Hi,
Here is my problem that I am trying to figure out.
In an x-ray tube, let's say we know the target material (say Tungsten) and we also know the tube potential (say 250 kV) so that we know the maximum possible energy of the photons (250 keV). We can also calculate (or find in a table such as NIST) the energies of all the possible characteristic lines. But how do I find the fraction of the characteristic lines in comparison to the Bremsstrahlung part in the spectrum? We can also consider that low energy x-rays below certain threshold (e.g. 10 keV) are filtered out. I could find a table in NPL,[ http://www.kayelaby.npl.co.uk/atomic_and_nuclear_physics/4_2/4_2_1.html ] which gives the K and L line intensities relative to the line in the series which is normally the strongest. I am looking for a way to find the fraction with respect to the Bremsstrahlung part in a given spectrum. I am assuming that due to the very high flux of the beam and other constraints it is impossible to measure the x-ray spectrum using any kind of detectors.
A complete treatment of the continuous X-ray spectrum and also charecteristic X-ray lines are treated in Chapter 2 and 3 of the book:
X-rays in atomic and nuclear physics, N.A. Dyson, second edition, Cambridge University Press (1990)
In the same book (given above) the ratio of the characteristic to continuous radiation from thick targets have been discussed on p. 120.
Your assumption:
I am assuming that due to the very high flux of the beam and other constraints it is impossible to measure the x-ray spectrum using any kind of detectors.
is not true. The above book gives the results of measurements of the intensities of both continuous and characteristic X-rays from the literature. There exists also theoretical estimates which have also been considered in the book.
I referred to the above book because it covers the literarture up to date. If you do not have this book (I have it on my bookself) then consult the older classic book " X-ray in theory and experiment" by Compton and Allison.
There is a number of simple computer programs that simulate the spectra emitted by an x-ray tube. I do not have the reference available right now, unfortunately. I will look for it.
It is possible to read also the "Handbook of X-ray Spectrometry", by Van Grieken and Markowitz. This is a very complete book.
Measurement is possible, but non-trivial. Modeling can surely provide an answer, but the required effort strongly depends on what you actually need the information for and how precise an answer you want. So you should give a bit more background information. A few things: do you consider fraction to be the relative photon counts or the energy carried by both types of radiation? Actual photon energy or air dose? Your 10 keV threshold is right in the middle of tungsten L-radiation. Attenuating that by varying amounts will for example strongly influence the relative photon counts. You will need more information about target angle and tube window, along with any other attenuating layers.
Hi Andreas, thank you for your reply. Here I am talking about the relative photon counts coming out of a target due to only characteristic emission in a whole x-ray spectrum and not the air dose but the actual photon energies. The x-ray machines that I am talking about are either diagnostic or the therapeutic x-rays that are being used in different hospitals. The whole purpose is to find the x-ray spectrum coming out of the machine without using a direct measurement. Yes you are right, the measurement is possible. But my understanding is to measure the x-ray spectrum directly one needs to attenuate the beam so much before it reaches to the detector and in this way I cannot get the exact spectrum that goes to the patient or any phantom. The detector may saturate soon due to high flux of the photons beam (efficiency of the detector). And several other reasons including the size of the detector relative to the field of view of the beam and etc.
I would be happy if you suggest some ways or the detectors that I can use in the kilo Volt and Mega Volt beams to measure the x-ray spectrum directly. Any useful links will be appreciable. I guess I may also be able to find the target information such as target angle, its thickness, tube window and additional filters if used any for a particular machine.
Thank you Javier for your reply. I will take a look at that book. Please provide me any additional information related to this question that you can find. I appreciate your time.
So, if I understood that right, you really want to know (an estimate of) the whole spectrum, not specifically the ratio of characteristic radiation to bremsstrahlung. Analytical models, as probably found in the books mentioned above, can likely give you a good general idea, but will not be very accurate for a particular tube. A semi-analytical model (most likely what Javier Miranda was referring to) should be suitable for standard x-ray tubes. SpekCalc (see attached link and related publications) is one from the medical field you might want to look at. I have not used that software, but would expect it to perform well for this purpose from reading two of their background papers. I could probably also provide you with a copy of my own model (developed for use in non-destructive testing). If you want a more general accurate model, a Monte Carlo code is an option. Among those BEAMnrc is fairly fast and not too complicated to use. In particular for Megavolt beams, which you mentioned in your answer, this is the way to go.
Measurement is indeed unlikely to be successful in the described situation. As you mention, filtration would strongly influence the result. The alternative is collimation and sufficiently increasing the distance between source and detector. For the sources you describe the latter is probably not feasible.
Article SpekCalc: a program to calculate photon spectra from tungste...
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