HRRL Simulations

Mark Balzer: 282-5652

Brian Oborn: 282- 6243

This document describes the simulations performed to estimate the radiological background in the event that a 1 nA electron current from the HRRL enters the experimental cell.

Radiation monitors: Ludlum Model 45-8.

Low energy gamma cutoff = 60 keV

Tungsten SImulation

I created a world volume filled with Air to represent the experimental cell.

I created a 2mm thick tungsten target that is 30 cm x 30 cm in area.

The image below shows several electrons hitting the tungsten foil, then scattering in air. The red lines are electrons and the green ones are photons.

Run 1

I then ran 1 million events in which an incident 7 MeV electron hit the 2 mm thick Tungsten with the physics processes

    if (particleName == "gamma") {
     // gamma         
   pmanager->AddDiscreteProcess(new G4PhotoElectricEffect);
     pmanager->AddDiscreteProcess(new G4ComptonScattering);
     pmanager->AddDiscreteProcess(new G4GammaConversion);
     
   } else if (particleName == "e-") {
     //electron
     pmanager->AddProcess(new G4MultipleScattering,-1, 1,1);
     pmanager->AddProcess(new G4eIonisation,       -1, 2,2);
     pmanager->AddProcess(new G4eBremsstrahlung,   -1, 3,3);      

I only kept gamma which had a momentum component towards the ceiling (p_y>0).

The energy distribution (in MeV) of the gammas headed towards the ceiling is shown below. Of the 1 million electrons incident on the 2 mm thick Tungsten target, only 70,000 gammas were headed towards the cieling. This does not mean that they hit it, they could have hit the wall.

If I sum the above distribution I see a total energy of 43,987 MeV going up from the 1 million 7 MeV electrons hitting the 2mm Tungsten target.

1 Rad =[math]\frac{J}{100 kg}[/math] = the amount of energy absorbed per 100 kg of material

To calculate the worst possible case lets assume all of the radiation is absorbed by a person (there is no concrete ceiling).

Converting the energy from MeV to Joules

[math]4.4 \times 10^4 MeV \times \frac{1.6 \times 10^{-19} J }{10^{-6} MeV} = 4.4 \times 10^{-9} J[/math]

In terms of the energy per beam current charge we would have

[math]\frac{4.4 \times 10^{-9} J}{10^6 e^-} \times \frac{1 e^-}{1.6 \times 10^{-19} C} = \frac {44 krad}{C}[/math]

I we ran the HRRL for 1 hour at the maximum beam current of 80 mA per 100 ns pulse and 1 kHz rep rate then the dose to the ceiling would be

[math]80 mA \times 100 ns = 8 \times 10^{-9} Coul \times \frac{1000 pulses}{sec} \times \frac{3600 sec}{hr} = 0.0288 Coul/hr \times \frac {44 krad}{C} = 1.4 kRad/hr[/math]

The total photon radiation hitting the upper half of the experimental cell is predicted to be 1.4 krad/hr. To determine the dose on a radiation detector you just need to scale by the solid angle.

Mark Balzer tells me that the ion chambers are cylinders of length 4 inches and 1 inch in diameter. The ion chamber's cylindrical axis is mounted parallel to the ceiling. We will be limited to running with beam current that generate 2 mRad/hr or less in a single ion chamber. As a first estimate I will treat the cylinder as having a rectangular surface area of 4 " x 1 " = 4 in^2 = 25.8 cm^2. The ion chamber is on the ceiling which is about 6 meters from the beam pipe. The solid angle is thus

[math]\frac{A}{r^2} = \frac{25.8}{600^2} = 7.2 \times 10^-5 strad[/math].

The predicted rate in an ion chamber would then be

[math]1.4 kRad/hr \times \frac{7.2 \times 10^-5}{2 \pi} = 16 mRad/hr [/math]

[math]\Rightarrow[/math] our max beam current for 1 mRad/hr would be [math]\frac{80}{16}[/math] = 5 mA peak

Or in terms of an average current

[math]5 mA \times 0.1 \mu s * 1000/sec = 0.5 \mu A[/math] average

Run 2: Ceiling Penetration

Setup

The picture below shows the simulation World volume. A red electron beam enters the HRRL experimental cell from the left side and hits a 2 mm thick Tungsten target shown as the white vertical line inside the white inner box. The yellow box is a detector tracking cell. The roof is shown as 2 horizontal lines near the top of the World volume.

A few interesting events:

Photon Energy -to- Dose

Photon Energy	Dose Conversion Coeff
(MeV)	rem [math]cm^2[/math] s/ hr
0.01	3.96E-6
0.03	0.582E-6
0.05	0.290E-6
0.07	0.258E-6
0.1	0.283E-6
0.15	0.379E-6
0.2	0.501E-6
0.25	0.631E-6
0.3	0.759E-6
0.35	0.878E-6
0.4	0.985E-6
0.45	1.08E-6
0.5	1.17E-6
0.55	1.27E-6
0.6	1.36E-6
0.65	1.44E-6
0.7	1.52E-6
0.8	1.68E-6
1.0	1.98E-6
1.4	2.51E-6
1.8	2.99E-6
2.2	3.42E-6
2.6	3.82E-6
2.8	4.01E-6
3.25	4.41E-6
3.75	4.83E-6
4.25	5.23E-6
4.75	5.60E-6
5.0	5.80E-6
5.25	6.01E-6
5.75	6.37E-6
6.25	6.74E-6
6.75	7.11E-6
7.5	7.66E-6
9.0	8.77E-6
11.0	10.3E-6
13.0	11.8E-6
15.0	13.3E-6

Concrete Definition and Stopping Power

A 6 inch concrete floor is assumed to exist on the top of the experimental cell which will block radiation from penetrating to the offices above the cell.

Stopping power from NIST

Composition of CONCRETE, PORTLAND: Density (g/cm3) = 2.30000E+00 Mean Excitation Energy (eV) = 135.200000

COMPOSITION:

Atomic Number	Fraction by Weight
1	0.010000
6	0.001000
8	0.529107
11	0.016000
12	0.002000
13	0.033872
14	0.337021
19	0.013000
20	0.044000
26	0.014000

(required)

Kinetic Energy(MeV)	Stopping Power (MeV cm2/g) || CSDA Range(g/cm2) || RadiationYield || Density EffectParameter
	Collision	Radiative || Total
1.000E-02	1.804E+01	5.754E-03	1.805E+01	3.207E-04	1.710E-04	0.000E+00
1.250E-02	1.526E+01	5.864E-03	1.526E+01	4.720E-04	2.072E-04	0.000E+00
1.500E-02	1.330E+01	5.942E-03	1.330E+01	6.480E-04	2.419E-04	0.000E+00
1.750E-02	1.184E+01	5.999E-03	1.184E+01	8.476E-04	2.755E-04	0.000E+00
2.000E-02 1.070E+01 6.044E-03 1.071E+01 1.070E-03 3.080E-04 0.000E+00
2.500E-02 9.049E+00 6.107E-03 9.056E+00 1.580E-03 3.704E-04 0.000E+00
3.000E-02 7.899E+00 6.153E-03 7.905E+00 2.173E-03 4.298E-04 0.000E+00
3.500E-02 7.049E+00 6.189E-03 7.055E+00 2.844E-03 4.867E-04 0.000E+00
4.000E-02 6.393E+00 6.220E-03 6.400E+00 3.589E-03 5.415E-04 0.000E+00
4.500E-02 5.872E+00 6.249E-03 5.878E+00 4.405E-03 5.944E-04 0.000E+00
5.000E-02 5.446E+00 6.276E-03 5.453E+00 5.289E-03 6.457E-04 0.000E+00
5.500E-02 5.092E+00 6.302E-03 5.099E+00 6.238E-03 6.955E-04 0.000E+00
6.000E-02 4.793E+00 6.328E-03 4.799E+00 7.250E-03 7.440E-04 0.000E+00
7.000E-02 4.315E+00 6.381E-03 4.321E+00 9.450E-03 8.375E-04 0.000E+00
8.000E-02 3.948E+00 6.437E-03 3.955E+00 1.187E-02 9.269E-04 0.000E+00
9.000E-02 3.659E+00 6.497E-03 3.665E+00 1.450E-02 1.013E-03 0.000E+00
1.000E-01 3.425E+00 6.560E-03 3.431E+00 1.732E-02 1.096E-03 0.000E+00
1.250E-01 2.996E+00 6.733E-03 3.003E+00 2.514E-02 1.292E-03 0.000E+00
1.500E-01 2.706E+00 6.925E-03 2.713E+00 3.393E-02 1.477E-03 0.000E+00
1.750E-01 2.498E+00 7.134E-03 2.505E+00 4.353E-02 1.652E-03 0.000E+00
2.000E-01 2.341E+00 7.357E-03 2.349E+00 5.385E-02 1.819E-03 0.000E+00
2.500E-01 2.124E+00 7.843E-03 2.132E+00 7.627E-02 2.137E-03 0.000E+00
3.000E-01 1.982E+00 8.377E-03 1.990E+00 1.006E-01 2.438E-03 0.000E+00
3.500E-01 1.883E+00 8.952E-03 1.892E+00 1.264E-01 2.728E-03 8.781E-04
4.000E-01 1.811E+00 9.563E-03 1.820E+00 1.534E-01 3.011E-03 1.827E-02
4.500E-01 1.756E+00 1.021E-02 1.766E+00 1.813E-01 3.290E-03 3.821E-02
5.000E-01 1.714E+00 1.088E-02 1.725E+00 2.099E-01 3.565E-03 5.986E-02
5.500E-01 1.681E+00 1.159E-02 1.693E+00 2.392E-01 3.839E-03 8.276E-02
6.000E-01 1.655E+00 1.231E-02 1.668E+00 2.690E-01 4.112E-03 1.066E-01
7.000E-01 1.618E+00 1.383E-02 1.632E+00 3.296E-01 4.657E-03 1.562E-01
8.000E-01 1.593E+00 1.543E-02 1.609E+00 3.914E-01 5.204E-03 2.072E-01
9.000E-01 1.577E+00 1.709E-02 1.594E+00 4.539E-01 5.754E-03 2.587E-01
1.000E+00 1.566E+00 1.882E-02 1.585E+00 5.168E-01 6.308E-03 3.102E-01
1.250E+00 1.553E+00 2.339E-02 1.577E+00 6.751E-01 7.716E-03 4.363E-01
1.500E+00 1.551E+00 2.828E-02 1.580E+00 8.335E-01 9.157E-03 5.566E-01
1.750E+00 1.555E+00 3.342E-02 1.588E+00 9.914E-01 1.063E-02 6.704E-01
2.000E+00 1.560E+00 3.876E-02 1.599E+00 1.148E+00 1.213E-02 7.777E-01
2.500E+00 1.575E+00 4.998E-02 1.625E+00 1.459E+00 1.520E-02 9.746E-01
3.000E+00 1.590E+00 6.176E-02 1.651E+00 1.764E+00 1.835E-02 1.152E+00
3.500E+00 1.604E+00 7.400E-02 1.678E+00 2.064E+00 2.155E-02 1.312E+00
4.000E+00 1.617E+00 8.662E-02 1.704E+00 2.360E+00 2.479E-02 1.459E+00
4.500E+00 1.630E+00 9.956E-02 1.729E+00 2.651E+00 2.805E-02 1.595E+00
5.000E+00 1.641E+00 1.128E-01 1.754E+00 2.938E+00 3.134E-02 1.721E+00
5.500E+00 1.651E+00 1.263E-01 1.778E+00 3.221E+00 3.465E-02 1.839E+00
6.000E+00 1.661E+00 1.400E-01 1.801E+00 3.501E+00 3.796E-02 1.949E+00
7.000E+00 1.678E+00 1.680E-01 1.846E+00 4.049E+00 4.459E-02 2.152E+00
8.000E+00 1.693E+00 1.968E-01 1.890E+00 4.584E+00 5.122E-02 2.334E+00
9.000E+00 1.706E+00 2.261E-01 1.932E+00 5.108E+00 5.781E-02 2.500E+00
1.000E+01 1.718E+00 2.558E-01 1.973E+00 5.620E+00 6.437E-02 2.652E+00
1.250E+01 1.742E+00 3.320E-01 2.074E+00 6.855E+00 8.050E-02 2.984E+00
1.500E+01 1.761E+00 4.102E-01 2.171E+00 8.033E+00 9.619E-02 3.267E+00
1.750E+01 1.777E+00 4.899E-01 2.267E+00 9.160E+00 1.114E-01 3.513E+00
2.000E+01 1.791E+00 5.707E-01 2.362E+00 1.024E+01 1.261E-01 3.731E+00
2.500E+01 1.813E+00 7.350E-01 2.548E+00 1.228E+01 1.540E-01 4.106E+00
3.000E+01 1.831E+00 9.020E-01 2.733E+00 1.417E+01 1.799E-01 4.422E+00
3.500E+01 1.845E+00 1.071E+00 2.916E+00 1.594E+01 2.041E-01 4.694E+00
4.000E+01 1.857E+00 1.241E+00 3.099E+00 1.761E+01 2.266E-01 4.934E+00
4.500E+01 1.868E+00 1.413E+00 3.281E+00 1.917E+01 2.476E-01 5.148E+00
5.000E+01 1.877E+00 1.586E+00 3.463E+00 2.066E+01 2.673E-01 5.342E+00
5.500E+01 1.886E+00 1.760E+00 3.646E+00 2.206E+01 2.858E-01 5.519E+00
6.000E+01 1.893E+00 1.934E+00 3.828E+00 2.340E+01 3.032E-01 5.681E+00
7.000E+01 1.906E+00 2.286E+00 4.192E+00 2.590E+01 3.350E-01 5.971E+00
8.000E+01 1.918E+00 2.639E+00 4.557E+00 2.819E+01 3.634E-01 6.225E+00
9.000E+01 1.928E+00 2.994E+00 4.922E+00 3.030E+01 3.891E-01 6.451E+00
1.000E+02 1.936E+00 3.351E+00 5.288E+00 3.226E+01 4.123E-01 6.654E+00
1.250E+02 1.954E+00 4.248E+00 6.203E+00 3.662E+01 4.620E-01 7.087E+00
1.500E+02 1.969E+00 5.151E+00 7.120E+00 4.038E+01 5.025E-01 7.443E+00
1.750E+02 1.981E+00 6.059E+00 8.040E+00 4.368E+01 5.363E-01 7.746E+00
2.000E+02 1.992E+00 6.969E+00 8.961E+00 4.662E+01 5.650E-01 8.010E+00
2.500E+02 2.010E+00 8.797E+00 1.081E+01 5.170E+01 6.114E-01 8.451E+00
3.000E+02 2.024E+00 1.063E+01 1.266E+01 5.597E+01 6.474E-01 8.813E+00
3.500E+02 2.036E+00 1.247E+01 1.451E+01 5.965E+01 6.764E-01 9.119E+00
4.000E+02 2.046E+00 1.432E+01 1.636E+01 6.290E+01 7.003E-01 9.385E+00
4.500E+02 2.055E+00 1.616E+01 1.822E+01 6.579E+01 7.204E-01 9.620E+00
5.000E+02 2.064E+00 1.801E+01 2.008E+01 6.841E+01 7.376E-01 9.830E+00
5.500E+02 2.071E+00 1.986E+01 2.194E+01 7.079E+01 7.525E-01 1.002E+01
6.000E+02 2.078E+00 2.172E+01 2.379E+01 7.298E+01 7.656E-01 1.019E+01
7.000E+02 2.090E+00 2.543E+01 2.752E+01 7.688E+01 7.874E-01 1.050E+01
8.000E+02 2.100E+00 2.914E+01 3.124E+01 8.029E+01 8.051E-01 1.077E+01
9.000E+02 2.109E+00 3.286E+01 3.497E+01 8.331E+01 8.197E-01 1.100E+01
1.000E+03 2.117E+00 3.658E+01 3.870E+01 8.603E+01 8.320E-01 1.121E+01

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