Geometry / radioactivity distribution with detector response (dose rate / CPS) widget
Published: Apr 13, 2025
Source: Design & implementation by Dr Chris Robbins (Grallator) / Facilitated by Ionactive radiation protection resource
To make the most of this widget a little background information is required - this is presented first, then the widget, and then we explore what this means for radiation protection. Whilst the widget reflects specific circumstances (e.g. neutron activation of a tungsten cone collimator), it can be used to illustrate generally how dose rate or other response (such as CPS), as measured by a radiation monitor, is influenced by geometry and radioactive source distribution.
Why this widget
We were at a client site considering neutron activation in tungsten collimators which are a component of linear accelerators, and how this might be measured to determine the activity, and therefore if the item would meet out of scope or exempt requirements for recycling. Noting the widget shape below, in simple terms an electron beam from a linear accelerator enters the collimator just inside the small hole where it hits a tungsten target. The resulting bremsstrahlung x-rays are directed through the collimator and exit at the larger end of the cone (for onward shaping). For energies above about 10MV, neutrons are produced, which for the application being considered, are adventitious. The production of neutrons will then lead to neutron activation of elements within the cone material (typically W-181, W-185, W-187). At the end of system life, and after a suitable decay period (typically required for systems operating > 10MV), the collimator is removed and considered for recycling.
It is at this point that the idea of the widget was conceived. How would the location and spread of neutron activated material effect the dose rate measured, and how could this be used to estimate radioactivity (e.g. in Bq/g). Radioactivity estimation is not considered in the widget, only how geometry and radioactivity distribution might effect what the dose rate monitor indicates. Whilst we mention dose rate, equally valid would be any suitable counter - such as a CPS (counts per second monitor).
The theory behind the widget can apply to any geometrical shape with radioactive surface contamination (and this does not need to be neutron induced). Have a play with the widget and then consider a worked example.
Tip: Upon first loading (or reloading) the webpage, the widget will reset to a particular set of conditions. Before changing the shape of the cone, or moving the detector, can you reach 100 dose rate /cps "units" - and where does this occur? Use the red controls to find out!
Further considerations
What the widget does (and how)
A basic explanation of what the widget is doing is available by clicking on the 'i' icons.
The first 'i' presents a schematic of the geometry and how it can be changed by the green and yellow sliders. It also shows how the position and extent of the activation can be set (using the red sliders). Think of the activation as being a band around the inner surface of the cone.
The second 'i' presents a basic schematic of the calculation process including the necessary simplifications (for example build up is not taken into account).
It should be noted that radioactivity (Bq) is not specified, and the output "dose rate" are in unspecified units. However, the output is proportional to the input (for a given geometry and activation spread). The output figures are as follows:
Dose rate, uniform distribution - This is the dose rate (which could also be CPS) in unspecified units, where the activation (radioactivity) is uniformly spread within a specified region of the inner surface of the cone.
Dose rate, linear reducing distribution - this is the dose rate (or CPS etc) where the radioactivity is reduced linearly with distance from the start point (along the inner surface of the cone).
Dose rate, point source - This is literally as described, and placed at the centre line of the cone (i.e. where the perpendicular height of a cone could be measured). Activation extent has no effect on this output (as expected). This is treated as a virtual source, whereas the two outputs above are representative of actual radioactivity distribution.
The dose rate from the point source (an idealised case and not always a good approximation), can then be compared with the more realistic geometry as already described (and which can be adjusted using the green sliders).
The effect of moving the detector away from the cone can also be explored using the yellow slider.
Practical example for radiation protection
[Ionactive comment: This widget is for educational use only, it is not designed to infer actual radiation protection decisions].
Consider the following situation:
- A dose rate measurement is made at the larger surface of the cone collimator. The indicated measurement is 5 micro Sv/h (beta / gamma).
- The cone has the following dimensions (which can be set using the widget above - try it). Small hole (2 cm), large hole (7 cm), block thickness (11 cm), activation start (0.0 cm), activation extent (1 cm), measurement distance (0.0 cm) - i.e. surface.
The situation should look as indicated in the diagram below.
Geometry / radioactivity distribution widget with settings as noted above.
An assessment is made that the likely radionuclides creating the dose rate observed are W-181, W-185 and W-187. The distance between the detector and the point source is 11 cm (i.e. the block thickness).
A software program such as MicroShield (or similar) is used to predict the activity from the dose rate (using the point source). This could also be calculated by looking up specific gamma ray constants for each radionuclide (i.e. X micro Sv/h per MBq per 10 cm etc). The actual technique is outside the scope of this widget discussion. It is shown that the point source (a virtual source) contains 820 kBq of each radionuclide.
Note that
- the calculated 820 kBq assumes a point source, where as
- the measured dose rate (5 micro Sv/h) is from the actual geometry described.
Note the results from the widget for the situation described:
- Dose rate, uniform distribution - 10.5 units
- Dose rate, linear reducing distribution - 10.2 units
- Dose rate, point source - 9.6 units
If we assume a uniform distribution (for example) we can now correct the assessed activity of each radionuclide as follows: 9.6/10.5 x 820 kBq = 750 kBq. A modest difference, and an understandable and sensible result.
If you are not quite sure where this subtle but important difference comes from, try something more extreme (far from realistic for our particular neutron activation example, but absolutely relevant for a different scenario). Set the activation extent to 7 cm so you get the following widget settings as indicted below.
Geometry / radioactivity distribution widget with activation extended to 7 cm
This yields the following:
- Dose rate, uniform distribution - 25.9 units
- Dose rate, linear reducing distribution - 18.4 units
- Dose rate, point source - 9.6 units
Recall we were measuring 5 micro Sv/h - now we are measuring 13.5 micro Sv/h. [Ionactive note: for this example we calculated the dose rate (for the purposes of illustration), however in reality this figure would be measured with a suitable radiation detector].
We can again assume there is a virtual point source - and it is still 11 cm from the detector.
Using the same shielding program or specific gamma ray data - we calculate there is now 2214 kBq (at the point source) - which yields the 13.5 micro Sv/h at 11cm. This is not true, since the activation is spread as shown above in the diagram, and remember the total activity (activation) has not changed, only it's distribution.
You can correct the activity back as follows (like before). 2214 kBq x (9.6 / 25.9) = 820 kBq (as expected).
Whilst this widget is for training / information purposes only, the principles it demonstrates could be used to correct activity assessments with variable source geometry and activation extent from detector measurements.