Energy-Power-Dose

Energy

Electron Accelerators. The energy, in joules, which a particle of charge q (coulombs) acquires when it accelerates in a field of V volts is E = V.q

When an electron (whose charge is 1.6 x10-19 coulombs) is accelerated in an electric field of 1 Volt its energy becomes 1.6 x10-19 joules. This is more commonly stated as one electronvolt or 1eV. In electron irradiation processing it is common to quote energies, not in microscopic numbers of joules but simply as electron-volts or millions of electron-volts (MeV) where the “volts” factor is equal to the accelerating potential of the source. Not all electrons in a beam have identical energies and it is common for there to be a spectrum or range of energies. The spectrum shape depends on the type of accelerator, and how it is adjusted.

X-Ray Sources. X-rays produced by bombarding heavy metals with electrons have energies which cover a wide range, but never exceed the maximum energy of the parent electrons. It is common to refer to an X-ray spectrum by the nominal energy of the electron beam which generated it. For example, a 5 MeV electron beam is said to generate 5 MeV X-rays even though the parent electron beam and daughter X-rays include a range of energies. For X-Rays, this “energy” is a label which is useful for comparing the penetration of X-Ray sources and for ensuring that the source will meet the international guidelines for maximum energy

Radioisotope Sources. Gamma ray energies depend on the characteristic energy levels of the nucleus of the source material. Cobalt emits two gamma rays with photon energies equivalent to 1.17 and 1.33 MeV. These are therefore less penetrating than the X-rays from a typical accelerator of 5 MeV. The difference is not however of major importance in the operation of the irradiator as both have quite sufficient penetration for most products and the configurations in which they may be packed.

Power

The rate at which radiation energy is delivered defines the power of the radiation source. For an electron beam source: Power (Watts) = Average beam current(amps) x Average beam energy (Volts).

For an X-Ray source the power is given by: Power = I_av.E_av..m where m is the conversion efficiency from electron beam power to X-Ray power. The conversion factor depends on the converter material, its geometry and the energy of the incident electrons. Values seldom exceed 10%. Low incident electron energies produce much lower conversion efficiencies.

A radioactive source is normally characterized not by its power but by its disintegration rate.

By definition:

Power = number of disintegrations/sec. X average energy released per disintegration

The S.I. unit of radioactivity (1 disintegration/sec.) is the becquerel (Bq). However, the bequerel is so small relative to the size of industrial sources that an old unit, the Curie (Ci) or the mega Curie (MCi), are almost always used. ( 1 Curie is 3.7 x 10^10.) For a cobalt-60 source, 67.578 Ci, (a number derived from adding the energies of each of the gamma ray emissions as known from basic physics) emits one watt of radiation power. Thus

1 kW of electron or X-ray radiation is equivalent to 67,578.00 Ci, and conversely
1MCi of cobalt 60 is equivalent to 14.8 kW of electrons or Xrays

Note that the above equations relate the power equivalence of the sources only. In practice, the efficiency with which the radiation is absorbed by the product is different for each source Thus the amount of material processed by 1 MCi is not the same as that by 14.8 kW of electrons or 14.8 kW of X-rays.

Maximum Energy Limits for Various sources

Many materials are naturally radioactive: part of the unavoidable radiation environment in which we have evolved. Bombarding materials with energy can induce further radioactivity. However extensive theoretical and practical research has shown that below certain energy thresholds, any induced radioactivity is insignificant compared with that which is naturally present. These limits have been agreed on by the Joint Expert Committee on Irradiated Foods of the UN Food and Agriculture Organization, the World Health Organization and the International Atomic Energy Agency and are published in the Codex Alimentarius . They have also been accepted by the USFDA and other national bodies.

These limits are;

For electrons	10 MeV
For x-rays	7.5 MeV

The energy maxima for food are generally applied as safe limits for the irradiation of all other items. However, higher energies may be used when the material contained in the product is rigorously controlled and can be shown not to contain any element that can be activated at the proposed beam energy.

Penetration

The different forms of radiation penetrate items to quite different degrees. Electrons are much less penetrating than X-Rays and gamma rays. Most electrons collide with the product irradiated within a few atomic layers of the surface but each collision creates secondary electrons under the surface. These continue to create more electrons in a shower effect. Radiation is scattered forward and the peak dose actually lies a short distance below the surface. Thereafter it diminishes quite quickly. Electrons from electron accelerators have a usable penetration of about 3 mm in water for each million volts of accelerating potential. A 10 million volt (MeV) beam will therefore penetrate about 3 cm. In lower density materials, the penetration will be correspondingly higher.

If the electrons are converted to X-Rays, the penetration of the X-Rays is an order of magnitude higher but there is a considerable loss of useful radiation power (see adjacent graph)

Dose

The dose of radiation is a measure of the radiation energy deposited in unit mass of the material. It is measured in Gray (Gy) and a dose of 1 Gy means 1 joule of radiation energy has been deposited in each kilogram of material. To achieve a specific radiation effect it is necessary to apply a specific dose. For example, to sterilize medical devices doses of the order of 25k Gy are required. Satisfactory control of pathogens such as salmonella and e-coli can be achieved with doses of 1.5 to 3.0 kGy.

Process	Dose Range (kGy)
Control of salmonella &c. in meat	1.5
Disinfestation of herbs and spices	~10
Medical product sterilization	10-25
Crosslinking of plastics,wire and cable coverings	~200
PTFE degradation	> 500
Gemstone coloring	~100 000

Max-Min ratios

To treat the internal portions of a product it is necessary for the radiation to penetrate all regions. The dose deposited depends on the type of radiation and the depth within the product. There is therefore a range of dose distributed through the product. The maximum must be less than the maximum permitted for the product (whether by law or by an unacceptable side effect). The minimum must be above the target dose for the process. Therefore it is important to know the maximum and minimum values. In qualifying a product for irradiation it is necessary to establish the typical distribution and statistical variance. Although sophisticated calculation can predict dose distributions in certain geometries, these generally need to be measured experimentally. When a product is thick and/or of non-homogeneous density it can be difficult to ensure the dose distribution is within the required range.

Temperature rise during irradiation

The energy deposited in the product by irradiation (the dose) will cause the temperature of the product to rise. Temperature rise is about 0.3 °C for each kilogray of dose when irradiating medical products or food. Temperature increases are important for other uses of radiation such as the degradation of Teflon or the curing of composites where doses required are much higher.

Power-Throughput Formula

The power of the radiation source determines the rate at which product can be processed and hence the maximum total capacity of the plant. In any practical situation, power is wasted in its application to the product. For example, some electrons spill over the edges of the packages in order that the edges be fully treated. Others pass right through the product and emerges on the other side to ensure that the material at the far side gets an adequate dose. Yet other “dose” is wasted because an excess must be provided in some regions to ensure all area are adequately exposed. The processing efficiency factor takes into account all losses and thus:

Throughput (T) = Power (W)/Dose (D) . Energy absorption efficiency(a)

where throughput is in kg/sec, power is in watts, efficiency of absorption (a) is in % and dose is in Grays.

Once the beam power needed to treat the plant capacity has been determined, the line speed can be calculated from the dimensions and unit weight of the product.

Line Speed (L) = W.a./(D.d.s)

where d = density and s is the cross sectional area of the product irradiated in the direction of travel of the conveyor.

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