Step IV Studies

Timothy CarlisleOxford

Intro.

• CM28 – Step III vs Step IV• Cooling formula & G4MICE disagree on

– Also observed in ICOOL (note #199 – Marco/John Cobb)

Step IV, 63mm LiH + AFC inc. windows

2

2 30

0.014 GeV

2tn nd dE

dz E dX Em X

0

[from CM28]

• Cooling formula assumes Gaussian approximation:

)ln(038.01MeV6.13

00 XxXxzcp

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PDG:From Moliere

G4MICEGEANT4:

uses Lewis Theory,

“develops a theory valid for any angle by using Legendre polynomials and then goes over into the small Angle”

...simple then!

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zxx PPa

)/tan(

Px

Pz

58cm LH2

G4MICE:Nm=10,000pencil beam on axis no fields

• Compare PDG with scattering in G4MICE.

Z Xo x [cm]

1 63.04 LH2 57.613 82.78 Li 10.064 65.19 Be 2.296 42.7 C 1.39

14 24.01 Al 0.5822 16.16 Ti 0.2329 12.86 Cu 0.09

2.00 79.62 LiH 6.305.44 44.77 Polyethylene (C2H4) 3.095.69 43.79 Polystyrene (C8H8) 2.68

• Absorbers in Step IV scaled so DE = const.

• Instead fix the scattering angle scaled to 63mm LiH

0Xx = const.

Scattering Angle

0 5 10 15 20 25 300.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

ElementsCom-poundsPDG

LH2

Li

Carbon CuAlLiH

Atomic Number Z

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Energy Loss

0 5 10 15 20 25 3002468

101214161820

Elements

Com-pounds

PDG

MeV

Atomic Number Z

LH2

LiH

Carbon CuAl

• Scattering isn’t so simple to predict it seems.• Energy Loss seems fine however.• MICE acceptance limited to

– i.e. measure up to Carbon (maybe Aluminium)

• Find in G4MICE in different materials, for:

pz = 207 MeV/c

Nm= 10,000

sPz = 1MeV/c

bT = 41cm

0

mminput 100

1

0

2

0 2

)c/MeV14(

dz

dE

XmT

Absorber study

0 1 2 3 4 5 6 7

-0.15

-0.1

-0.05

0

0.05

0.1 BeLiLH2LiHCarbon

Input emittance [mm]

De

LH2

C

Equilibrium Emittance

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7 Elements: G4MICE

Elements: Theory

Compounds: G4MICE

Compounds: Theory

][0 mm

Atomic Number Z

LH2

LiLiH

Be

C

PolyE

15.9cm LH2 Target

MuScat Experiment• Measured muon scattering.• Compared with – GEANT 4.7.0 (10yrs old now)– ELMS

Summary

• Cooling formula/Moliere disagree with G4MICE– 1.5-2x less than predicted– Particularly bad with LH2

• MuScat– Moliere & GEANT 4.7.0 overestimate scattering at low Z– ELMS code much better

• G4MICE uses GEANT 4.9.2 however...– Is this closer to MuScat?– ELMS in MAUS?

0

Scattering Angle (Li fraction)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.0000.0020.0040.0060.0080.0100.0120.0140.0160.018

G4MICE

PDB

G4MICE: LiH

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Li mass fraction

(mLi/mLi+mLH2)

LH2LiLiH