exposure rate calculations

www.gonuke.org/acad/Exposure%20Rate.ppt

may be useful

Thank you, Dr. Mushtaq Ahmad. 

Dear Md Firoz,

The right address: [email protected]  

(Luka Perazic)

Regards,

Branislav Vulevic

The calculation of air kerma rates at different distances from line sources is given in standard texts of radiation dosimetry or physics of radiology. It is a simple exercise to do this calculation mathematically (requires knowledge of integral calculus). See for example the latest edition of Physics of Radiology by H.E. Johns and J.R.Cunningham, cheaper editions of which may be available on enquiry.

Radpro just calculates point sources no lines, and especially no lines which shield each other.

Most cobalt-60 sources for industrial or medical use are made of cobalt pellets double encapsulated in stainless steel tubes. These pellets can be mounted with small gaps between them and larger gaps on the pencil's corners (or heads). The lengths of those pellets is the real source length. The encapsulation's radiation absortion and the self-absortion of the cobalt pellets should be accounted, too. It is not only a pure line source, but a series of small line sources. I advise you to get the sources and sources rod designs to calculate it. Integral formulas can be used were each infinitesimal pellet length can be treated as point kernel source. A good mathematics exercise. 

Good job. 

To add to my comments above, I agree with the suggestions given above by Hanno Krieger and Nelson Omi above. Vide your experimental measurements for the cylindrical geometry with the Fricke dosimeter, for verifying by actual calculation at a specified distance, the contribution by all the line sources (perpendicular to their centres) must be integrated, taking into account the self-absorption by needles, the absorption by the encapsulation and the attenuation of other line sources coming in a particular direction. This may explain the difference in dose at a given distance in four directions given in your reference. Since these theoretical calculations(though worth a trial) may be cumbersome, I feel it is better to measure the dose quickly using a remote-operated calibrated ion chamber system for better accuracy and precision. Alternatively, you can also use calibrated TL or OSL dosimeters as replacements for the Fricke dosimeter.

Mr Sankaran is righ, but sometimes it is not possible to place probes due to its size or the radiation resistance of the electronics or cables reaching the ion chamber.

Another alternative is to use Alanine dosimeters and EPR instead of the Fricke dosimeter, they also have a wide range of total dose absortion. The irradiator shown in the document is useful for small amounts of products. For these irradiators, the source exposure takes some time and the source lifting and lowering exposure rates should be accounted, too. The longer the source is exposed, the better the average dose rate measuring fits the calculations.

Other deviations are the walls around the device. In some cases, the backscattered radiations are not small enough. The table scattering is another way to add doses to the product.

For practical use it is better to determine the real dose rates using the dosimeters as long as the product amount, densities and shapes also change the product absorbed doses.   

Thank you everyone for your informative comments.

FYI, I would like to mention few things:

1. We use Fricke dosimetry system for low-dose (

it is better to look at Rad Pro Calculator

http://www.radprocalculator.com

Try the Engineering Compendium on Radiation Shielding. This compendium, although a little old (1968 edition) is very useful. It was edited in times were computational methods were rare and, thus, is full of mathematical equations and graphics. If it don't solve your practical problem, at least it will give you a view without our modern tools, as many other old books.

I'm sure that linear sources, as long as planar sources are studied there (and math equations). Some nuclear data may be outdated (although not far from the updated ones), but the physical principles doesn't change with time. The modern tools lead us to forget the origin of the calculations.

Of course, there may be other good books to be reviewed.

R. G. Jaeger, E. P. Blizard, A. B. Chilton, M. Grotenhuis, A. Honig, T. A. Jaeger, and H. H. Eisenlohr, Eds., Engineering Compendium on Radiation Shielding, Springer-Verlag, New York (1968). 

Re: comments of Nelson Omi: Nowadays, cable-connected precision ion chamber-electrometer systems with miniature ion chambers(for high range) are available. The electrometer reading system can be therefore located in a radiation-free area. As per the table, the dose at 1m distance for the source configuration is about 600 rads/min which can be accurately estimated. The cables used are double-screened antimicrophonic type with minimum noise and radiation-induced conductivity. If needed, the cable can be routed so the exposed parts may be kept away from the radiation sources. Both dose and dose rates can be measured here. The errors due to the addition of doses contributed by raising and lowering of sources and room/table scatter can be taken into account by measuring the TOTAL dose to the sample under actual conditions. This method will thereby provide a secondary check on the Fricke dosimetry which involves some assumptions for spectrophotometer dosimetry calculation. Besides, ion chamber dosimetric systems calibrated against primary standards in NIST/BIPM/NPL laboratories are available from several companies. Hope this helps. Thanks.

Well, Dr. Sankaran Ananthanarayanan  comments are very helpful. I do agree that there is no better way to determine the total dose or dose rates than using calibrated measuring devices. It will be very difficult to estimate the real doses or dose rates, even considering the conditions stated in this question. That's why the product irradiation process certification must be done using dosimeters and the process unchanged (shapes, densities, positioning and other parameters like product initial bioburden in the case of biological control). Even with a known irradiation setup very well studied, you may not extrapolate to other setup just replacing the product with other with similar weight and external dimensions. The product's internal arrangements may be different and the minimum dose place and value may change, for example.

If your question is only provide estimative doses, then a number of ways of calculating was presented, but exact numbers (with about 1% error, for example) is got only with measured processes.

And, unfortunately less than 1% errors in usual processes can take substantial efforts an become not practical.

I hope all of our comments help you.

Best regards