Performance Study of Pair-monitorPerformance Study of Pair-monitor

2009/06/30Yutaro Sato

Tohoku Univ.

Pair-monitorPair-monitor2

Pair-monitor is a silicon pixel detector to measure the beam profile at IP.

• The distribution of the pair B.G. is used.– The same charges with respect to the

oncoming beam are scattered with large angle.– The scattered particles have information on beam shape.

• The pair-monitor is required to measure the beam size with 10% accuracy.

e-

e+

IPe+ beam

e- beam

Pair-monitor

Distribution of pair B.G.

X [cm]

Y [

cm]

Y [

cm]

X [cm]

1σx (nominal) 2 σx

Tohoku group has developed

– development of the readout ASIC for the pair-monitor.

– the performance study of pair-monitor.

• The combined analysis with BeamCal was performed.

– Pair-monitor is a silicon pixel detector to measure hit counts.

– BeamCal is a calorimeter to measure energy deposit.

• Beam parameters (σx, σy, Δy/σy ) were reconstructed using the matrix

method (second order).

ContentContent3

Offset Δy [nm]e - bunch

e+ bunch

Simulation setupSimulation setup

Simulation setup• CM energy : 500GeV

• Noinal beam size (σx0, σy

0, σz0, ) = ( 639nm, 5.7nm, 300 μm )

• Tools : CAIN (Pair background generator)

Jupiter (Tracking emulator)

• Magnetic field : 3.5 T + anti-DID

• Pair-monitor is located in front of the BeamCal.

• Scattered e+ was studied.

4

LumiCal

BeamCal

BeamCal

Pair-monitor

IP

The beam parameters are reconstructed by the Taylor expansion.

→ The measurement variables were studied.

yy

y

x

yyyx

yy

y

x

n

BA

m

m

m

M

σΔ

σ

σ

σΔσσ

σΔ

σ

σ

/

/,,

/

2

1

Matrix method for reconstructionMatrix method for reconstruction5

MBXAX T

yy

y

x1

/

σΔ

σ

σ

Matrix of the first order term Matrix of the second order termMeasurement variable

Beam parameter (X)

The beam parameters are reconstructed by the inverse matrix.

The radial distribution changes, due to the difference of Pt’ kick at IP.

( Pt’ is the perpendicular momentum to the e- beam line. )

Measurement variables were defined.

• Rmax : Radius to contain 97.5% of the all hits. ( Pair-monitor )

• Rave : Average radius weighted energy deposit. ( BeamCal )

Radial distributionRadial distribution6

σx = 639 [nm]σx = 958.5 [nm]

Pt’ [MeV]

i

iiave Edep

EdepRR

( Ri is the radius of the i-th cell )

e - bunchz’ axis

Pt’

e+ bunch

e+

Rmax and Rave were obtained with various beam parameters.

Rmax and Rave decrease for larger horizontal beam size (σx).

Variable : RVariable : Rmaxmax and R and Raveave

7

σy = 5.7 [nm]σy = 8.55 [nm]σy = 11.4 [nm]σy = 17.1 [nm]

Rmax [cm] v.s. Horizontal beam size (σx) [nm]

Rave [cm] v.s. Horizontal beam size (σx) [nm]

Rm

ax [

cm]

Rav

e [cm

]Horizontal beam size (σx) [nm] Horizontal beam size (σx) [nm]

The azimuthal distribution at IP also changes with the beam parameters.

The measurement variables with the pair-monitor were defined.

→ ND1/Nall for vertical beam size (σy)

NU/ND2 for relative offset (Δy/σy)

e - bunch (z’ axis)

e+ bunch

e+

e+

Azimuthal distributionAzimuthal distribution8

σy = 5.7 [nm]σy = 17.1 [nm]

φ’ [rad]

Hit distribution

ND1/Nall and NU/ND2were obtained with various beam parameters.

ND1/Nall and NU/ND2change as a function of the beam parameters.

Variable : NVariable : ND1D1/N/Nallall, N, NUU/N/ND2D2

9

NU/ND2 v.s. Vertical beam size (σy) [nm]

Vertical beam size (σy) [nm]

NU/N

D2

ND1/Nall v.s. Vertical beam size (σy) [nm]

Vertical beam size (σy) [nm]

ND

1/N

all

σx = 639 [nm]σx = 702.9 [nm]σx = 798.75 [nm]σx = 958.5 [nm]

Δy / σy = 0Δy / σy = 0.2Δy / σy = 0.4

The total number of hits (Nall) and total energy deposit (Edepall)

also have information of the beam parameters.

1/Nall and 1/Edepall change as a function of the σx and σy.

Variable : 1/NVariable : 1/Nallall, 1/Edep, 1/Edepallall 10

σx = 639 [nm]σx = 702.9 [nm]σx = 798.75 [nm]σx = 958.5 [nm]

Δy / σy = 0Δy / σy = 0.2Δy / σy = 0.4

1/Nall v.s.Vertical beam size (σy) [nm]

Vertical beam size (σy) [nm] Vertical beam size (σy) [nm]

1/N

all

1/N

all

Measurement variables • Pair-monitor … Rmax, ND1 / Nall, NU / ND2, 1 / Nall

• BeamCal … Rave, ND / Nall, NU / ND, 1 / Edepall

Matrix components were determined by the fitting with the second polynomials.

yy

y

x

yyyx

yy

y

x

n

BA

m

m

m

M

σΔ

σ

σ

σΔσσ

σΔ

σ

σ

/

/,,

/

2

1

Reconstruction of beam sizeReconstruction of beam size11

MBXAX T

yy

y

x1

/

σΔ

σ

σ

Matrix of the first order term

Matrix of the second order termMeasurement variableBeam parameter (X)

Beam parameter can be reconstructed.

Results (σResults (σyy))

Beam sizes were reconstructed using the matrix.

The combined analysis provides more precise measurement.

12

Acc

urac

y [%

]

Vertical beam size (σy) [nm]

Pair-monitor

BeamCal

Pair-monitor +

BeamCalAcc

urac

y [%

]

Acc

urac

y [%

]

Vertical beam size (σy) [nm]

Measurement of σy

Results (σResults (σxx, σ, σyy, Δ, Δyy/σ/σyy))

The accuracy of measurements is as follows.

13

Pair-monitor BeamCal Pair-monitor + BeamCal

σx 3.2 % 4.1 % 2.8 %

σy 10.1% 15.6 % 8.6 %

Δy/σy 8.6 % 9.4 % 7.4 %

SummarySummary• Pair-monitor and BeamCal measures the beam profile at IP.

– Pair-monitor is a silicon pixel detector to measure the hit count.

– BeamCal is a calorimeter to measure the energy deposit.

• The combined analysis with BeamCal was performed.

• Beam parameters (σx, σy, Δy/σy ) are reconstructed using the matrix

method (second order).

• The combined analysis can provide more precise measurement.

14

Pair-monitor BeamCal Pair-monitor + BeamCal

σx 3.2 % 4.1 % 2.8 %

σy 10.1% 15.6 % 8.6 %

Δy/σy 8.6 % 9.4 % 7.4 %

BackupBackup

15

• Inverse matrix of a non-square matrix A is defined as follows.

Matrix method for reconstructionMatrix method for reconstruction16

1

11

11

AAAAAA

AAAATT

TT

2

/

2

1

OA

m

m

m

M

yy

y

x

n

σΔ

σ

σ

Matrix of the first order term

Measurement variable Beam parameter (X)

yyyx

yy

all

y

all

x

all

RRR

NNN

AσΔσσ

σΔσσ

/

/

/1/1/1

maxmaxmax

RRmaxmax and R and Raveave

17

Δy / σy = 0Δy / σy = 0.2Δy / σy = 0.4

Rmax [cm] v.s. Horizontal beam size (σx) [nm]

Rave [cm] v.s. Horizontal beam size (σx) [nm]

Rm

ax [

cm]

Rav

e [cm

]

Horizontal beam size (σx) [nm] Horizontal beam size (σx) [nm]

i

iiave Edep

EdepRR

( Ri is the radius of the i-th cell )

Azimuthal distributionAzimuthal distribution18

Δy / σy = 0Δy / σy = 1.0

φ’ [rad]

The measurement variable was defined.→ NU/ND2

e - bunch (z’ axis)

e+ bunch

e+

e+

Variable : NVariable : ND1D1/N/Nallall, N, NUU/N/ND2D2

19

Δy / σy = 0Δy / σy = 0.2Δy / σy = 0.4

NU/ND2 v.s. Vertical beam size (σy) [nm]

ND1/Nall v.s. Vertical beam size (σy) [nm]

Vertical beam size (σy) [nm]

ND

1/N

all

NU/N

D2

Vertical beam size (σy) [nm]

σx = 639 [nm]σx = 702.9 [nm]σx = 798.75 [nm]σx = 958.5 [nm]

Variable : 1/NVariable : 1/Nallall, 1/Edep, 1/Edepallall 20

Δy / σy = 0Δy / σy = 0.2Δy / σy = 0.4

σx = 639 [nm]σx = 702.9 [nm]σx = 798.75 [nm]σx = 958.5 [nm]

Vertical beam size (σy) [nm] Vertical beam size (σy) [nm]

1/Edepall v.s. Vertical beam size (σy) [nm]

Result (σResult (σxx))21

BeamCal

Pair-monitor Pair-monitor+ BeamCal

Result (ΔResult (Δyy/σ/σyy))22

BeamCal

Pair-monitor Pair-monitor+ BeamCal