# Presentation: 805303

## Radiation Shielding Assessment for MuCool Experimental Enclosure

- C. Johnstone1), _I. Rakhno__2_)
- 1)*Fermi National Accelerator Laboratory, Batavia, Illinois*
- 2)*University of Illinois at Urbana-Champaign, Urbana, Illinois*

- 3D Geometry Model of the MuCool Test Area (MTA)
- Proton Beam & Target

## Elevation View of the MARS Model of the MTA

##     Plan View 

##     Plan View 

## Beam & Target

_*Beam*_:  400-MeV protons;  σr = 1cm
-             1014 p/s or 6.7x1012 p/pulse at 15 Hz repetition rate
-   _*Proton interaction lengths, *__*λ*__* (cm)*_                                             _*Targets*_

| Target |   L (cm) |   R (cm) | % of λtot |
| --- | --- | --- | --- |
|      
   LH2 | 
     21 | 
    10.5 | 
      2 |
| 
    Cu | 
       1 | 
    10 |  
    10 |

|  |     LH2 |      Al |     Cu |
| --- | --- | --- | --- |
|      
   λtot | 
     910 | 
     29 | 
    10 |
| 
   λinel  | 
   1110 | 
     41 | 
    16 |

## Spallation neutron studies  →  full absorption (≈100%) targets of heavy & dense materials (Pb, Unat) 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.

## Dose Equivalent above the Berm (normal operation) 

|        Material
(density, g/cm3) | Attenuation
length, α (cm) |
| --- | --- |
|  Compacted soil
 (2.24) |       39 |
|  High-density
 concrete (3.64) |       28 |
|  Iron (7.87) |       23 |

## 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.

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

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

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

## 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.

## Sensitivity Study for a MICE Hydrogen Absorber 

- D. Errede1), _I. Rakhno_1), S. Striganov2)
- 1)*University of Illinois at Urbana-Champaign, Urbana, Illinois*
- 2)*Fermi National Accelerator Laboratory, Batavia, Illinois*

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

- 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.)

## 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.

## Monte Carlo approach

- g = xx ́  
- n = xpx /mc  
**                     ********xx********   ********xx********   ********xy********   ********xy******
**                     ********x********x********  ********x********x********  ********x********y********  ********x********y******
**                     ********yx********   ********yx********   ********yy********   ********yy******
**                     ********y********x********  ********y********x********  ********y********y********  ********y********y******
**x  ********  x - ********x********  *****etc*****.**
**x******** ******** p****x****/**mc  ***etc*****.**

## Magnetic field distribution in the central hydrogen absorber(field direction, not magnitude, is shown)

- Magnetic field map bfield.sfofo  (Yagmur Torun)

## MARS model of a hydrogen absorber                             100 muon tracks

## Monte Carlo results

- _Monte Carlo results_

-                                                          200 MeV/c muons
**0.1% in ********n**** ******** 2% in ********H**

##                              Multiple Coulomb Scattering

**                             **_**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 ***

## Multiple Coulomb Scattering

_**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.**

- FH

- FL

- FH

- FL

- FH

## 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.