**Energy Deposition on the Roman pot window of the pp2pp/STAR
experiment.**

**March 13, 2007**

**Kin Yip**

**Collider-Accelerator Department**

This is a summary of the energy deposition simulation on the steel
window of the Roman pot of the pp2pp/STAR experiment.

# Simulation Details

The simulation software used is "MCNPX" with the newest version 2.6.c
(at the time of writing). In the simulation, a proton beam of 100 GeV is
bombarded with normal incidence onto the center of a steel window of a
Roman pot with a cross-section of 5 cm (in x-direction) 10 cm (in
y-direction) and the thickness in the beam (z) direction is *t* =
0.03048 cm ( 12 mils ).

One version of the input file is as shown below.

Roman Pot (pp2pp)

c

10 1 -7.8 -10 imp:n,p,h,/,z=1

c

11 0 10 -11 imp:n,p,h,/,z=1

c

999 0 11 imp:n,p,h,/,z=0

10 rpp -2.5 2.5 -5. 5. 0. 0.03048

11 rpp -3.0 3.0 -6. 6. -1. 1.

mode n p h / z

c

c Steel

c

m1 6000 -.0003 \$ .0003 carbon

7014 -.0009963 7015 -.0000037 \$ .001 nitrogen

14000 -.0075 \$ .0075 silicon

15031 -.00045 \$ .00045 phosphorous

16032 -.0003 \$ .0003 sulpher

24050 -.00862 24052 -.16752 \$ chromium

24053 -.0191 24054 -.00476 \$ .20 chromium

25055 -.02 \$ .02 manganese

26054 -.03785619 26056 -.5962025 \$ iron

26057 -.01424486 26058 -.002146485 \$ .65045 iron

28058 -.0814176 28060 -.0314736 \$ nickel

28061 -.0014256 \$ nickel

28062 -.0043896 28064 -.0012936 \$ .12 nickel

mx1:p 6012 j j 14028 18j

mx1:h 6012 j j 14028 18j

c

c

sdef par=9 erg=100000 dir=1 vec=0 0 1 x=D1 y=D2 z=-0.1

c

SP1 -41 0.131869922522 0. \$ sigma = 0.056 cm =\> FWHM = 2 sqrt(2 ln
2)sigma

SP2 -41 0.101257261936 0. \$ sigma = 0.043 cm =\> FWHM = 2 sqrt(2 ln
2)sigma

c

F6:n 10

F16:h 10

F26:p 10

c

e0 1000 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

c

nps 10000000

c

phys:n 100001

c

c phys:p 100001 2j -1 =\> analog 1 =\> biased

c

phys:p 100001 2j -1

c

phys:h 100001

phys:z 100001

phys:/ 100001

c

print

prdmp 2j 1

c

tmesh

rmesh3 total

CORA3 -2.5 100i 2.5

CORB3 -5.0 100i 5.0

CORC3 0.0 0.03048

endmd

As shown in the above input file, the beam is assumed to have a Gaussian
distribution in x and y with 's of 0.056 cm and 0.043 cm respectively.
The above input file also includes the detailed composition of steel,
which is what the author has typically used for steel. Photo-nuclear
reactions are switched on.

# Results

The simulation results are shown in the mesh tally plots over the
cross-section of the steel window. The colored contours shown in the
figures below have the unit of MeV/cm^3^ per incident proton. The energy
depositions are averaged over the entire thickness of the steel window
(0.03048 cm).

For the mesh tally plots as in both Figure 1and Figure 2 below, only
protons, neutrons and photons are transported in the MCNPX simulation.
The maximum energy deposition is 1.310^3^ MeV/cm^3^ per incident proton
in the center of the window. In Figure 3, ^0^ and are also transported
in the MCNPX simulation. This gives rise to a higher maximum energy of
2.110^3^ MeV/cm^3^ per proton in the center of the window.

![](media/image1.jpeg){width="5.993055555555555in"
height="4.861111111111111in"}

Figure 1: Mesh tally of energy depositions with 100 divisions in both x
and y directions.

![](media/image2.jpeg){width="5.995138888888889in"
height="4.968055555555556in"}

Figure 2: Same as Figure 1 but zoomed-in in the middle of the steel
window.

![](media/image3.jpeg){width="5.995833333333334in"
height="4.711111111111111in"}

Figure 3: Same as Figure 1 but ^0^ and are added in the MCNPX
simulation.

# Comparison with the old calculation

From the note with the subject title "Sample Calculations Relevant to
Roman Pot Protection" written by A.J. Stevens on Feb. 12, 2001, the
effective energy deposition determined was 2.7 MeV/g-cm^-2^. With this
number, a density of 7.8 g/cm^3^ and a window thickness of t = 0.03048
cm, the energy deposited would be about 2.7 7.8 t = 0.642 MeV.

The energy density would be 0.642/(t A~xy~) = 21.1/A**~xy~** MeV/cm^3^,
where A**~xy~** is the cross-section (the interaction area between the
beam and the surface) considered. If I take A**~xy~** to be 6**~xy~**
(\~95% of the beam), ie., A**~xy~ =** 60.056 0.043 cm^2^, the energy
density would be about 1.46 GeV/cm^3^.

This number obviously depends on what the "interaction area" is but the
energy density result is in the same order of magnitude as the present
result shown here.

# Comparison between MCNPX and MARS

MARS version 15.05 has been used to find the same energy deposition
peaks in the same geometry. In fact, in this simulation, the same MCNPX
geometry has been used as an input to the MARS program. The energy
deposition densities as a function of grid sizes are shown in Table 1
and Table 2. As the grid areas become smaller, it has becoming
increasingly difficult to gather enough statistics and a lot of
computational time has been spent in the last couple points. The last
point in each simulation has the largest uncertainty.

  ----------------------- ----------- ----------- ----------- ------------
  Grid (cm^2^)            0.050.1     0.020.025   0.0160.01   0.0080.005

  Energy Density          2.50        2.67        2.69        2.93
  (GeV/cm^3^)                                                 
  ----------------------- ----------- ----------- ----------- ------------

Table 1: Energy deposition densities on the Roman pot window by the
MCNPX simulation.

  ------------- --------- ----------- ----------- ----------- ------------ ------------- --------------
  Grid (cm^2^)  0.050.1   0.0250.05   0.020.025   0.0160.01   0.0080.005   0.0040.0025   0.0020.00125

  Energy        0.554     0.930       1.12        1.17        1.20         1.24          1.31
  Density                                                                                
  (GeV/cm^3^)                                                                            
  ------------- --------- ----------- ----------- ----------- ------------ ------------- --------------

Table 2: Energy deposition densities on the Roman pot window by the MARS
simulation.

The MCNPX and MARS energy density seem to settle down at different grid
areas. For the maximum energy deposition densities, the MCNPX results
seem to be slightly more than a factor of 2 over the MARS results. From
the MCNPX experts, their data file for electron stops at 1 GeV and the
same cross-section at 1 GeV is probably used for higher energies. This
might be one reason for the difference between these two simulation
packages.