑅𝑅

𝑑𝐵𝐵

=𝛾𝑡𝑟2 𝑑𝑓𝑓

+𝛾 2−𝛾 𝑡𝑟

2

𝛾2𝑑𝑝𝑝

𝑑𝐵𝐵

=𝛾2𝑑𝑓𝑓

+(𝛾 2−𝛾𝑡𝑟2 ) 𝑑𝑅𝑅

𝑝=𝑒𝜌0( 𝑅𝑅0)1𝛼𝑝 𝐵

𝛼𝑝=𝑝𝑅 (𝜕𝑅𝜕𝑝 )

𝐵

𝑓 =𝛽𝑐2𝜋 𝑅

: radius of the beam trajectory : momentum : magnetic field intensity

𝑑𝐵𝐵

=𝛾2𝑑𝑓𝑓

+(𝛾 2−𝛾𝑡𝑟2 ) 𝑑𝑅𝑅

𝑑𝑓𝑓

=𝛾 𝑡𝑟2 −𝛾 2

𝛾 2𝑑𝑅𝑅

Radial excursion: a frequency offset at constant B field results in a radial excursion which can’t be fully handled during the transfer.

0𝑑𝑓𝑓

=𝛾 2−𝛾𝑡𝑟

2

𝛾𝑡𝑟2 𝛾 2

𝑑𝑝𝑝

0

𝑑𝐵𝐵

=𝛾𝑡𝑟2 𝑑𝑓𝑓

+𝛾 2−𝛾 𝑡𝑟

2

𝛾2𝑑𝑝𝑝

𝑑𝑓𝑑𝑡

= ∆ 𝑓𝑇𝑟𝑒𝑣

=−η𝑓 0𝑝0

𝑞𝑉𝑠𝑖𝑛𝜑𝑠

2𝜋 𝑅0

∆ 𝑝=𝑞𝑉𝑠𝑖𝑛𝜑 𝑠

2𝜋 𝑅 𝑓 𝑟𝑒𝑣∆ 𝑓 =

𝛾2−𝛾𝑡𝑟2

𝛾𝑡𝑟2 𝛾 2

𝑓 0𝑝0

𝑞𝑉𝑠𝑖𝑛𝜑 𝑠

2𝜋 𝑅 𝑓 𝑟𝑒𝑣

Limitation on the frequency rate: the instant speed and the momentum of the synchronous particle are linked.


Limitations: Adiabaticity

|Ω𝑠 0

𝑑𝑡Ω𝑠 0

|2𝜋Ω𝑠0

=𝑒− 1

∆ 𝑡𝑝𝑘∝1𝑓 𝑅𝐹

4√ |η|𝛾𝑉𝑐𝑜𝑠𝜑𝑠

∆𝐸𝑝𝑘∝ 𝑓 𝑅𝐹4√𝛾𝑉𝑠𝑖𝑛𝜑 𝑠

|η|

The evolution is adiabatic if the relative variation of the synchrotron frequency in one synchrotron period is small :

V

∆ 𝑡

∆𝐸

This conditions sets also some limits to the shape change ratio of the bucket :


Plan



• Limitations

• Beam synchronous transfer timing• Applications




Signal synchronisation

• Re-synchronisation: one machine should synchronise on the second one or both machines must synchronise on an external clock. In both case the reference signal must be re-synchronised.

• Possibility to wait for a confirmation signal after both machines are perfectly synchronised and phased.

• The master machine or the master timing sends the extraction pre-pulse.• The different extraction, injection and instrumentation pulses are timed, taking

into account the different hardware delays (kickers, pick-ups…)

ControlTarget

machineSource

machine

Shared timing


Plan



• Limitations• Beam synchronous transfer timing

• Applications• Booster – PS and LEIR – PS • PS – SPS• SPS – LHC



Booster – PS and LEIR – PS

In both cases the PS imposes a relative narrow RF-frequency range which is suitable for the transfer. The source-machine must tune its revolution frequency on the PS revolution frequency (with respect of the harmonic number).

Transfer PSB – PS protons:

• GeV• GeV/c• kHz• kHz• G• G

Since the fluctuations of the B-field are not taken into account anymore during the synchronisation process, the frequency matching must be corrected by observing the bunch’s drift at fixed external revolution frequency:• and are evaluated• The B-field is adapted in the target machine

• The B-field is adapted in the source machine


LEIR – PS rephasing

Figure: Measured synchronisation phase for different correctors. Plot (a): second-order PD2 only. Plot (b): third order corrector PID2 obtained by cascading a first-order PI and a second-order PD correctors. Data are acquired every 37.5 μs.PSB Tests 2008, M.E. Angoletta


PS – SPS (1)

Transfer for protons :

𝐶𝑆𝑃𝑆

𝐶𝑃𝑆 =11 𝑓 𝑅𝐹𝑆𝑃𝑆= 𝑓 𝑅𝐹

𝑃𝑆→𝐶𝑆𝑃𝑆 h𝑃𝑆

𝐶𝑃𝑆h𝑆𝑃𝑆=1

h𝑆𝑃𝑆=11h𝑃𝑆

h𝑆𝑃𝑆=4620

h𝑃𝑆=420

Transfer for Pb ions:

200.264545 MHz at 26 GeV

25 ns bunch spacing

h𝑆𝑃𝑆=4653

h𝑃𝑆=423

199.926 MHz at 5.1 GeV/u

100 or 200 ns bunch spacing

199.948 MHz at 14 GeV


PS – SPS (2)

PEX.W10

PEX.SSYNC

PEX.SSYNC2

PEX.MW8RF

TFID

TREV

TREV

TRF

TFID TREV

TREV TRF


PS – SPS (3)

𝑓 𝑐

Pre-pulse PS

Warning PS

Kicker PS

Kicker SPS

Master timingPEX.W10

Sync Sync2

2 ms

8 ms

PEX.WSPS


PS – SPS rephasing

Figure: PS-SPS synchronisation (phase advance in yellow)Heiko Damerau

Extraction


SPS – LHC (1)

Transfer for protons :

𝐶𝐿𝐻𝐶

𝐶𝑆𝑃𝑆 =277

𝑓 𝑅𝐹𝐿𝐻𝐶

2= 𝑓 𝑅𝐹

𝑠𝑃𝑆→𝐶𝐿𝐻𝐶h𝑆𝑃𝑆

𝐶𝑆𝑃𝑆h𝐿𝐻𝐶=2 h𝐿𝐻𝐶=2

277h𝑆𝑃𝑆

Bunch compressed to 1.7 ns2100 bunches with 25 ns bunch spacing

Transfer for ions:

MHz,

Bunch compressed to 1.2 ns358 bunches with 200 ns bunch spacing

MHz at 450 GeV/c T 4620 35640


SPS – LHC (2)

𝑓 𝑐

Pre-pulse SPS

Extraction SPS

Injection LHC BT

Injection LHC BI

~90 ms

~990 ms

SEX.F-W20

17 ms

60000 300 s

376222

7

2


SPS – LHC rephasing

Ph

ase

ad

van

ce

Figure: SPS-LHC synchronisationThomas Bohl

LHC

SPS

Periodicity of 1 turn LHC turns SPS

at most turn rephasing ms beating


Plan







Remaining issues

• Each synchronization scheme is designed to fit in the machine and energy requirements according to the type of the accelerated particles.

• Since the batch matching starts only after acceleration, significant time is lost during this procedure on the flat top.

• Some schemes are being considered to start the synchronization during acceleration.

• Synchronising more than two machines according to eventually different reference frequencies can be challenging


Acknowledgement

Thank you for your attention

This short study has been led over four quite intensive weeks at CERN. Many aspects of the bunch-to-bucket transfer however remain to be discussed and investigated before a reliable time-efficient scheme might be plotted. For their helpful pieces of advise and their kindness I want to thank : Maria Elena Angoletta, Philippe Baudrenghien, Thomas Bohl, Elena ChapochnikovaHeiko Damerau, Harald Klingbeil,

To be continued…


Sources

• DSP Software Implementation, Dr. H. Klingbeil, GSI documentation, Version 41, 04.01.2012.

• Modellierung des Regelungs- und Steuerungssystems einer Beschleunigungseinheit für Synchrotrons, U. Hartel, TU-Darmstadt, Diplomarbeit, 02.05.2011.

• Main Technical Parameters of SIS100, N. Pika, GSI, 2010.

• The white rabbit project, J. Serrano, P. Alvarez, M. Cattin, E. Garcia Cota, J. Lewis, P. Moreira, T. Wlostowski, G. Gaderer, P. Loschmidt, J. Dedi\v{c}, R. Bär, T. Fleck, M. Kreider, C. Prados, S. Rauch, CERN, Cosylab, GSI, 2009.

• Entwurf und Implementierung eines digitalen Phasen- und Amplitudendetektors für eine HF-Beschleunigerkaviät,Tobias Wollmann, TU- Darmstadt, Diplomarbeit, 2009.

• Time Optimal Synchronisation Procedure and Design of Associated Feedback Loops, F. Pedersen, M.E. Angoletta, CERN, 2008.

• Rephasing SPS-LHC,P. Baudrenghien, A. Butterworth, F. Dubouchet, A. Pashnin, J. Noirjean, R. Olsen,CERN, 2008.

• Rephasing,P. Baudrenghien, CERN, 2007.

• Synthesizer Controlled Beam Transfer from the AGS to RHIC,J. DeLong, J. M. Brennan, W. Fischer, T. Hayes, K. Smith, S. Valentino, Brookhaven National Laboratory, Upton N.Y. 11973, 2001.

• Vorschlag eines Beschleunigungsschemas für die Maschinen SIS12/18 und SIS100 bei GSI, H. Damerau, M. Emmerling, P. Hülsmann, GSI, 2001.

• A Straightforward Procedure to Achieve Energy Matching Between PSB and PS, M. Benedikt, H. Damerau, S. Hancock, CERN, 2000.

• Beam Control for Protons and Ions, P. Baudrenghien, CERN, 1999.

• SPS Beams for LHC: RF Beam Control to Minimize Rephasing in the SPS, P. Baudrenghien, T. Linnecar, D. Stellfeld, U. Wehrle, CERN, 1998.

• Proposal to Transfer 8 SPS Bunches into 8 LEP Buckets,P. Baudrenghien, E. Brouzet, D. Boussard, T. Linnecar,CERN, 1991.

• Synchronisation RF CPS-SPS-LEP. Méthode et Contrôle dans le SPS,P. Baudrenghien, C. Despas, CERN, 1989.

• Matching the Energies of the CPS and SPS MachinesR.J. Lauckner, CERN, 1988.

•SIS Parameter List,B. Franczak, GSI, 1987.


Existing bunch-to-bucket transfer schemes

Synchronisation solutions for accelerator facilities

march 20 th 2014 | tu darmstadt | fachbereich 18 | institut theorie elektromagnetischer felder |...

Documents

tu darmstadt fachbereich

gsi cern introduction

gsi cern introduction

gsi cern batch synchronization

gsi cern energy matching

gsi cern existing bunch

leir ps ps sps sps lhc

bucket transfer bunch