1. Radiation Shielding Assessment for MuCool Experimental Enclosure C. Johnstone 1), I. Rakhno 2) 1) Fermi National Accelerator Laboratory, Batavia, Illinois 2) University of Illinois at Urbana-Champaign, Urbana, Illinois

2. 3D Geometry Model of the MuCool Test Area (MTA) Proton Beam & Target Calculated Dose Distributions & Neutron Energy Spectra

3. Elevation View of the MARS Model of the MTA

4. Plan View

6. Beam & Target Beam: 400-MeV protons; σ r = 1cm 10 14 p/s or 6.7x10 12 p/pulse at 15 Hz repetition rate Proton interaction lengths, λ (cm) Targets Target L (cm) R (cm)% of λ tot LH 2 21 10.5 2 Cu 1 10 10 LH 2 Al Cu λ tot 910 29 10 λ inel 1110 41 16

7. Spallation neutron studies → full absorption (≈100%) targets of heavy & dense materials (Pb, U nat ) are used. It is claimed that the facility can serve as a multi- purpose one for future operations. The 1-cm thick copper target (10% of interaction length) is considered as a generic (modest “averaged”) target.

8. Dose Equivalent above the Berm (normal operation) Material (density, g/cm 3 ) Attenuation length, α (cm) Compacted soil (2.24) 39 High-density concrete (3.64) 28 Iron (7.87) 23

9. Dose Equivalent above the Berm (normal operation) Calculated shielding compositions which provide the dose level of 0.5 mrem/hr on the top of the MTA shielding.

10. Dose Equivalent in the Access Pit (normal operation) Lower Level Upper Level

11. Dose Equivalent in the Cryo Room (normal operation) 10" penetration 4" and 8" penetrations

12. Neutron Energy Spectra in the 10" Penetration Near target hall Near cryo room

13. Conclusions About 14' of heavy concrete is required above the MTA ceiling to provide 0.5 mrem/hr. High dose is expected at the parking lot and access pit (≈10 and 10-30 mrem/hr, respectively) within framework of the current design. Additional shielding is required in the target hall and/or cryo room. No access to the cryo room is permitted with the beam on. The access pit should be fenced.

14. Sensitivity Study for a MICE Hydrogen Absorber D. Errede 1), I. Rakhno 1), S. Striganov 2) 1) University of Illinois at Urbana-Champaign, Urbana, Illinois 2) Fermi National Accelerator Laboratory, Batavia, Illinois

15. Some uncertainties for emittance measurements & calculations Analytics & Monte Carlo results New multiple Coulomb scattering theory

16. One of the goals of MICE is “… achieving an absolute accuracy on the measurement of emittance of 0.1% or better”   n vs.  H (hydrogen density variations due to temperature variations). d  n /dz = -(Cooling/dE/dz) + (Heating/M.C.S.) Re-evaluated heating term due to multiple scattering for muons in hydrogen.

17. Analytical Approach  n  /  n  = -1/  2  dE  /dz   z/E  + … Phys. Rev. E52 (1995) 1039 -1/  2  dE  /dz   z/E   -0.065 at p  = 200 MeV/c with dE  /dz from At. Data & Nucl. Data Tables 78 (2001) 183.

18. Monte Carlo approach  g =  x  x´    n =  x  px /m  c    xx   xx   xy   xy   yx   yx   yy   yy  x  x -  x  etc. x  p x /m  c etc.

19. Magnetic field distribution in the central hydrogen absorber (field direction, not magnitude, is shown) Magnetic field map bfield.sfofo (Yagmur Torun)

20. MARS model of a hydrogen absorber 100 muon tracks

21. Monte Carlo results 200 MeV/c muons 0.1% in  n  2% in  H

22. Multiple Coulomb Scattering GEANT4: “ In the case of heavy charged particles ( , , p) the mean free path (MFP) is calculated from the electron or positron 1 values with a “scaling” applied. This is possible because the MFP 1 depends only on the variable P , where P is the momentum, and  is the velocity of the particle”. 1/ k = 2  n a The cross-section  describes projectile-nucleus elastic scattering AND projectile-electron scattering. As for the integrand, the “scaling” is OK. However the integration limits behave differently (by relativistic kinematics): M p  M t 0     projectile-nucleus M p  M t 0     /2 electron-electron M p  M t sin   M t /M p muon-electron

23. Multiple Coulomb Scattering G. Moliere 1948 Z 2 H. Bethe 1953 Z 2  Z(Z+1) U. Fano 1953  max (E), different screening for nucleus and electron, non-relativistic energies. A distribution with undefined region of applicability. …………………………………… A.Tollestrup, J. Monroe  2000 MuCool 176 Analogous to Fano + correct atomic form-factors for light elements. R. Fernow 2000 NuMu Note #123 Moliere Z(Z+1) is good for heavy projectiles Measurements by G. Shen et al. PR D20 (1979) 1584 for 50 to 200 GeV/c protons. S. Striganov 2003  max (E), relativistic energies. A distribution for all thicknesses and defined region of applicability of Fano correction. Measurements by B. Gottschalk et al. NIM B74 (1993) 467 for 159 MeV protons in 14 materials and analysis for 6 other proton measurements (1 MeV to 200 GeV). It was shown that Moliere theory with Fano correction is accurate to better than 1% on the average for protons.

25. FH FL FH FL FH

27. Conclusions Hydrogen density variation of 2% gives rise to  n  variation of about 0.1%. New multiple Coulomb scattering theory enables to describe experimental data for protons within 1% accuracy on the average and adjust employed m.c.s. distributions to simulation step-sizes.