The effectiveness of a Two-Foot Thick Inner Heavy Concrete Wall

D. Beavis

Dec. 11, 2006

The outside shield wall of the ERL test area is four feet of light
concrete. This shield does not provide sufficient (ref. 1) attenuation
for the potential radiation from forward faults of the 25 MeV electron
beam. Various schemes have been suggested for introducing shielding
close to the beamline for additional radiation reduction. In this note
the effectiveness of using two feet of heavy concrete as an inner shield
wall will be examined. It will be concluded that this should provide
sufficient reduction of the radiation.

MCNPX (Ref. 2) can be used to estimate the dose due to photons.
Azimuthal symmetry will be used for the problem. The front face of the
target is placed 300 cm in front of the four feet thick light concrete
shield wall. The 25 MeV beam strikes the front of the target with a
direction perpendicular to the shield wall. Initial calculations are
done with the existing light concrete wall and then a two feet thick
layer of heavy concrete is added 1 meter from the target. The photon
doses are tallied on the inner and outer surface of the light concrete
wall.

The composition of heavy concrete was obtained by supplementing the
composition of the light concrete with iron to achieve a density of
3.5gm/cc. The density for light concrete is 2.35 gm/cc. The compositions
by atomic fractions are given in Table I.

## Table I. Atomic Fractions

  ----------------- ------------------------- ---------------------------
  atom              Light concrete            Heavy concrete

  H                 0.135                     0.107

  O                 0.6529                    0.515

  Si                0.1185                    0.094

  Al                0.0182                    0.014

  Ca                0.0754                    0.060

  Fe                0.0                       0.21
  ----------------- ------------------------- ---------------------------

The target used for the calculations was a steel cylinder with a radius
of 2 cm and a length of 5 cm. Most materials close to the beam are
similar in atomic number to iron so steel was a natural choice for the
target material. The forward losses of electrons and photons typically
have several inches of steel equivalent in their path due to the
beampipe, quadrupoles, and dipoles. The sensitivity to the target
geometry was examined and some results for the forward position
(radius\<15cm) on the inner surface of the light concrete shield wall
are shown in Table 2. The dose at large distances can decrease as the
target becomes thin and more of the electron energy is lost in the
initial part of the concrete wall rather than the target. Although
smaller targets can give higher radiation doses on the shield wall it
was decided that the target parameters above were a reasonable
approximation for the target mass.

Table 2. Photon Dose at R\<15cm

+------------------+-------------------------+-------------------------+
| Target Length    | Target Radius           | Rem per                 |
| (cm)             |                         |                         |
|                  | \(cm\)                  | Incident electron       |
+------------------+-------------------------+-------------------------+
| 10               | 2                       | 1.2E-14                 |
+------------------+-------------------------+-------------------------+
| 5                | 2                       | 4.4E-14                 |
+------------------+-------------------------+-------------------------+
| 2.5              | 2                       | 8.1E-14                 |
+------------------+-------------------------+-------------------------+
| 1.5              | 2                       | 1.1E-13                 |
+------------------+-------------------------+-------------------------+
| 1.5              | 1                       | 1.1E-13                 |
+------------------+-------------------------+-------------------------+
| 1.5              | 0.5                     | 1.1E-13                 |
+------------------+-------------------------+-------------------------+
| 0.75             | 0.5                     | 1.3E-13                 |
+------------------+-------------------------+-------------------------+

The dose as a function of distance from the beam axis is shown in
Figure 1. The data are averaged over radial bins ranging from 15cm to 50
cm in width. The red circles display the photon dose on the inner
surface of the concrete wall. The green squares show the dose on the
outside of the four feet of light concrete. The radial bin with R\<15cm
has the dose decrease by 0.0015 after 4 feet of light concrete. The blue
triangles display the dose on the inner surface with the heavy concrete
wall present. The dose for R\<15 is reduced by 0.005. The application of
concrete and steel TVLs would have given a reduction of 0.007 (see Ref.
1). The statistics in the simulation are not sufficient to extract the
dose at the outer surface. The factor of 0.0015 from the light concrete
can be used to estimate the dose for R\<15cm on the outer surface to be
3.3E-19 rem/e.

![](media/image1.png){width="5.997222222222222in"
height="3.7430555555555554in"}

The dose rate can be estimated assuming a rate of beam loss. A 50kW beam
loss (0.926 mA) has an estimated dose rate of 3000 rem/hr (R\<15cm) for
the configuration without the inner heavy concrete wall. This result
compares well with a thick target formula with concrete TVL's, which
would estimate 6600 rem/hr (Ref. 1 with geometry differences taken into
account). The addition of the two feet of heavy concrete reduces the
maximum dose to 15 rem/hr for a 50 kW beam loss. Most situations have
the source of forward radiation at greater distance from the shield wall
and have a non-zero angles to the shielding. The routine losses are
expected to be at least 1000 times lower than a 50 kW loss.

# Conclusions

A simple estimate of the dose rate outside the ERL test area sidewall
shielding is made incorporating a proposed two-foot thick inner heavy
concrete wall. The estimate of 15 rem/hr for a 50 kW beam loss would be
within guidelines with chipmunks distributed to detect large beam
losses. Actual beam loss configurations are expected to have reduced
radiation due to increased distance and angles relative to the
shielding. In addition, a 50 kW localized beam loss is not expected to
be possible.

# References

1)  D. Beavis Memorandum, "Simple Estimate of ERL Radiation", August 9,
    2006.

2)  D. B. Pelowitz,Ed. "MCNPX User's Manual, Version 2.5.0", April 2005;
    version 2.5f was used for these calculations