CM34 RAL Timothy Carlisle 1 Intro MICE performance predicted using the cooling formula CF G4MICE CF see prev CMs Simulation disagrees with CF by up to 20 MS calc typically approx ID: 502126
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Slide1
Multiple Scattering
CM34 @ RALTimothy Carlisle
1Slide2
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
NSlide3
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
:
3
Rutherford Form. I
with hard limits for scattering Slide4
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*
PDG values for
X
0
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
X
0
:
Log terms cancel..., substitute
X
0
into diff. eqn
. Slide5
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
5Slide6
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
6
Integrate to get:Slide7
Comparison of Formulae
7
Mean Sq. Angle of scattering / X
0
(Z). Muons at 200 MeV/c.electrons (W-M)Total – Wentzel-Moliere
nuclei (W-M)
Total – Rutherfordw. hard limits
PDG
R-GSlide8
Simulation of Multiple Scattering
8Slide9
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.ELMSUses 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?
9* Geant4 models for simulation of multiple scattering
V N Ivanchenko et al 2010
J. Phys.: Conf. Ser. 219 032045
YES!Slide10
Cobb-Carlisle Model
New Monte Carlo Model, based on Wentzel-Moliere X-sectionSimulates 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...
10Slide11
MuScat Absorbers
11Slide12
Comparison for 10.9cm lh
2
c
2
~12c2~15vs. MuScat
12Probability / radian
Cobb-Carlisle Model
MuScat
ELMS
Geant4.7.0p01Slide13
c
2
~130
vs. MuScat
Probability / radian13Comparison for 0.15cm alCobb-CarlisleMuScat
Geant4.7.0p01Slide14
Fe
Al
C
Be
14
Comparison with
muscatSlide15
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?
MICE Note #90
15Slide16
AFC +
LH
2
Smear
10 20 30 40 50 60 70 80
No Smear
16Slide17
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.
17Slide18
Extras
18Slide19
19Slide20
20Slide21
21
1990 - 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…Slide22
22
G4MICE: Step IV 63mm
LiH
Note: known Step Length problems at 1mm, as used in these simulations [old Geant4 version]. Slide23
23
D
z
LiH
= 6.3 cmDzLH2 = 57.6 cm Note: known Step Length problems at 1mm, as used in these simulations [old Geant4 version]. Slide24
Eq. Emittance & Scattering Angle (Step Length)
Pencil beams
sent through
absorber block
24