Multiple Scattering CM34 @ RAL Timothy 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. N
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: • Rutherford Form. I • with hard limits for scattering
Deriving the PDG form Definition of X0: Log terms cancel..., substitute X0into diff. eqn. 1941: Rossi-Greisen 1974 - PDG - log correction to R-G (by Highland) • removes strong path length dep. • *Z dep. remains however* 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
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
Atomic Screening e- screened nucleus • Atomic e-s reduce nuclear charge seen by muon. • 1927: Wentzel assumed exponential scattering potential, used Born Approximation. • later corrected by Moliere N Integrate to get: Wenztel-Moliere Form.
Comparison of Formulae R-G PDG Total – Rutherford w. hard limits nuclei (W-M) Total – Wentzel-Moliere electrons (W-M) • Mean Sq. Angle of scattering / X0 (Z). Muons at 200 MeV/c.
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 photoabsorptioncooeffs 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? YES! * Geant4 models for simulation of multiple scattering V N Ivanchenkoet al 2010 J. Phys.: Conf. Ser.219 032045
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...
Comparison for 10.9cm lh2 Probability / radian Cobb-Carlisle Model MuScat c2~12 c2~15 ELMS vs. MuScat Geant4.7.0p01
Comparison for 0.15cm al Probability / radian Cobb-Carlisle c2~130 vs. MuScat MuScat Geant4.7.0p01
Comparison with muscat Be C Al Fe
ms measurements in Step IV [CM32] MICE Note #90 • 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?
AFC + LH2 • No Smear • Smear 10 20 30 40 50 60 70 80
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.
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…
G4MICE: Step IV 63mm LiH Note: known Step Length problems at 1mm, as used in these simulations [old Geant4 version].
DzLiH= 6.3 cm DzLH2 = 57.6 cm Note: known Step Length problems at 1mm, as used in these simulations [old Geant4 version].
Eq. Emittance & Scattering Angle (Step Length) Pencil beams sent through absorber block