Penetration |
Energy
The total distance which electrons can penetrate into a given material is more or less a linear function of the energy of the electrons (more energy = more penetration).
Density
The total distance which electrons can penetrate into a given material is a linear function of the density of the material (higher density = less penetration).
However, the dose is not at all equally spread within the product depth.
For a monoenergetic beam, a beam in which all the electrons have the same energy, the radiation effect varies approximately with depth in accordance with a curve known as the depth dose curve.
A family of such curves are shown below (graph #1) for four different energies.
As the beam penetrates further into the medium, the radiation effect continually increases until it reaches a maximum, after which it decreases to zero at the end of the "range". |
Graph #1
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Graph #2
Graph # 2 illustrates the fact that at the same energy level, penetration will be double in a product having half of the density.
In most industrial applications it is a common practice to consider that the energy level is adequate when the dose deposited inside the product is at least the same as the dose deposited at the surface. This point, for each energy, is known as the equal-entrance-exit point.
The Third graph illustrates the fact that an energy level of 3 MeV (light greed line) is required to irradiate the product over a depth of X with a minimum dose of A (MeV.cm2/g).
Would the energy used to irradiate that product be 1.5 MeV (dark green line), the dose inside the product (A) would be at least equal to the surface dose for a depth of Y. The product would not have a proper dose for a thickness of X. |
Graph #3
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The maximum thickness to be considered for practical industrial irradiation will depend on this “equal-entrance-exit point”. Would the effective thickness of the product be more than what is shown by the curves, two options are possible to reach the appropriate dose;
- increase the energy level in order to increase the irradiation depth
- use double side irradiation.
Double side irradiation
If irradiation is performed from both sides, the resulting dose distribution (if the thickness of material is "just right") shows a considerably greater thickness than the "one-side" one (fourth graph).
Practically, the penetration of the electrons into the material will depend on the energy of the electrons, the density of the material considered and the implementation of single/double side irradiation.
As an illustration, using an energy of 10 MeV, the single side penetration of the electrons in a product having a density of 1 (water = 1 g/cm3) is 3,6 cm (considering the “equal-entrance-exit point” concept). The same product irradiated from both sides could have a penetration of up to 9 cm. |
Graph #4
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Note : The industry commonly refers to products characteristics in terms of weight per surface ratio (gr/cm2) and will figure out the approximate energy level requirement accordingly. Indeed, since the penetration depth (cm) is a function of the density (gr/cm3), it makes sense to express the product in terms of density x depth to find out if the energy will be sufficient to penetrate the product. Units: density (gr/cm3) x depth (cm): gr/cm2.
This hybrid unit can be considered as the weight of a 1cm x 1cm column all the way through the material to be irradiated.
Practically, if one knows that a 10 MeV beam can irradiate properly through a depth of 3,6 cm @ density 1, this means that if the weight per surface ratio (gr/cm2) of a product to irradiate – whatever its thickness - is less than 3,6, this product should be irradiated properly with that level of energy.
