Beam Dynamics Studies in Recirculating Machines · 2018. 11. 19. · Introduction PLACET2 CTF3 LHeC...

Introduction PLACET2 CTF3 LHeC Conclusion

Beam Dynamics Studiesin Recirculating MachinesPresentation for the Final Oral Exam

Dario Pellegrini (CERN, EPFL)

Will take place at Lausanne on 29 Feb 2016

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A Multi-turn Energy Recovery Linac

Up to 5000 bunches circulate inthe LHeC, total current up to150mA in the Linacs!

• New bunches are continuously injected and spent bunches are continuouslydumped,

• In the linacs bunches at different turn numbers and energies are interleaved.

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The CLIC Drive Beam ComplexRecombines trains of bunches to power the 1.5 TeV main linacs

244 ns244 ns

244 ns

244 ns

24 pulses folded 24 times - 100 A - 12 GHz Bunches

Each pulse is directed to one of the 24 decelerators

24 pulses folded 8 times - 25 A

24 pulses folded 2 times - 8 A 24 sub-pulses to be folded 24 times, 4 A

0.5 GHz Bunches, 142 μs train length

488 ns

1464 ns

5856 ns

Drive Beam Linac - 2.4 GV - Fully Loaded Operation

Delay Loop

1st Combiner Ring

2nd Combiner Ring

Decelerators and Power Transfer

Main Linac

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What do they have in common?

Beam

Recirculation

Not RingsNot Linacs

Complexlattice

topologies

Unfixedtime structureof the beam

Highbeam

currents

Collective andmulti-bunch

effects

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Outline

Tool creation:PLACET2

Motivation,Capabilities,Concepts.

Validation:CTF3

Past andOriginal

Measures.

Application:LHeC

Design,Simulations,

Improvements.

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Outline

Tool creation:PLACET2

Motivation,Capabilities,Concepts.

Validation:CTF3

Past andOriginal

Measures.

Application:LHeC

Design,Simulations,

Improvements.

Doctoral Objectives (from the candidacy proposal)

• [...] development of a computer code which allows for a straightforwarddescription of complex machine topologies and automated tracking ofparticles following the foreseen operation scheme [...];

• [...] should be validated through experimental data. CTF3 offers a possibilityto achieve this [...];

• [...] test cases could be taken into consideration: CLIC drive beam complex,CTF3, LHeC and LHeC Test Facility.

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The Tool: PLACET2


PLACET2Why a code designed to handle such machines?

Compute multi-bunch effects with a dynamic structure of the bunch train:

• Long Range Wakefields - Higher Order Modes,

• ion/electron clouds.

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...on top of a full 6D tracking with many single particle/single bunch effects:

• Incoherent and Coherent Synchrotron Radiation,

• Short Range Wakefields and Impedances,

• Beam-Beam.

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...on top of a full 6D tracking with many single particle/single bunch effects:

• Incoherent and Coherent Synchrotron Radiation,

• Short Range Wakefields and Impedances,

• Beam-Beam.

Additional objectives of the design:

• Clearer and easy-to-maintain scripts (no multiple definition of the sameelement, lattice unrolling, ...),

• Alignment and timing errors are correctly applied and propagated to thewhole machine in a transparent way,

• Can do global optimisations taking into account the whole beam.

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Operation of PLACET2

• Definition of one or more injectors:• create and store bunches for tracking,• define the initial beam structure.

• Definition of one or more beamlines:• standard, simple sequences of components,• include "beam instrumentation",• equip the elements with the required physics effects,

• Definition of one or more dumps:• delete the bunches, freeing the memory,• provide additional instrumentation.

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• Connect together injectors, beamlines and dumps to create a machine:• complete description of the accelerator,• possible to adjust/edit properties after the previous definitions.

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• Connect together injectors, beamlines and dumps to create a machine:• complete description of the accelerator,• possible to adjust/edit properties after the previous definitions.

• Run the machine to obtain beam data!

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Machine operation and Synchronisation

• The machine owns global timer used for synchronisation → increases at smallsteps;

• Each bunch owns an internal timer → increases as bunch travels through thickelements;

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• Bunches travel straight down beamlines, their timer can be greatly increased,

• but are forced to wait at the subsequent joints until the global timer exceedstheir internal one.

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• Bunches travel straight down beamlines, their timer can be greatly increased,

• but are forced to wait at the subsequent joints until the global timer exceedstheir internal one.

• Global timer steps smaller than shortest beamline ⇒ bunch order is preserved;

• Elements always see bunches in the correct time sequence ⇒ element time isthe being-tracked-bunch time.

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Validation: CTF3


CTF3 RF deflectors

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CTF3 RF deflectors

• RF deflector are used toinject in the CR.

• Multiple pulses are mergedin four turns.

• Bunches at different turnssee different RF phases.

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The Combiner Ring Lattice

Wiggler

Extraction Kicker

beam energy 150 MeVring length ∼ 84 m

pulse length 140 ns ≈ 42 mbunch frequency 3 to 15 GHz

bunch charge 2.33 nCpulse current up to ∼ 30 A

norm emittance 150 µmenergy spread 0.5%bunch length 5mm

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Four turns Orbit and DispersionDispersion and centroid position are collected in the same way across multipleturns, with automatic handling of time dependencies:

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Wakefields in the CTF3 RF deflectors

During the commissioning of the combiner ring, an unforeseen vertical instabilityappeared, limiting the operability to short trains and low charge.

A circulating (not recombined)beam of 400 bunches issubjected to heavy losses due tothe excitation of the trappedvertical mode:

Frequency 3.0443 GHzImpedance 1.6 MΩQ-value 11500

The circulating beam establishes afeedback whose sign depends on:

• Betatron phase advance,

• Mode Frequency,

• Time of flight.

Defl 1Defl 2

φ12

φ21Inj

Extr

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Vertical Instability @ CTF3 Combiner Ring

A dedicated tracking code waswritten by D. Alesini to simulatethe excitation1, it takes optics pa-rameters (beta, phase advance,...) as input, while PLACET2uses the full model of the com-biner ring.

Track 400 bunches with 2 mm ini-tial offset for 4 turns. Look at theaverage action of the out comingtrain.

Defl 1Defl 2

φ12

φ21Inj

Extr

Published by Alesini:

PLACET2:

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1D. Alesini et al. Physical Review ST 14 022001, 201113/26


Beam-based length measurement @ CTF3 CR• The combiner ring adopts RF-injection to combine multiple trains of bunches

in a single one with higher bunch frequency.

• The regularity of the recombined train influences the effectiveness of thedeceleration.

• The fractional length of the combiner ring determines the final trainstructure.

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• A wiggler allows to control the length increasing it, cannot make a ringshorter.

• In a previous run the optics was slightly detuned to reduce the length of thering.

• Achieved empirically by simultaneously adjusting:• dipole strengths,• quadrupole strengths.

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• A wiggler allows to control the length increasing it, cannot make a ringshorter.

• In a previous run the optics was slightly detuned to reduce the length of thering.

• Achieved empirically by simultaneously adjusting:• dipole strengths,• quadrupole strengths.

• Wanted to have a systematic investigation:• Experimental activity: operation of the phase monitor, data acquisition and

analysis, control room experience,• Better understanding of the machine, benefiting the operation,• Experimental evidences supporting the results from PLACET2.

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PLACET2 simulation of optics detuning

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Non-linear profile:contributions fromparticle losses.


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Extracting the length with a Phase Monitor• The phase monitor BPR multiplies the signal coming from a button BPM for

an internal sine signal, fref = 3 GHz.

• Turn after turn the phase slippage at 3 GHz becomes evident.

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• Apply an FFT to the BPR signal: the revolution frequency splits into twosidebands

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• Apply an FFT to the BPR signal: the revolution frequency splits into twosidebands

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• The fractional length is directly obtained from the sidebands distance, ds ,knowing the revolution frequency, frev :

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Beam-based length measurement @ CTF3 CR

Reconstructed from thereal phase monitor:

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Phase monitor signalsynthetized with PLACET2:

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• Both are processed with the same signal analysis algorithms.

• Demonstrated the possibility to make the ring shorter.

• The vanishing T566 was investigated with all the available resources, aftermany efforts it was decided to stop.

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Application: LHeC


The Large Hadron Electron Collider60 GeV multi-turn energy recovery linac

Recombiner 38m

+ Matching 20m

Linac2 1008m IP Line 196m

Bypass

Linac1 1008m RF Compensation

+ Doglegs

+ Matching 120m

RF Compensation

+ Doglegs

+ Matching 96m

Spreader 38m

Spreader 38m Recombiner 38m

Arc1,3,5 3142m Arc2,4,6 3142m

Dump

Injector

Injection energy: 300 to 500MeV Maximum energy: 60GeVNormalized emittance: <50 µm Bunch Length: 0.6 mm

Average current: 25 (×6) mA Bunch spacing: 25 (/6) nsRF frequency: 801.58 MHz Duty Factor: CW

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LHeC End-to-end Optics

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Notable: the energy loss due to synchrotron radiation in Arc 6, the different average β in the arcs,the recovery of the mismatch generated in the linacs.

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Longitudinal Phase Space at DumpOptics only:

Non perfect isochronicity together with the RF curvature.

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Longitudinal Phase Space at DumpShort Range Wake Fields:

Lower energy in the rail, higher in the head.

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Longitudinal Phase Space at DumpShort Range Wake Fields + Synchrotron Radiation:

The energy spread from quantum excitation masks optics and wakes!

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Transverse Plane at DumpSynchrotron Radiation and Beam-Beam

Iris radius of the cavity > 50 mm.

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Long Range Wakefields in the LHeC

• Fill the machine with perfectly centred bunches,

• Inject a bunch with some offset,

• Keep injecting perfect bunches and see how they are perturbed.

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Proposed design improvements• Superconducting linacs → possibility to enhance the focussing → better

stability, lower injection energy.

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stability, lower injection energy.• Recirculating arcs → combined function lattice → less radiation, less bunch

lengthening, potential transport of different energies in the same pipe.

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lengthening, potential transport of different energies in the same pipe.• Spreaders/Recombiners → proposed a new design aimed at containing the

radiation and reducing β.

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LHeC Spreader

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lengthening, potential transport of different energies in the same pipe.• Spreaders/Recombiners → proposed a new design aimed at containing the

radiation and reducing β.• Detector bypass → Designed from scratch.

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Proposed design improvements

• Superconducting linacs → possibility to enhance the focussing → betterstability, lower injection energy.

• Recirculating arcs → combined function lattice → less radiation, less bunchlengthening, potential transport of different energies in the same pipe.

• Spreaders/Recombiners → proposed a new design aimed at containing theradiation and reducing β.

• Detector bypass → Designed from scratch.

• Compensating RF → Definition of a preliminary set of parameters.

Frequency 1604 MHzGradient 30 MV/mDesign 9 cellsCells length 841 mmStructure length <1 mCavity per cryomodule 6Cryomodule length ∼6 mCryomodule voltage 150 MV

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Proposed design improvements

• Superconducting linacs → possibility to enhance the focussing → betterstability, lower injection energy.

• Recirculating arcs → combined function lattice → less radiation, less bunchlengthening, potential transport of different energies in the same pipe.

• Spreaders/Recombiners → proposed a new design aimed at containing theradiation and reducing β.

• Detector bypass → Designed from scratch.

• Compensating RF → Definition of a preliminary set of parameters.

• Path length adjusting → cannot be done with chicanes at high energy →distribute the perturbation over the whole arc with orbit oscillations.

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Summary

• When it comes to beam recirculation the machine zoology is variegated

• ...but many issues and beam effects are shared among different designs.

• PLACET2 was created as an evolution of PLACET to setup beam dynamicssimulations in recirculating lattices.

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Summary




• A setup to measure the length of the CTF3 Combiner Ring was put in place,the possibility to make it shorter by means of optics detuning was assessed.

• The multibunch instability originating from the initial design of the RFdeflector was reproduced in simulation.

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Summary




• A setup to measure the length of the CTF3 Combiner Ring was put in place,the possibility to make it shorter by means of optics detuning was assessed.

• The multibunch instability originating from the initial design of the RFdeflector was reproduced in simulation.

• The first end-to-end tracking simulation, including realistic multi-bunchtracking, was performed.

• The feasibility of the LHeC has been assessed and its design improved:• Good beam quality at IP;• Can transport the beam to the dump and possibly reduce the injection/dump

energy;• The LHeC Higgs Factory parameters look safe for BBU even with the

beam-beam amplification.

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Outlook

There exists an ongoing effort to train people and diffuse the code into thecommunity (conferences and workshop). Receive external suggestions andcontributions so that it may become the only maintained version of the PLACETcode.Concrete examples of follow-ups (subjected to the availability of resources):

• PLACET2 is now being used to model the CLIC drive beam → the firstsimulation tacking into account beam recombination is in progress.

• Sharpening the LHeC simulation, adding the ion-cloud and studying itscoupling with wakefields and beam-beam.

• Envisage simplecticity to use it for LHC / FCC simulations → potential toexploit the native multi-bunch tracking to investigate long range interactionsand pacman bunches.

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Publications and Contributions List2016 “Status of PLACET2”, Invited Talk at CLIC Workshop

2015 “Beam Dynamics Driven Design of the LHeC Energy Recovery Linac” , D. Pellegrini, A. Bo-gacz, A. Latina, D. Schulte, Phys. Rev. ST Accel. Beams 18, 121004 (2015).”Development of an ERL based TeV energy ep and eA Collider at CERN”, O. Brüning etal., ICFA Beam Dynamics Newsletter No. 68.“CERN ERL Facility CDR”, many authors, to be published“Progress on the Large Hadron electron Collider”, O. Brüning et al., EPS-HEP2015 Vi-enna, Austria.“Single and Multi-bunch End-to-end Tracking in the LHeC”, D. Pellegrini, A. Bogacz,A. Latina, D. Schulte, IPAC’15, Richmond VA, USA, MOPJE066“Applications of PLACET2 to the CTF3 Combiner Ring”, D. Pellegrini, D. Gamba,A. Latina, R. Corsini, IPAC’15, Richmond VA, USA, MOPJE067“PLACET2: A Novel Code for Beam Dynamics in Recirculating Machines”, D. Pellegrini,A. Latina, D. Schulte, IPAC’15, Richmond VA, USA, MOPJE068“Multi-bunch Tracking in Recirculating Machines”, Invited Seminar at JLab“Wake field effects in LHeC ERL”, Invited Talk at LHeC Workshop“CERN SC RF and ERL Test Facility Plans”, Plenary Talk at ERL’15, substituting A. Val-loni“LHeC ERL Design and Beam-Dynamics Issues”, Invited Talk at ERL’15, shared withA. Bogacz“Recirculation in PLACET and measurements at CTF3”, Invited Talk at CLIC Workshop

2014 “The LHeC project”, Invited Talk at POETIC V Workshop at Yale University“Introduction to simulations of recirculating machines such as the CLIC Drive Beam Com-plex and CTF3”, Invited Talk at CLIC Workshop“Multi-bunch wakefield effects”, Invited Talk at LHeC Workshop

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Backup Slides

One turn Beta Functions in the CROptics parameters are collected following a test bunch along its path in themachine. Good agreement with MAD-X computation.

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BPR Signal Analysis• Apply FFT to the signals;

• Fit the background;

• Find and fit the peaks;

• Reconstruct the sidebands;

• Compute the length averaging overthe available sidebands.

Apply the same algorithm also to BPRsignal synthetized by PLACET2.

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Losses• Without any counter measure the scaling of the optic pushes part of the

beam outside the momentum acceptance, creating losses;

• The average energy of the beam is modified, affecting the measure.

• Size of the CR vacuum chamber at dispersive locations: 90 × 37 mm;

• The simulation does not include misalignments/orbit errors ⇒ aperture:50 × 37 mm.

• All the simulated data is taken after 10 turns (allows losses stabilisation).

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Energy and Betatron Losses

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Fitting the loss profile

Losses are particularly sensitive to:

• aperture at dispersive locations,

• position of injection and extraction septa;

• beam orbit (residual at injection and coming from misalignments),

• energy spread.

Hard to find perfect agreementover a wide range of machineconfigurations.

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The effect of the wigglerA scan of the wiggler allows to verify that the measure and the analysis areworking:

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m]

Wiggler Current [A]

• The new measurement (left) is in good agreement with the one made duringthe commissioning (right)

• Several years of drifting;• Machine realignments.

32/26

Interaction Region

Good results recentlyachieved, still some opendiscussion on parametersoptimization.

• One proton beam is even more focussed than in Atlas/CMS → need tocontrol aberrations,

• The electron beam goes across the Q1 → delicate magnet design with avanishing-field region.

• Detector integrated dipoles for head-on collisions → parasitic interactions arenegligible (36σp separation at the first encounter).

33/26

Beam at the IPHiggs Factory Parameters - L = 1034

Injection/Dump Energy 500MeVBunch Spacing 25 ns

Particles per bunch 4 × 109 = 640 pCNormalised RMS Emittance 50µm

IP β function 0.032 m

Longitudinal phase space at IP

initial/CDR IPεx [µm] 50 57.4εy [µm] 50 50.8

δ 0.0020 0.0026RMS x [µm] 7.20 7.66RMS y [µm] 7.20 7.21RMS z [mm] 0.600 0.601RMS e [MeV] - 15.4

The beam at the IP maintains a very good quality (still need to verifyimperfections and stability).

34/26

Modeling of Short-Range Wake Fields

1 Wake Function:• Tells the electric potential felt by a test charge following an exciting charge at

a given distance;• Depends on the cavity geometry;• Can be computed numerically, but analytical approximations exist2.

WL(s) =Z0c

πa2exp

(√

s

s00

)

,

WT (s) =4Z0cs00

πa4

[

1+

−

(

1 +

√

s

s00

)

exp

√

s

s00

]

.

2K. Bane, SLAC-PUB-9663, 200335/26




WL(s) =Z0c

πa2exp

(√

s

s00

)

,

WT (s) =4Z0cs00

πa4

[

1+

−

(

1 +

√

s

s00

)

exp

√

s

s00

]

.

2 Total potential obtained convoluting the wake function with the actualcharge distribution:

• Bunch slicing in the longitudinal direction;• Speed up by applying the FFT;

2K. Bane, SLAC-PUB-9663, 200335/26




WL(s) =Z0c

πa2exp

(√

s

s00

)

,

WT (s) =4Z0cs00

πa4

[

1+

−

(

1 +

√

s

s00

)

exp

√

s

s00

]

.

2 Total potential obtained convoluting the wake function with the actualcharge distribution:

• Bunch slicing in the longitudinal direction;• Speed up by applying the FFT;

3 Kick the particles in the bunch.

2K. Bane, SLAC-PUB-9663, 200335/26

Origin of Long-Range Wake FieldsFrom the ERLF cavity design3

10-2

10-1

100

101

102

103

0 0.802 1.604 2.406 3.208 4.01 4.812 5.614

Tra

nsvers

e Im

p [kΩ

/m]

Frequency [GHz]

Transverse Impedancever 1

ver 2

• Some modes can have big Q value and slow damping;

• Dipole modes are particularly strong and easy excited by orbit displacements;

• With many bunches, modes can build up leading to Beam Break Up.

3R. Calaga, CERN-ACC-NOTE-2015-015, 201536/26

Modeling of Long-Range Wake Fields

The status of a mode is represented with a complex numbers: z = ρe iθ

V

V

ρθ

37/26



• Time evolution: z(t + dt) = z(t) exp

(

− ω

2Qdt

)

︸︷︷︸

damping

exp

(

iωdt

)

︸︷︷︸

rotation

V

V

ρθ

37/26




(

− ω

2Qdt

)

︸︷︷︸

damping

exp

(

iωdt

)

︸︷︷︸

rotation

• Bunch → mode interaction:

ℑ(z) = ℑ(z0) + Ne ALcav δx

V

V

ρθ

37/26




(

− ω

2Qdt

)

︸︷︷︸

damping

exp

(

iωdt

)

︸︷︷︸

rotation



• Mode → bunch interaction (kick):

x′ = x

′

0 +e ℜ(z)γme c2

Iterated over all the HOMs of the cavity.

V

V

ρθ

37/26




(

− ω

2Qdt

)

︸︷︷︸

damping

exp

(

iωdt

)

︸︷︷︸

rotation



• Mode → bunch interaction (kick):

x′ = x

′

0 +e ℜ(z)γme c2

Iterated over all the HOMs of the cavity.

In single-pass, single-cavity,single-mode ERLs can estimatethe threshold current:

Ith =2c2

eRω

1

T12 sin(ωt)

V

V

ρθ

37/26

Detuning of the cavities• Small imperfection in the manufacturing of the cavities leads to slightly

different frequencies for the HOMs;• The same modes in different cavities decohere and their effect can be

mitigated;• The frequencies of the HOMs of the cavities are picked from a Gaussian

distribution with: σ = δf /f = det.

1e-10

1e-08

1e-06

0.0001

0.01

1

100

10000

0 0.5 1 1.5 2

Am

plit

ud

e

time [ms]

Detuning

det = 1e-3det = 0

38/26

Impact of Detuning• 351 machines with a detuning factor of 1 ‰ have been simulated.

• The distribution of the slopes of the amplitudes is shown:

slopes0

Entries 351Mean -4413RMS 496.3

Slope-6000 -5000 -4000 -3000 -2000 -1000 0

Counts

0

10

20

30

40

50

slopes0

Entries 351Mean -4413RMS 496.3

No Detuning

39/26

Recombination Pattern

Multi-bunch effects are enhanced by the value of:∫

linacs

β

Eds → low energy particles are more susceptible.

The filling of the RF buckets of the LHeC can be controlled tuning the lengths ofthe arcs → maximise the separation between the bunches at first and sixth turn.

t

1 120 λ ≈ 25 ns

40/26



linacs

β



t

1 127 λ

36 λ 7 λ

40/26



linacs

β



t

1 127 λ

36 λ 7 λ

4

40/26



linacs

β



t

1 127 λ

36 λ 7 λ

4 5 6

• Pattern 162435 is bad!

40/26



linacs

β



t

1 127 λ

36 λ 7 λ

4


40/26



linacs

β



t

1 127 λ

36 λ 7 λ

45 6


• Pattern 152634 is better!

40/26

Pattern and Long Range WakefieldsThe pattern has an influence on the threshold current

1e-10

1e-08

1e-06

0.0001

0.01

1

100

10000

0 0.5 1 1.5 2

Am

plit

ude

time [ms]

Bad Pattern (no detuning)

162435152634

41/26

Phase Advance in the IP line (I)

Transport of the beam from the end of Linac 2 to the IP is done with the matrix:

√βIP

βL(cosψ + αL sinψ)

√βIPβL sinψ

αL−αIP√βIPβL

cosψ − 1+αIPαL√βIPβL

sinψ√

βL

βIP(cosψ − αIP sinψ)

And similar to go back into Arc 6.

• The phase advance ψ does not affect the shape of the beam

• ...but it determines how the centroid offset and angle mix together.

• A scan of this parameter has been done.

42/26

Phase Advance in the IP line (II)

-5500

-5000

-4500

-4000

-3500

-3000

0 20 40 60 80 100 120 140 160 180

Slo

pe

[a

.u]

Phase advance [deg]

Phase advance Scan

43/26

Phase Advance in the IP line (II)

-5500

-5000

-4500

-4000

-3500

-3000

0 20 40 60 80 100 120 140 160 180

Slo

pe

[a

.u]

Phase advance [deg]

Phase advance Scan

1e-10

1e-08

1e-06

0.0001

0.01

1

100

10000

0 0.5 1 1.5 2

Am

plit

ud

e

time [ms]

Phase advance effect

phase = 100´°det = 160´°

43/26

Powerful Energy Recovery Linac ExperimentsPreviously known as LHeC Test Facility

Designed as a proof of concept of the LHeC technology:

• Multi-turn recirculation with energy recovery;

• High gradient, CW, SC RF.

Performed studies:

• End-to-end tracking;

• Optimization of the recombination pattern;

• Estimation of the BBU Threshold current.

44/26

PERLE End-to-end Optics

0

20

40

60

80

100

120

140

160

180

200

0 50 100 150 200 250 300 350 400 450 500 550 0

100

200

300

400

500

600

700

800

900

1000

Beta

[m

]

Energ

y [

MeV

]

s [m]

energybetaxbetay

45/26

BBU threshold current @ PERLE

• Track many bunches composed by many particles (including energy spread);

• The seeding of HOMs comes from stochastic oscillations of the bunchcentroid;

• Look at all the modes into one cavity (much faster response).

A mode starts to build up for a bunch charge more than five time higher than theforeseen.

46/26

Beam Dynamics Studies in Recirculating Machines · 2018. 11. 19. · Introduction PLACET2 CTF3 LHeC...

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Transcript of Beam Dynamics Studies in Recirculating Machines · 2018. 11. 19. · Introduction PLACET2 CTF3 LHeC...