Field Precision title

Target optimization and forward dose calculation for a pulsed radiographic facility (1)

A common application of GamBet (our Monte Carlo radiation code) is the determination of the X-ray distribution emitted from a bremsstrahlung target and the forward dose at a distance. In this note and the next, I will work through an example to suggest the best approach to a solution. I will use parameters typical of my area of expertise, high-energy pulsed radiography for defense applications. In particular, I will consider a 6.0 MeV, 60 ns electron beam focused to a point on a tungsten target. We want to answer two questions: 1) what is the best choice of target thickness? and 2) how is the beam current related to the forward dose 1 m from the target? I will address the second issue in another note.

We will use cylindrical coordinates in a 2D GamBet calculation and assume a 1.0 A point beam of electrons moving in z at r = 0.0 mm. The beam strikes a tungsten plate of thickness D. To begin, we need to find what range of D is of interest. Clearly D must be less than the electron range in the material. A thicker target has higher self-absorption of the photons with no increase in bremsstrahlung radiation, while a thin target has low conversion efficiency. We expect that there is an optimum thickness to maximize the forward energy-flux of X-rays.

I used information available on the NIST EStar site to find the range of 6.0 MeV electrons in tungsten. Here is a link:

http://physics.nist.gov/PhysRefData/Star/Text/ESTAR.html

Select Tungsten (Z = 74) and press Submit. Check the boxes CSDA range and Radiation yield and click Download data to create a text list that you can copy and paste. I used Show composition data to find the normal density of tungsten, 19.3 gm/cm3. The radiation yield is 21.57% and the normalized range is Rn = 4.265 g/cm2. Dividing by the density, the range in solid tungsten is R = 2.210 mm. This value is the integrated length along an electron path. Because there is strong scattering, the average distance of penetration into material is smaller. With this in mind, I investigated a series of sheets with thicknesses from D = 0.1R to D = 0.7R (1.5469 mm).

For a thin target, the mean angle of forward bremsstrahlung emission for a relativistic electron beam is approximately 1/γ. The value γ = 1.0 + 6.0/0.511 = 12.74 corresponds to 4.5 deg. The emission for a thick target is considerably larger because of electron scattering. I picked the following mesh dimensions:

  • Along z, I set up a zone from 0.0000 mm to 1.5469 mm (the maximum target thickness) with 14 divisions to resolve the different thickness.
  • I included an axial zone at coarse resolution that extended to 20.0 mm. This zone had the Void property in the GamBet calculation. The intention is to record photon positions in the escape file at 20.0 mm rather than at the target exit surface. The purpose will be apparent when we discuss dose calculations in the next post.
  • I extended the simulation volume to 20.0 mm in the radial direction.

Here is a full listing for the GamBet control script TARGET60.GIN:

GEOMETRY
  DUnit 1000.0
  GFile2D TARGET60.MOU Cylin
END
COMPOSITION
  Material W
  Region(1) = Void
  Region(2) = 1
END
SOURCE
  SList
    E  6.0E6  0.00001 0.00 0.00001  0.00 0.00 1.00  1.00
  End
  NPMult = 20000
END
PROCESS
  EAbs Electron 5.0E4
  EAbs Photon 5.0E4
  EAbs Positron 5.0E4
  C1 0.10
  C2 0.10
  WCc 5.0E4
  WCr -5.0E4
  DsMax(1) = 0.01
  Force Brems 50.0
END
ENDFILE

The commands of the Geometry section load the mesh created from TARGET60.MIN, interpreting dimensions in cylindrical coordinates with units of mm. In the Composition section, Material 1 is set as tungsten and associated with Region 2. The Source section defines a mono-enegetic 6.0 MeV point electron beam. For good statistics, I used 20,000 primaries. In the Process section, I set cutoffs to ignore photons and electrons with energy less than 50 keV and employed a bremsstrahlung forcing factor of 50.0.

The escape file for the run contained all the electrons, photons and positrons that left the solution volume. It is important to remove the electrons and positions because they would skew the dose calculations discussed in the next post. I also wanted to limit photons to those traveling in the forward direction (i.e., those that left the boundary at z = 20.0 mm with radius less than 9.99 mm). To perform the operations, load the file TARGET60ESC.SRC into GenDist. The load takes several seconds because of the large number of photons. Click on Analysis/Apply filter and use the radio buttons to include only photons. Choose plot type 1D bins and plot quantity f(Angle). Click on Record/Plot data to file and supply a file prefix. The plot of df/dθ shows that the flux density is uniform out to about 10 deg and then falls slowly. From an inspection of the integrated probability, we find that 50% of the photons are contained within an angle of 47.23 deg. The value is much higher than the thin-target prediction because of electron scattering.

Return to Apply filter to limit photons to those in the forward direction. Set ZMin = 19.99 mm and RMax equal to 9.99 mm (i.e., include electrons to an angle of about 26.6 deg). Now click on File/Write SRC file and save the filtered distribution. This file will be used in the calculations discussed in the next post. Now load the filtered file. GenDist displays a dialog of statistical information including the number of photons and their average energy. For the target D = 0.4*R, the numbers are about 178,267 photons and 1.113 MeV. We can use the values to calculate an effective energy conversion efficiency for forward-directed photons. The value equals the number of photons times their average energy divided by the number of primary electrons times 6.0 MeV. We must also include a factor 1/50 because the number of photons in the escape file has been increase by the bremsstrahlung forcing factor. The result is 3.307%. The value is well below the total radiation yield of 21.57%, primarily for two reasons: 1) a significant fraction of photons have angles larger than 26.6 deg and 2) electron energy is lost by transmission or backscatter. For comparison, GamBet accounts for all energy conversion processes to an accuracy of 0.068%.

The following table shows results as a function of target thickness. There is a broad maximum in energy conversion efficiency at a target thickness of D = 0.4*R = 0.8839 mm. Inspection of the average photon energy shows the the spectrum hardens as the target thickness increases, the result of target absorption of low-energy photons. The illustration below shows the energy-weighted spectrum for the optimal target.

Range fraction Filtered escape file Radiative efficiency Average energy (MeV)
0.1 target0601.src 2.072% 1.084
0.2 target0602.src 2.810% 1.081
0.3 target0603.src 3.201% 1.109
0.4 target0604.src 3.307% 1.113
0.5 target0605.src 3.284% 1.155
0.6 target0606.src 3.230% 1.205
0.7 target0607.src 3.158% 1.250

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