font collaboration p burrows, g christian, c clarke, c swinson, h dabiri khah, g white, s molloy

March 2006March 2006

The International Linear Collider at the IP The International Linear Collider at the IP – from feedback hardware to – from feedback hardware to electromagnetic backgroundselectromagnetic backgrounds

FONT collaboration

P Burrows, G Christian, C Clarke, C Swinson,

H Dabiri Khah, G White, S Molloy

Tony Hartin


OutlineOutline HardwareHardware

Ground motion and the need for stablisationGround motion and the need for stablisation IP feedback and the FONT projectIP feedback and the FONT project FONT results and BPM sensitivityFONT results and BPM sensitivity

SimulationSimulation Modification of GEANT for low energy transportModification of GEANT for low energy transport 20 mrad crossing angle with different sets of accelerator 20 mrad crossing angle with different sets of accelerator parametersparameters Origin of BPM sprayOrigin of BPM spray Variation with Solenoid and DiD magnetic field Variation with Solenoid and DiD magnetic field

TheoryTheory The background generators: GUINEA-PIG and CAINThe background generators: GUINEA-PIG and CAIN New, non-linear sources of e+e- backgrounds at the IPNew, non-linear sources of e+e- backgrounds at the IP


Luminosity Loss at IP due to ground motionLuminosity Loss at IP due to ground motion

• Relative offsets in final Quads due to fast ground motion leads to beam offsets of several y (2.7 nm for ILC 500 GeV).

•Correct using beam-based feedback system near IP or by active mechanical stabilization of Quads or both.


Intra-train Beam-based Feedback Intra-train Beam-based Feedback

Intra-train beam feedback is Intra-train beam feedback is

last line of defence against last line of defence against

relative beam misalignmentrelative beam misalignment

Key components:Key components:

Beam position monitor (BPM)Beam position monitor (BPM)

Signal processorSignal processor

Fast driver amplifier Fast driver amplifier

E.M. kickerE.M. kicker

Fast FB circuitFast FB circuitTESLA TDR: principal IR

beam-misalignment correction


(FONT1 +) FONT2: beamline configuration(FONT1 +) FONT2: beamline configuration

Dipole and kickers

BPMs


FONT2 results: feedback BPM (Jan 04)FONT2 results: feedback BPM (Jan 04)

Feedback on

Beam flattener on

Beam starting positions

Delay loop on

beam start beam end

1 2 3 4

Latency 54ns, correction factor 14/1


BPM noise from backgroundsBPM noise from backgrounds

Noise form factor sinc(Noise form factor sinc(π.f.T)π.f.T)

Secondary emission down to Secondary emission down to 100 eV needs to be considered100 eV needs to be considered

Geant3 minimum transport is 10 Geant3 minimum transport is 10 keV!keV!

Copper strips with 1 mm gap to wallCopper strips with 1 mm gap to wall

Noise from secondary charges crossing strip-wall gapNoise from secondary charges crossing strip-wall gap

~1pm error for each charge absorbed or emitted. 1e6 hits ~1pm error for each charge absorbed or emitted. 1e6 hits per b.c. would be a problem!per b.c. would be a problem!


Geant model of 20mrad designGeant model of 20mrad design

Background primaries are traced through from Background primaries are traced through from

the IPthe IP

Optimal position for the BPM can be Optimal position for the BPM can be

establishedestablished

BPM hits vary with parameter sets, geometry BPM hits vary with parameter sets, geometry

and magnetic fields.and magnetic fields.

BPM

0

10000

20000

30000

40000

50000

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S14n

scheme

hits

2mrad 20mrad 93443


Geant3/4 mod for Low Energy TransportGeant3/4 mod for Low Energy Transport

Geant3 X-section Geant3 X-section parametrization parametrization wrong below wrong below 10kev cut10kev cut

Recode Geant3 Recode Geant3 to parametrize to parametrize real data from real data from NEA siteNEA site


Geant3 total BPM hits and emitted charges Geant3 total BPM hits and emitted charges

LowE mods reveal significant LowE mods reveal significant increase in BPM hits at 100eV increase in BPM hits at 100eV cut. cut.

Generally Factor of 5 increase Generally Factor of 5 increase in BPM compared to default in BPM compared to default Geant cut of 1 MeV, and Geant cut of 1 MeV, and factor of 2 increase against factor of 2 increase against Geant default minimum cutGeant default minimum cut

Can define Geant areas (ROIs) Can define Geant areas (ROIs) around BPMS which are tuned around BPMS which are tuned for Low Energy particlesfor Low Energy particles

Worst case scenario Worst case scenario (scheme14 in the 20mrad (scheme14 in the 20mrad case) ~ 10case) ~ 105 5 hits per strip per bchits per strip per bc

20mrad - Scheme14

0

20000

40000

60000

80000

100000

1MeV 10keV 1keV 100eV 100eV

Geant cuts

Hits


Background Primaries – ILC parameter Sets Background Primaries – ILC parameter Sets High Lumi sets produce the greatest numbers of background pairsHigh Lumi sets produce the greatest numbers of background pairs

Guinea-Pig and Cain include L-L, B-H and B-W processesGuinea-Pig and Cain include L-L, B-H and B-W processes

Beam field is treated linearly i.e. equivalent photon method scaled Beam field is treated linearly i.e. equivalent photon method scaled by the number density of beam field photonsby the number density of beam field photons

BUT.. The beam fields are intense – 10% of Schwinger critical fieldBUT.. The beam fields are intense – 10% of Schwinger critical field

What about non-linear sources of background pairs?What about non-linear sources of background pairs?

High LumiScheme14

Low PScheme13

Large YScheme12

Low QScheme11

NominalScheme10

USSCScheme9

1 TeV TESLA

Scheme 8

High LumiScheme7

Low PScheme6

Large YScheme5

Low QScheme4

NominalScheme3

USSCScheme2

500 GeV TESLA

Scheme 1

0

100000

200000

300000

400000

500000

600000

700000

800000

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S14n

G-P CAIN


Where does BPM spray originate from? (20mrad)Where does BPM spray originate from? (20mrad)

X,Y view at z=3.12mX,Y view at z=3.12m

E+ and E- have different E+ and E- have different trajectoriestrajectories

spray originates from annulus spray originates from annulus around extraction linearound extraction line

B


Relation of E distribution of BPM spray-Relation of E distribution of BPM spray-producing pairs to Solenoid fieldproducing pairs to Solenoid field

Increase in leads to energy Increase in leads to energy

peak shiftingpeak shifting

With stronger magnetic field,With stronger magnetic field,

(a)higher energy pairs, and (a)higher energy pairs, and

(b) pairs with lower transverse (b) pairs with lower transverse

momentum will produce spray on momentum will produce spray on

the mask hole edgethe mask hole edgeEnergy(MeV)

BS


The impact of a Detector Integrated Dipole(20mrad)The impact of a Detector Integrated Dipole(20mrad)(Seryi & Parker, Phys Rev ST Accel Beam (Seryi & Parker, Phys Rev ST Accel Beam 8, 8, 041001 (2005)041001 (2005)

Introduced to offset Y displacement Introduced to offset Y displacement at the IP due to solenoid fieldat the IP due to solenoid field

Steers more primaries into Lumi Steers more primaries into Lumi Cal (K. Busser). Extra BPM spray Cal (K. Busser). Extra BPM spray sourcessources

30% more spray hits delivered to 30% more spray hits delivered to the BPMthe BPM


Is there another non-linear source of pairs at the IP?Is there another non-linear source of pairs at the IP?

KnownKnown: multiphoton pair production : multiphoton pair production

rate described by Sokolov-Ternov and onset rate described by Sokolov-Ternov and onset

governed by beam parameter governed by beam parameter Y=E/EY=E/Ecc~0.3. Scheme1 has Y=0.054, ~0.3. Scheme1 has Y=0.054,

Scheme14 has Y=0.376Scheme14 has Y=0.376

•2nd order process rather than 1st order

•Rules for onset are different

•Calculation is complicated, but simplified when the photons are co-linear

eenkkb

eenkkk bb 21 UnknownUnknown: Multiphoton Breit-Wheeler: Multiphoton Breit-Wheeler

2bk1bk

e- e+


Resonances in multiphoton B-WResonances in multiphoton B-W

Multiphoton Breit-Wheeler Resonances

Multiphoton Bremstrahlung (non-resonant)

Ordinary Breit-Wheeler

)1()( 222 mnkqPairs created in intense e-m field have a quasi-level structure and resonant Pairs created in intense e-m field have a quasi-level structure and resonant transitions can occur (Zeldovich, 1967)transitions can occur (Zeldovich, 1967)

22ndnd order IFQED x-section can exceed normal x-sections by orders of magnitude order IFQED x-section can exceed normal x-sections by orders of magnitude (Oleinik, JETP 25(4) 697, 1967)(Oleinik, JETP 25(4) 697, 1967)

22ndnd order Breit-Wheeler process in CIRCULARLY POLARISED field shows the order Breit-Wheeler process in CIRCULARLY POLARISED field shows the same featuresame feature

hepwww.ph.qmul.ac.uk/~hartin/thesis


Experimental evidence for the IFQED Experimental evidence for the IFQED processesprocesses

1st order: One photon pair productionExperiment E144 SLAC. 46 GeV beam with Nd:glass laser peak intensity 0.5x1018 Wcm-2. Up to 4 photons contributed to each event Meyerhofer et al (1996) other non-linear phenomena such as electron mass shift observed

2bk1bk

e- e+

1bk

e- e+

2nd order: Substantial theoretical studies but no experimental efforts yet!

BUT potentially more detectable because of resonances


The field of the relativistic charge beamsThe field of the relativistic charge beamsWith low disruption, approximate to a constant crossed e-m field perpendicular to direction of propagation

SIMPLIFICATION: Beamsstrahlung photons k1 and k2 emitted forward. Assume they are collinear

COMPLICATION: Symmetry of the field seen by the synchrotron photons

AiJ P,n J0Pt2 cos nt+t3 3 dt Ai n cos nt+t3 3 dt K

1 3


Including the external field in IFQED Including the external field in IFQED calculationscalculations

‘Operator Method’: quantum interaction of electron and external field photons but electron trajectory is considered classical. Due to Baier et al (JETP 28(4) p.807, 1969)

Full quantum treatment: Horrendously complex but potentially doable with Vermaseren’s FORM

‘Semi-classical method’: Dirac equation is solved exactly for interaction with a classical plane-wave e-m field. Most common method. Used originally by Narozhnyii, Nikishov and Ritus in the mid 1960s

Ufi

f eiÏ ‰tMfit dt i


IFQED – Dirac Equation SolutionIFQED – Dirac Equation SolutionExponential dependency on external field 4-potential

Fourier Expansion in contributions of n external field photons

Different external field polarisations lead to different “form factor” functions

Circular polarisation Bessel functions n Jn(Q)

Linear polarisation Generalised Bessel–type functions

Constant crossed field-Azimuthally symmetric Airy functions n Ai(n Q)

Constant crossed field –Nonazimuthally symmetric New ‘AiJ’ functions n AiJn(Q)

exp dÏ † i Ae p i Ae2


Calculation of Resonance widthsCalculation of Resonance widthsThe Electron Self Energy must be included in the Multiphoton Breit-Wheeler process

This is a 2nd order IFQED process in its own right.

Renormalization/Regularization reduces to that of the non-external field case

The Electron Self Energy in external CIRCULARLY POLARISED e-m field originally due to Becker & Mitter 1975 for low field intensity parameter =(ea/m)2. Has been recalculated for general

ESE in external CONSTANT CROSSED field is due to Ritus, 1972

Optical theorem: the imaginary part of the ESE is the same form as the Sokolov-Ternov equations


Where do the resonances occur?Where do the resonances occur?Beamsstrahlung photon ES >> 0.511 MeV

Beam photon EB < 0.511 MeV

Processes which give/take energy to the field allowed and mass shell can be reached for physical values

For collinear beamstrahlung photons, resonance condition is r (external field photons) ~ ES/EB

Resonance Peak Resonance Width


Notes on the cross-section calculationNotes on the cross-section calculation

Full trace contains ~ 100,000 termsFull trace contains ~ 100,000 terms

Dramatically simplified byDramatically simplified by

Special “centre of mass-like” reference frameSpecial “centre of mass-like” reference frame

Assume beamsstrahlung photons and beam field photons Assume beamsstrahlung photons and beam field photons are collinearare collinear

Only insert Imaginary part of self energy to get resonance Only insert Imaginary part of self energy to get resonance widthwidth

k1k

2q q r k 0

And the PRELIMINARY results…..?


Results:Results: Stimulated Breit-Wheeler (Non-Resonant)

Compare Stimulated Breit-Compare Stimulated Breit-Wheeler process with ordinary Wheeler process with ordinary Breit-Wheeler processBreit-Wheeler process

Examine the resonant and non-Examine the resonant and non-resonant contributions to the resonant contributions to the cross-section separatelycross-section separately

Nonresonant Stimulated Breit-Nonresonant Stimulated Breit-Wheeler cross-section only a few Wheeler cross-section only a few percent of the ordinary Breit-percent of the ordinary Breit-Wheeler cross-sectionWheeler cross-section

Can be neglected as a source of Can be neglected as a source of extra pairsextra pairs


Results:Results: Stimulated Breit-Wheeler (Resonant)

Differential cross-section can exceed Differential cross-section can exceed the ordinary Breit-Wheeler processthe ordinary Breit-Wheeler process

Stimulated Breit-Wheeler Cross-Stimulated Breit-Wheeler Cross-section up to 2 orders of magnitude section up to 2 orders of magnitude greater than ordinary breit-wheelergreater than ordinary breit-wheeler

Transverse production of pairs seems Transverse production of pairs seems favouredfavoured

PROVISO – calculation for special reference frame. Need to generalise the case!


Summary and Future WorkSummary and Future WorkFONT project continues with digital version and experiments planned at FONT project continues with digital version and experiments planned at ATF2 (KEK)ATF2 (KEK)

GEANT tweakingGEANT tweaking Modified Geant 3 for low energy transportModified Geant 3 for low energy transport Ran pair files through Geant 3 simulation of BDSRan pair files through Geant 3 simulation of BDS

BPM hits are within a factor of 10 of problem levels. More detailed studies BPM hits are within a factor of 10 of problem levels. More detailed studies are needed. Simulation support for planned ESA testsare needed. Simulation support for planned ESA tests

LowE modification's reveal an increase in hits by a factor of 2 and were LowE modification's reveal an increase in hits by a factor of 2 and were important to take into accountimportant to take into account

22ndnd order, nonlinear interactions of beamsstrahlung photons with order, nonlinear interactions of beamsstrahlung photons with the beam fields should be taken into account because the cross-the beam fields should be taken into account because the cross-sections are potentially resonant and can exceed 1sections are potentially resonant and can exceed 1stst order and order and “linear” ordinary cross-sections – established by substantial “linear” ordinary cross-sections – established by substantial theoretical work by several groupstheoretical work by several groups

Preliminary calculations of the Stimulated Breit-Wheeler process Preliminary calculations of the Stimulated Breit-Wheeler process (simplified case) suggests that this will be an issue at the ILC(simplified case) suggests that this will be an issue at the ILC


3 GeV electrons

Focussed Tabletop TeraWatt Laser

low spec laser

Australian Synchrotron

Experimental detection of Stimulated Breit-Experimental detection of Stimulated Breit-Wheeler resonancesWheeler resonances

font collaboration p burrows, g christian, c clarke, c swinson, h dabiri khah, g white, s molloy

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