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Beam Optics & Dynamics Studies for LHC

Alexander Koschik

ETH Zurich, Integrated Systems Laboratory

(Swiss Federal Institute of Technology Zurich)

SLAC, Aug. 2010

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Master’s degree in physics from University of Technology Graz, Austria.

PhD degree in accelerator physics from CERN (AB-ABP) and TU Graz.Francesco Ruggiero, Bruno Zotter

Fellowship (AB-ABP & AB-BT) at CERN.Helmut Burkhardt, Brennan Goddard

Research assistant at IIS, ETH Zurich.

What am I doing at ETH Zurich?

Simulation of low energy (1 eV – 1 keV) electron beam – matter interaction for SEM critical dimension nanometrology.

Simulation of SEM image formation.

Development of fast CD extraction and surface reconstruction methods from SEM images.

Background Information

Graz●

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Simulation of multi-bunch instabilities

Transverse multi-bunch instabilities, high energy proton beams (LHC)

Beam optics & design

LHC injector complex upgrade, beam optics design PS2 transfer line

Beam dynamics simulation with MAD-X

Abort gap cleaning in the LHC (simulation & benchmark measurementsin the CERN SPS)

Outline – Beam Optics & Dynamics Studies for LHC

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SIMULATION MULTI-BUNCH INSTABILITIESTransverse multi-bunch instabilities, high energy proton beams (LHC)

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PhD title: Simulation of transverse multi-bunch instabilities of proton beams in LHC

Development of a particle tracking code that is able tostudy the stability behavior of the multiple bunches of LHC (2808)model the long-range impedance effects correctly (resistive wall)do the computation sufficiently fast!

Simulating LHC beam stability

Instabilities(Motion of Particles becomes unstable)

Cross section variation and/or finite wall conductivity

Collective Effects(caused by fields acting back on the beam)

LHC (Large Hadron Collider) at CERN

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Simulating beam stability: Wake Summation Problem

Summation of wake field contributions of ~3000 bunches over ~100 turns

For each bunch at each time step:Recomputewake function ofall precedingbunches and allpreceding turns!

Addition + Multiplication in complex plane

Time

Wak

e fu

nctio

n (v

olta

ge)

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Simulating beam stability: Wake Summation Problem

Effect of preceding bunches of preceding turns on current bunch at current turn

Brute force summation results in computation times in the order ofdays/weeks!

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Simulating beam stability: Wake Summation Solution

Discrete FFT Convolution algorithm used to speed up the computation significantly (N2 N log N)

Brings computation times from days/weeks down to hours!

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Simulating beam stability: Impedance/Wake Models

Knowledge of correct impedance model critical for machine performance!

Frequency range interesting for LHC

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Simulating beam stability: Impedance/Wake Models

Classical resistive wall impedance model was found to be an inappropriatedescription for the physical situation in the LHC.

For one new model, which fits well with measurement the corresponding wake function was computed and implemented in the code MTRISIM.

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Simulating beam stability: The code MTRISIM

Classical tracking codeTransfer matrices + non-linear kicks

Rigid bunch approximation

Wake function approximation

Lumped impedance approximationImpedance modelled by 1 kick per turna

Non-circular vacuum chamber geometries: Yokoya factors used!

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Simulating beam stability: LHC Simulations

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Simulating beam stability: LHC Simulations

Non-linearities (octupoles) provide amplitude dependent detuning and stabilize the beam.Important result for stability and performance of the LHC machine!

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Objectivesstudy the stability behavior of the multiple bunches of LHC (2808)model the long-range impedance effects correctly (resistive wall)do the computation sufficiently fast!

Achievements

Efficient implementation of wake summation via discrete FFT convolution algorithm approach (N2 N log N).

Brings computation time from days/weeks down to hours!

Resistive wall impedance models in a new parameter regime, corresponding wake function computed and used in simulation.Code benchmarked with measurements in CERN SPS.Simulation of LHC. Present octupole design will provide enough Landau damping to stabilize beam at top energy.

Follow-up work, latest developmentsFast wake summation algorithm used for CLIC damping ring studies at Cockcroft Institute, Daresbury, UK:K.M.Hock, A.Wolski: „Transient jitter from injection in storage rings“; Phys.Rev. ST-12,091001(2009)MTRISIM recently added to CERN BE-ABP code-pool for thorough re-study of LHC impedance issues (Elias Metral, Benoit Salvant, Nicolas Mounet)

Simulating beam stability: Summary

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BEAM OPTICS & DESIGNLHC injector complex upgrade, beam optics design PS2 transfer line

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Beam optics & design

Several work packages in the context of LHC commissioning preparation (new & proposed) accelerator optics design design & commissioning of beam transfer systems

LHC injection optics (transfer lines TI2, TI8)Dispersion matching knobs LHCSolenoid coupling compensation LHCBeam Commissioning of the SPS LSS6 Extraction and TT60 Beam Commissioning of the SPS-to-LHC Transfer Line TI 2LHC sector test: Magnet quench testPS2 Injection, Extraction and Beam Transfer ConceptsInitial design of the PS2-SPS transfer line

Resonant orbit bumps Localized dispersion wave

Coupling compensation by skew quads

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Beam optics & design

Several work packages in the context of LHC commissioning preparation (new & proposed) accelerator optics design design & commissioning of beam transfer systems

LHC injection optics (transfer lines TI2, TI8)Dispersion matching knobs LHCSolenoid coupling compensation LHCBeam Commissioning of the SPS LSS6 Extraction and TT60 Beam Commissioning of the SPS-to-LHC Transfer Line TI 2LHC sector test: Magnet quench testPS2 Injection, Extraction and Beam Transfer ConceptsInitial design of the PS2-SPS transfer line

Measured horizontal aperture of transfer line TI2

LHC beam steered into MQY magnet for quench testing.

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Beam optics design: PS2 – SPS Transfer Line Design

PS2

SPS

PS2 – SPS transfer line

PS

LINAC4

Design GoalShortest possible transfer line accomplishing

all required features:- Matched optics at both ends (PS2, SPS)- Meet space/geometry requirements- Low β insertion (stripping foil)- Emittance exchange scheme- Switch to experimental area

PS Booster(SPL)

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Beam optics design: PS2 – SPS TL Design Approach

Start from SPS injection optics and calculate Twiss parameters in backward manner through SPS injection region, TT10 and the transfer line

Match optics (β,α,D,D’) at virtual PS2 extraction point.Assumptions extraction point: βx = 6.25 m, βy = 36.0 m, α,D,D’ = 0.0

Get dispersion function D under control! Achromats!

Match space/geometry requirementsTransfer Line defines location of PS2!15m separation between PS2 tunnel and existing tunnels (radiation protection)

Length limits for Transfer Line! MAD-X matching with survey coordinates!

Include: low β insertion for ion stripping (Pb ), emittance exchange scheme, switch to experimental area, …

Beam momentum: 50 GeV/c

Dipole Magnets: l = 3.0 m1.6 T field strength1/ρ = 9.59 mrad/m bending angle

Quadrupole Magnets: l = 1.75 m16 T/m field gradientkmax = 0.0959

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Beam optics design: PS2 – SPS TL Design

Matching section (with low-β insertion) near SPS

2 bending sections (opposite direction) as achromats (D=D’=0 at each end)

Matchingsection

Achromat 1

Achromat 2

PS2 extractionregion

PS2 LSSregular cells

SPS injectionregion αbend = – 320 mrad

αbend = + 160 mrad

Matching section:Used to match SPS to achromat entry conditions

Achromat 1 + Achromat 2:Used to match to PS2 extraction conditions

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Beam optics design: PS2 – SPS TL Design

700 800 900 1000 1100 1200 1300 1400 1500

2200

2300

2400

2500

2600

2700

X [m]

Y [m

]

Survey Plot CCS coordinates

SPS

PS2

TI2

TT10

TT12~21m

~15m

MAD-X optics matching:Achromat dipole strenghtsdefine location of PS2 machine (survey coordinates)

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Beam optics design: PS2 TL Optics β – functions

SPS injection region

Matching section Achromat 1Achromat 2

PS2 extraction region

PS2 LSS regular cells

Low-β

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Beam optics design: PS2 TL Optics Hor. Dispersion

SPS injection region

Matching section Achromat 1 Achromat 2

PS2 extraction region

PS2 LSS regular cells

( )

( )DDJ

DDDJ

D

D

αββ

αβ

+′⋅Θ=Δ

+′+=

2

22dispersion

action

dispersion modifierat bend with angle Θ

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Beam optics design: PS2 TL Emittance Exchange

Possible solution:3 additional cells (2+1 because of asymmetry) with skew quads inbetween the two achromats (because dispersion free there!)

Fits space requirements if injection/extraction areas in PS2 are swapped

Note:Used MAD-X PTC!

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Beam optics design: PS2 TL Design Summary

Objectivesfeasibility study of transfer line connecting PS2 - SPS meet tight space/geometry requirementsLow-β insertion, emittance exchange scheme, …

Achievements

Design goals can be achieved with this initial layout, in particular the tight space and geometry requirements!Optics design using MAD-X (with PTC), plus a lot of experienced/educated guesses!Optics matching with survey coordinates (user defined macro function matching in MAD-X).

Follow-up work, latest developmentsHessler, C; Bartmann, W; Benedikt, M; Goddard, B; Meddahi, M; Uythoven, J: „Transfer Lines to and from PS2“; Proc. of 1st IPAC, Kyoto, Japan, 23 - 28 May 2010, sLHC-PROJECT-Report-0043; CERN-sLHC-PROJECT-Report-0043Hessler, C; Goddard, B; Meddahi, M; „PS2 Transfer Lines“; sLHC Project Note 0013, 2010-02-04CERN management has stopped PS2 project in favor of refurbishing the old PS (Chamonix Meeting 2010).

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BEAM DYNAMICS SIMULATION MAD-X

Abort gap cleaning in the LHC (simulation & benchmark measurements in the CERN SPS)

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Abort Gap Cleaning

LHC beam dump kicker systemfield rise time 3 μs

Particle-free abort gap of 3 μs needed for clean beam dump process

Particles filling abort gap see sweeping kicker field and may be lost at various positions in the machine, possibly causing a magnet quench.

Assuming quench limit of 4 mJ/cm3, maximum abort gap population tolerated at 7 TeV corresponds to 1.7 × 107 p+/bunch (2 × 106 p+/m)

Abort gap population from uncapturedbeam or longitudinal diffusion processes: ~ 3 × 1010 p+/100 ns (450 GeV)~ 3 × 1080 p+/100 ns (7 TeV)

1. E. Shaposhnikova, “Abort Gap Cleaning and the RF System”, LHC Performance Workshop – Chamonix XII, 2003, CERN AB-2003-008, p. 182, Geneva, 2003.2. E. Shaposhnikova, S. Fartoukh, B. Jeanneret, “LHC Abort Gap Filling by Proton Beam”, EPAC 2004.3. E. Shaposhnikova, “Longitudinal motion of uncaptured particles in the LHC at 7 TeV”, LHC Project Note 338, CERN, Geneva, 2004.

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Abort Gap Cleaning – Principle

Tune modulated kicker signal

Resonantly excite increasing transverse particle oscillations

Loose particles on aperture limits (ideally collimators) in controlled way

Particle tunes off from nominal tune due to:ChromaticityNon-linearities (amplitude-dependent tune change)

Tracking studies to investigate cleaning efficiency dependent on non-linear effects. Kick

Kick

Kick in-phase with particle betatron phase

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Motivation: Assess feasibility and performance of LHC abort gap cleaning systemObjective: Benchmark simulation against measurements to gain confidence for LHC

Investigate influence of non-linearities (octupoles) and chromaticity on cleaning speed and efficiency Experiment with different excitation programs (fixed freq., sweep, freq. modulation)

MAD-X full 6D element-by-element tracking with aperture. Additionally: Implementation of time (i.e. turn by turn) varying kicks in MADXSimulation:

Set optics (e.g. nominal SPS optics, LHC beam & working point) and beam parametersVary ξ chromaticityVary k3 octupole strength (simulate non-linearities)Different transverse damper excitation progamsRecord loss rate, integrated loss and loss pattern

Used MADX model: SPS 2007 sequence/strength/aperture set-upσΔp/p = +/- 2.37 x 10-3

central tunes: QH = 26.13QV = 26.18

transverse emittances: εn = 3 μm

σV = 2.96 mm @ TIDV.11892 (β=81 m) @ 26 GeV/c Beam should be mainly lost at TIDV with half gap of 20.4 mm corresponding to 6.9 σ

Abort Gap Cleaning – SPS Simulations with MADX

TIDV

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Abort Gap Cleaning – SPS Simulations with MADX

-20 0 5 10 15 20 40 60 80 1000

1

2

3

4

5Simulation SPS 2007 AbortGapClean 26GeV ξx= 0.02, ξy= 0.03

time [ms]

ΔN

Lost

[%]

Loss Rate

-20 0 5 10 15 20 40 60 80 1000

20

40

60

80

100

time [ms]

NLo

st [%

]

Integrated Losses

Chromaticity low (ξH=0.02, ξV=0.03) Octupoles OFF

Loss time ≈ 5-7 ms (250 turns) Loss time ≈ 25-30 ms (1100 turns)

Full longitudinal motion simulated, i.e. RF on

-20 0 20 40 60 80 1000

0.5

1

1.5

2Simulation SPS 2007 AbortGapClean 26GeV ξx= 0.02, ξy= 0.43

time [ms]

ΔN

Lost

[%]

Loss Rate

-20 0 20 40 60 80 1000

20

40

60

80

100

time [ms]

NLo

st [%

]

Integrated Losses

Chromaticity medium (ξH=0.02, ξV=0.43) Octupoles OFF

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0 200 400 600 800 1000 1200 1400 16000

100

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600Abort gap cleaning MD 2007/11/05 15:05:49.898000 SuperCycle 20180

Time [ms]In

tens

ity [1

08 pro

tons

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Cleaning← Efficiency

97.3%

BCT signal

Abort Gap Cleaning – SPS Measurements

Chromaticity low (ξH=0.02, ξV=0.03), Octupoles offfixed frequency excitation

Loss time ≈ 5 ms (220 turns)

Loss signal BLM @ TIDV SPS.BCTDC.41435

-20 0 20 40 60 80 1000

1

2

3

4

5x 107 Abort gap cleaning MD 2007/11/05 15:05:41

time [ms]

lost

pro

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-20 0 20 40 60 80 100-5

0

5

10

15

20x 108 ΔtLoss = 5.2 ms

inte

grat

ed lo

ss [p

roto

ns]

time [ms]

Raw dataDenoised

Optimized excitation frequency

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100

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600Abort gap cleaning MD 2007/11/05 17:47:40.298000 SuperCycle 20469

Time [ms]In

tens

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08 pro

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Cleaning← Efficiency

95.9%

BCT signal

Abort Gap Cleaning – SPS Measurements

Chromaticity medium (ξH=0.02, ξV=0.43), Octupoles ON: LOF +20.0frequency sweep

Loss time ≈ 20 ms (870 turns)

Loss signal BLM @ TIDV SPS.BCTDC.41435

-20 0 20 40 60 80 1000

2

4

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10

12

14x 106 Abort gap cleaning MD 2007/11/05 17:47:47

time [ms]

lost

pro

tons

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0

5

10

15

20x 108 ΔtLoss = 13.9 ms

inte

grat

ed lo

ss [p

roto

ns]

time [ms]

Raw dataDenoised

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0 10 20 30 40 50 60 70 80 9034

34.2

34.4

34.6

34.8

35

35.2

35.4

35.6

35.8

36

Time - [ms]

Freq

uenc

y - [

kHz]

MD 2007/11/05 - Frequency Program

16:23:1017:55:0118:02:3318:13:2218:15:2618:45:0119:07:2319:12:12

Abort Gap Cleaning – Optimizing frequency programsExcitation conditions:Vertical damper V1 (BDV 214.55) on, V2 (BDV 221.76) off, Amplitude: 2.89 μrad per turnExcitation at 1-qfrac (for better efficiency due to hardware limitations) at t = 1000ms in the cycle.

Programmable arbitrary waveform generator used (Agilent 33250 A). Limitation 65536 points, use of low-pass filter to smooth wave form. Max. ~4000 turns excitation.

The revolution frequency at 26 GeV is 43.347282 kHzexcitation was always at(1-q_frac) x f_rev, i.e. around 35 kHz

Programs used for MD:

Fixed frequencygood for constant tune

Swept frequencytune changes with amplitude

Modulated frequency(FM, modulation depth, modulation freq.) efficient in presence of chromaticity

FM on a carrier that is itself sweptoctupoles + chromaticity

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Chromaticity medium (ξH=0.02, ξV=0.43) Octupoles ON

Simulated and measured loss rates in very good agreementLoss time ≈ 25-30 ms (1100 turns)

-20 0 20 40 60 80 1000

0.5

1

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2Simulation SPS 2007 AbortGapClean 26GeV ξx= 0.02, ξy= 0.43

time [ms]

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Lost

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Loss Rate

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40

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80

100

time [ms]

NLo

st [%

]

Integrated Losses

Abort Gap Cleaning – Summary

Close collaboration with BI and RF group!

ObjectivesTransient simulations using MAD-X tracking, full 6D + time-varying kicksBenchmark measurements in the SPS

AchievementsTool to test & develop best cleaning strategy for the LHC

Follow-up work, latest developments

“LHC Abort Gap Monitoring and Cleaning”; Meddahi, M; Gianfelice-Wendt, E et al.; 1st IPAC, Kyoto, Japan, 23 - 28 May 2010; CERN-ATS-2010-124“LHC Abort Gap Cleaning with the

Transverse Damper”; Gianfelice-Wendt, E; Goddard, B; Höfle, W et al.; PAC 2009, Vancouver, Canada, 04 - 08 May 2009; CERN-ATS-2009-016

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FINAL WRAP-UP

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Final Wrap-up

Simulation of transverse multi-bunch instabilities (LHC)physical modeling, algorithm design, simulation development, beam measurements

Beam optics & design, PS2 transfer line opticslinear optics design, optics matching, MAD-X (PTC),commissioning with beam

Beam tracking with MAD-X (Abort Gap Cleaning)simulation & benchmark measurements

-20 0 20 40 60 80 1000

2

4

6

8

10

12

14x 106 Abort gap cleaning MD 2007/11/05 17:47:47

time [ms]

lost

pro

tons

20x 108 ΔtLoss = 13.9 ms