1

MULTIPLE SCATTERING

CM34 @ RALTimothy Carlisle

INTRO. MICE performance predicted using the cooling formula (CF): G4MICE ≠ CF

(see prev CMs)

Simulation disagrees with C.F by up to 20%. MS calc. typically approx.:

CF uses Rossi-Greisen (1941). Somewhat crude.

Rutherford scattering law - simplest description of MS.

2

2 30

0.014 GeV

2tn nd dE

dz E dX Em X

pXXrms

plane0/

MeV14

2N

RUTHERFORD MS Rutherford

tends to infinity at θ=0

Apply limits:

Lower cut-off by Uncertainty Principle:(Thomas-Fermi model of the atom)

Upper by rel. size of nucleus:

Integrate, giving:

3Rutherford Form. I-with hard limits for scattering

DERIVING THE PDG FORM

1941: Rossi-Greisen

1974 - PDG - log correction to R-G (by Highland)• removes strong path length dep.• *Z dep. remains however* )ln(038.01MeV6.13

00 XxXXzp

rmsplane

PDG values for X0 include e- R-G implicitly incl. atomic e- scatters.

However... Heavy particle scatters off e- have a rel. small max.

angle.Limited by kinematics.Not incl. by R-G/PDG

4

4

Definition of X0:Log terms cancel..., substitute X0 into diff. eqn.

5

SCATTERING OFF ATOMIC ELECTRONS e- collisions are significant, increasingly at low Z. Include e- by using different limits for e- scatters.

... integrate to get:

However - Also need to include screening of the nuclear potential by e-s.

Rutherford Form. II-with sep. hard limits for nuclear & electron scatters

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ATOMIC SCREENING

N

e- screened nucleus

Wenztel-Moliere Form.

• Atomic e-s reduce nuclear charge seen by muon.

•1927: Wentzel assumed exponential scattering potential, used Born Approximation.

later corrected by Moliere

Integrate to get:

COMPARISON OF FORMULAE

7Mean Sq. Angle of scattering / X0 (Z). Muons at 200 MeV/c.

electrons (W-M)

Total – Wentzel-Molierenuclei (W-M)

Total – Rutherford

w. hard limits

PDG

R-G

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SIMULATION OF MULTIPLE SCATTERING

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SCATTERING IN SIMULATION CODE Geant4: several different scattering models!

Urban (default), Wentzel-VI & CoulombScattering model Compared with MuScat in *, Urban ‘worst’ of the 3. Urban used by LHC sim. exps., quoted as 1% precision. Used by MAUS – now builds with the latest version G4.9.5.p01.

ELMS Uses knowledge of photoabsorption cooeffs to describe atomic structure. Only for LH2, only useable through ICOOL at present...

Can we build a Monte Carlo using the Wentzel-Moliere Z-section?

* Geant4 models for simulation of multiple scattering V N Ivanchenko et al 2010 J. Phys.: Conf. Ser. 219 032045

YES!

COBB-CARLISLE MODEL New Monte Carlo Model, based on Wentzel-Moliere X-section Simulates muons fired through block of absorber material. Predicts . Integrate over angle and thickness

Gives Nnucleus & Nelectron scatters. E.g. for 10.9cm LH2 ~ 36,000 scatters (total).

Nuclear scattering angles distributed as:

Integrate over angle, solve:

Sum for all collisions = total scat. angle. Can compare with MuScat results... 10

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MUSCAT ABSORBERS

12

COMPARISON FOR 10.9CM LH2

c2~12c2~15

vs. MuScat

Probability / radian Cobb-Carlisle

ModelMuScatELMSGeant4.7.0p01

13

c2~130

vs. MuScat

Probability / radian

COMPARISON FOR 0.15CM AL

Cobb-CarlisleMuScatGeant4.7.0p01

0.3 3 300

100

200

300

400

500

600

700

ELMSGeant4.7.p01Cobb-Carlisle

log Z

c2LH2 Li

Fe

Al

C

Be

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COMPARISON WITH MUSCAT

15

MS MEASUREMENTS IN STEP IV [CM32]

Use MAUS to evolve tracks to downstream face of absorber.

Use tracker hits as starting values.

Scattering angle is the angle between two vectors.

Model tracker resolution by smearing.

Tracker code status?

q

qpqpspace

rms

.cos

p

MeV/c58.4

MeV/c52.1MeV/c05.2

mm44.0mm54.0

Pz

Py

Px

y

x

MICE Note #90

AFC + LH2

Smear

][mradspace

10 20 30 40 50 60 70 80

No Smear

16

17

SUMMARY Longstanding disagreement between Geant4/ICOOL & CF. New Monte Carlo model.

Simple, uses 4 parameters. Doesn’t incl. energy loss correlations (unlike ELMS).

V. good agreement with LH2, less so at higher Z. Unclear why! Thomas-Fermi model less accurate at low Z... Need to explain atomic structure better encapsulated by . Eq. Emittance lower than CF, ~20% less for LH2 – consistent with Geant4.

New Geant4.9.5.p01 to be tested shortly. How close to MuScat? Step Length dependencies fixed?

Step IV can & should measure MS. Complement MuScat measurements. Test of physics models. Resolution covered @ CM32 – to be revisited.

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EXTRAS

19

20

21

1)1ln(11 2

22

, c

Fc

planerms1990 - Lynch & Dahl expression

• “much better approximation...agrees with Moliere scattering to 2% for all Z”• ...Derivation / comparison with Highland / Moliere not supplied!• doesn’t seem to have replaced Highland…

22

G4MICE: Step IV 63mm LiH

Note: known Step Length problems at 1mm, as used in these simulations [old

Geant4 version].

23DzLiH = 6.3 cmDzLH2 = 57.6 cm

Note: known Step Length problems at 1mm, as used in these simulations [old

Geant4 version].

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EQ. EMITTANCE & SCATTERING ANGLE (STEP LENGTH)

Pencil beams sent through absorber block