Anomalous change of observed energies in Sandwich … · • Step Limit • Summary • Appendix – EM Packages – Boundary Crossing – Nut-Husk – Configuration – Shower Shape

Anomalous change of observed energies in Sandwich Calorimeter

Anomalous change of Anomalous change of observed energies in observed energies in Sandwich CalorimeterSandwich Calorimeter

Koi, TatsumiKoi, TatsumiSLAC/SCCSSLAC/SCCS

Overview• What is an anomalous change?• Range Cut• Step Limit• Summary• Appendix

– EM Packages– Boundary Crossing– Nut-Husk– Configuration– Shower Shape

What is a problem?• Liner Collider Simulation and Reconstruction group at SALC

reported anomalous change of observation energies in Sandwich Calorimeter according to the range cut values.

• Global Linear Collider group also aware this anomalous change independently.

• We SLAC Geant4 team considered this problem was quite important and started investigation with Geant4 EM developers.

• This report provides what we are observed and what efforts are carried out at SLAC, and Michel will report the current status of this problem from EM developers side.

Energy Deposition vs Range Cut

Sandwithc calorimete (Pb 8mm+Scinti 2mm) x 120 layer

70

75

80

85

90

95

100

105

110

0.00001 0.0001 0.001 0.01 0.1 1

RangeCut [mm]

Depo

sit Ener

gy [M

eV]

Eth. of e- in Abssorber (Lead) become 990eV

1μ

Eth. of γ in Abssorber (Lead) become 990eV

Eth. of e- in Gap (Scintilator) become 990eV

Eth. γ in Gap (Scintilator) become 990eV

about 30% increase

Energy Depositions increase until absorber’s production thresholdbecome minimum(990eV).

Simulation overview• Material

– Pb (Lead)-Scinitillator• Thickens

– Pb: 8.0 mm/layer, Sci: 2.0 mm/layer• Layers

– 120 layers– 1 m x 1 m – interaction surface

• Beam– Electon 4 GeV

• Range Cuts– 1 mm to 100nm (4 orders range)

• Geant4 v7.0.p01• This setup is referring to Suzuki et al., NIM A432 1999 p.48

Pb

8mm

2mm

Sci.

・・・・・・・・e-

Energy Deposition vs Range Cut


70

75

80

85

90

95

100

105

110

0.00001 0.0001 0.001 0.01 0.1 1

RangeCut [mm]

Depo

sit Ener

gy [M

eV]

Eth. of e- in Abssorber (Lead) become 990eV

1μ

Eth. of γ in Abssorber (Lead) become 990eV



about 30% increase

Energy Depositions increase until absorber’s production thresholdbecome minimum(990eV).

Energy Resolution vs Range Cut

Sandwich calorimeter (Lead 8mm+Scinti. 2mm) x 120 layer

0.09

0.095

0.1

0.105

0.11

0.115

0.12

0.125

0.13

0.00001 0.0001 0.001 0.01 0.1 1

RangeCut [mm]

σ/E

Eth. of e- in Abs. (Lead) become 990eV

1μ

Eth. of γ in Abs. (Lead) become 990eV



Data

First suggestion is using MaxStepLimit

• Physics List ExN03 + Step Limitter

• Step Limits do not apply forγ• Step Limits apply both Absorber

and Gap

Energy Deposition vsMaxStepLength


70

75

80

85

90

95

100

105

110

0.00001 0.0001 0.001 0.01 0.1 1

RangeCutn or MaxStepLength [mm]

Depo

sit Energ

y [M

eV]

No StepLimit

RC 1mm

RC 0.1mm

RC 0.01mm

RC 1μm

RC ０.1μm

1μ

Average Step length vsRange Cut

Average Step Length Absorber LEAD 8mm, Gap Scintillator 2mm

0.01

0.1

1

10

0.00001 0.0001 0.001 0.01 0.1 1

Range Cut [mm]

Ave

rage

Ste

p L

eng

th [m

m]

Absorber

Gap

1μ

Limit byGeometry (transpotation) ~2mm

Limit byProduction threshold

Small Range Cut might correspond to MaxStepLimit of 0.1mm in Gap

and 0.01mm in AbsorberSee next Plot.

Range cut and MaxStepLength


70

75

80

85

90

95

100

105

110

0.00001 0.0001 0.001 0.01 0.1 1

RangeCut [mm]

Depo

sit Ene

rgy [M

eV]

1μ

MaxStepLimit 0.1mm in Gap 0.01 mm in Absorber

Differences still remain ~3%However it is same level to uncertainties.

Energy Resolution vsMaxStepLimit


0.09

0.095

0.1

0.105

0.11

0.115

0.12

0.125

0.13

0.00001 0.0001 0.001 0.01 0.1 1

RangeCut or MaxStepLength [mm]

σ/E

No StepLimit

RC 1mm

RC 0.1mm

RC 0.01mm

RC 1μm

RC0. 1μm

1μ

DATA

Computing Speed

1

10

100

1000

0.0001 0.001 0.01 0.1 1

Range Cut or Max Step Length [mm]

Rel

ative

CPU tim

e

[ unit is

Rc

1m

m n

o S

tep

Lim

it]

No Step Limit

1mm

0.1mm

0.01mm

1μm

0.1μm

Range Cut

almost same deposit energyDeference of computing speed factor ~5

Range cut 0.1 mmMax Step Limit 0.01mmis current recommendation values from Michel.

ResultsDeposit energy

• Deposit energy increased about 30% by change of Range Cut from 1mm to 0.1μm.

• This increase stopped at where secondary production limit of absorber became minimum (990eV).

• Limitation of Max Step Limit also increase deposit energy.

• This increase terminated around limitation of 2.5μm without dependence of Range Cut.

• Both end points are same within uncertainties.

Results Cont.Energy resolution (σ/E)

• Although average values of deposit energies are converged, energy resolutions are not converged at all and well scattered distributed with no significant trend.

• The agreement of energy resolutions to data (Suzuki et al.,) is not so bad(????) about 2~3σ level however it seems to incline toward the underestimate side.

Results Cont.• Small Range cut values corresponds to apply small

Max Step Length.• If we uses small Range cut value (<0.01mm) then

we do not need to apply Step Limit to Gaps. This should effect computing speed. (Unfortunately, Absorbers mass is greater than Gaps, so the effect is limited.)

• Applying very small Max Step Length ( less than few μm) is more CPU intense than the minimum range cut.

• For average energy deposition, a result with Range Cut 0.01mm and MaxStepLenght 0.01mm gives almost same value as result with minimum range cut. Former is five time faster than later.

Further investigation • I calculated several sandwich calorimeter,

i.e., changing material (ex. W-Si) and ration between Absorber and Gap. Similar results are gotten.

• I calculated sandwich calorimeter which has same material for absorber and Gap. The feature we discussed here disappeared.

• I also did simulation without Multiple Coulmb Scattering. The results shows very small or no increase on energy depositions.

(Lead 4 mm + Scinti. 2mm) x 210 layer


140

150

160

170

180

190

200

210

0.00001 0.0001 0.001 0.01 0.1 1

RangeCutn or MaxStepLength [mm]

Depo

sit Energ

y [M

eV]

No StepLimit

RC 1mm

RC 0.1mm

RC 0.01mm

RC 1μm

RC ０.1μm

1μ



0.05

0.055

0.06

0.065

0.07

0.075

0.08

0.085

0.09

0.00001 0.0001 0.001 0.01 0.1 1


σ/E

No StepLimit

RC 1mm

RC 0.1mm

RC 0.01mm

RC 1μm

RC 0.1μm

1μ

DATA



30

35

40

45

50

55

60

0.00001 0.0001 0.001 0.01 0.1 1

RangeCutn or MaxStepLimit [mm]

Depo

sit Energ

y [M

eV]

No StepLimit

RC 1mm

RC 0.1mm

RC 0.01mm

RC 1μm

RC ０.1μm

1μ



0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.2

0.00001 0.0001 0.001 0.01 0.1 1


σ/E

No StepLimit

RC 1mm

RC 0.1mm

RC 0.01mm

RC 1μm

RC 0.1μm

1μ

DATA

Same material for Absorber and Gap.

Sandwithc calorimete (Pb 8mm+Pb 4mm) x 120 layer

775

780

785

790

795

800

805

810

0.00001 0.0001 0.001 0.01 0.1 1

RangeCutn [mm]

Dep

osit E

nerg

y [M

eV]

1μ

1~2%increase???

Same material for Absorber and Gap.

Sandwich calorimeter (Lead 8mm+Pb 2mm) x 120 layer

0.04

0.045

0.05

0.055

0.06

0.065

0.07

0.075

0.08

0.00001 0.0001 0.001 0.01 0.1 1

RangeCut[mm]

σ/E

1μ

Without Multiple Coulomb Scattering

Sandwithc calorimete (Pb 8mm+Scinti 2mm) x 120 layerWithout MCS

90

95

100

105

110

115

120

125

130

0.00001 0.0001 0.001 0.01 0.1 1

RangeCutn[mm]

Dep

osit Energ

y [M

eV]

1μ

Without Multiple Coulomb Scattering

Sandwich calorimeter (Lead 8mm+Scinti. 2mm) x 120 layerWithout MCS

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.00001 0.0001 0.001 0.01 0.1 1

RangeCut [mm]

σ/E

Eth. of e- in Abs. (Lead) become 990eV

1μ

Eth. of γ in Abs. (Lead) become 990eV



DATA

So that, Multiple Coulomb

Scattering is most likely responsible to

this problem.

• Try for understood– EM package dependency– History ( especially for resolution) – Changing Configuration of a layer

• Try for Speed up– Boundary Crossing– Nut-Husk

Comparison among EM packages

Sandwich calorimeter (Pb 8mm+Scinti 2mm) x 120 layer

70

75

80

85

90

95

100

105

110

115

0.0001 0.001 0.01 0.1 1

Range Cut [mm]

Dep

osit Ener

gy [M

eV]

STD

v5.2

LEEM

e- prodction threshold in absorber (lead) become 250 eV

e- prodction threshold in absorber (lead) become 990 eV

gamma prodction threshold in absorber (lead) become 990 eV and also reach 250 eV.

Extend number of samplefrom 100 to 10000 (1000)

Sandwithc calorimeter (Pb 8mm+Scinti 2mm) x 120 layer

75

80

85

90

95

100

105

110

0.0001 0.001 0.01 0.1 1

Rc [mm]

Depo

sit Ener

gy [M

eV]

100

10000

1000

Nut-Husk• Divide Absorber two parts as Nut

and Hask.• Apply different Range Cut values for

Nut and Hask.

Nut

Husk

Thickness of Hask

Nut-HuskPb 8mm Sci 2mm Nut-Husk

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80

85

90

95

100

105

0 0.5 1 1.5 2 2.5 3 3.5

Husk Thickness [mm]

depo

sit

energ

y [M

eV

]

RC 1mm

RC 0.1mm

RC 0.01mm

RC 0.001mm

Extend number of samplefrom 100 to 10000 (1000)

Sandwithc calorimeter (Pb 8mm+Scinti 2mm) x 120 layer

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.0001 0.001 0.01 0.1 1

Rc [mm]

σ/E

100

10000

1000

Boundary Crossing limitation.

• If backward scattering of slow electrons from absorber makes increase of energy deposition, we may limit applying MaxStepLegnth only for several series of steps after crossing boundary.

• Check, is PreStepPoint limited by Geometrical Boundary.

• Then, n successive steps after crossing boundaries, MaxStepLength is artificially limited to x.

• The implementation is achieved in G4MultipleScatering.

Bounary

Until nth step,

Step Limit artificially small.

Boundary Crossing Process

70

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100

105

110

0.00001 0.0001 0.001 0.01 0.1 1

Range Cut [mm]

Depo

sition E

nerg

y [M

eV] 100μm　5th

100μm　50th

100μm　500th

100μm　5000th

10μm　5th

10μm　50th

10μm　500th

10μm　5000th

1μm　5th

1μm　50th

1μm　500th

1μm　5000th

Max

StepLength X

Limit

until n

Boundary Crossing Results

• I create Step Limits which only effect n steps after boundary crossing.

• However this limitation gives smaller energy deposition than usual MaxStepLength limitation.

Boundary Crossing Summary

• Both range cut and max step length effects average energy deposition of sandwich calorimeter.

• The amount of increases reaches about 30%.

Changing Configuration of a layer

• Keep ratio of material• Keep total matter of each materials

,,,,,,Abs 8mm Sci. 2mm x 120 layer

,,,,,,Abs 4mm Sci. 1mm x 240 layer

Conf. A

Conf. B

,,,,,, 3840 layer

Changing the Configuration of a Layer

Sandwich Calorimeter

70

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90

100

110

120

130

140

0.00001 0.0001 0.001 0.01 0.1 1

RangeCut [mm]

Depo

sit Ene

rgy [M

eV]

Pb 8mm Sci 2mm

Pb 4mm Sci 1mm

Pb 2mm Sci 0.5mm

Pb 1mm Sci 0.25mm

Pb 0.5mm Sci 0.125mm


1μ

configuration of a layerAbsorber Gap

Total matters in eachconfiguration are same, iethe number of layers haschanged in eachconfiguration.

120 layers

240

3840 layers

Comparison of Shower ShapeBetween Different Range Cut

0

2

4

6

8

10

12

14

16

18

20

0 100 200 300 400 500

Depth [mm]

Depo

sit

Energ

y [M

eV

/cm

]

1mm

3.75μm

100nm

8mm Pb, 2mm Sci. x 120 layer


8mm Pb, 2mm Sci. x 120 layers

0

0.5

1

1.5

2

2.5

0 100 200 300 400 500

Depth [mm]

Rat

io 3.75μm／1mm

100nm/1mm


8mm Pb, 2mm Sci. x 120 layers

0

0.5

1

1.5

2

2.5

0 100 200 300 400 500

Depth [mm]

Rat

io 3.75μm／1mm

100nm/1mm

0

2

4

6

8

10

12

14

16

18

20

0 100 200 300 400 500

Depth [mm]

Depo

sit

Energ

y [M

eV

/cm

]

1mm

3.75μm

100nm

Comparison of Shower ShapeBetween Different Configuration

0

2

4

6

8

10

12

14

16

0 100 200 300 400 500

Depth [mm]

Obs

erv

e E

nerg

y [M

eV

/cm

]

Pb8mmSci2mm3.75μm

Pb0.25mmSci0.0625mm 3.75μ

Comment from MichelIn your exercises, of course the global ratio scintillator/lead is unchanged, but however the geometry is changed. The results are not directly comparable. I switch off the msc. We know that in this case, the energy deposit is practically independent of cut or stepmax. But it not the same in the 6 cases you have shown : It ranges from 121 MeV (120 layers) to 137 MeV ( 3840 layers)

Changing the Configuration of a Layer (Cont.)

Sandwich Calorimeter

75

80

85

90

95

100

105

110

115

0.001 0.01

RangeCut [mm]

Depo

sit

Energ

y [M

eV

]

Pb 8mm Sci 2mm

Pb 4mm Sci 1mm

Pb 2mm Sci 0.5mm

Pb 1mm Sci 0.25mm



1μ

configuration of a layer

Absorber Gap

Total matters in each

configuration are same, iethe number of layers haschanged in eachconfiguration.

e- Scinti.

Fin.

Documents

Anomalous change of observed energies in Sandwich … · • Step Limit • Summary • Appendix – EM Packages – Boundary Crossing – Nut-Husk – Configuration – Shower Shape