ElEctron BEam crosslinking of WirE and caBlE ... - IBA Industrial

IBA Industrial - White PaperPhysical Aspects of Electron BeamProcessingElectron Energy RequirementThe amount of crosslinking increases with the dose,which is defined as the absorption of energy per unitmass. The common unit of dose for electron beamprocessing is the kilogray (kGy) or the absorption ofone joule (watt-second) per gram of material. Polymercrosslinking usually requires doses in the range of 50to 150 kGy, depending on the chemical composition ofthe material.The dose within the material is usually not uniform.With electron energies above 500 kiloelectron volts(keV), the dose tends to increase with depth in thematerial to about half of the maximum electron rangeand then decrease to nearly zero at a greater depthwhere the electrons have dissipated most of theirkinetic energy. A useful quantity is the depth where theexit dose has diminished to 50 percent of the entrancedose. The electron energy should be enough to makethis quantity, usually named R(50e), equal to or greaterthan the thickness of the insulation. Values of R(opt),the depth where the exit dose equals the entrancedose, R(50), the depth where the exit dose equals 50percent of the maximum dose, and R(50e) are given inTables 2A and 2B for a wide range of electron energiesin flat materials, assuming the material compositionlisted in Table 1 above [34-36].Table 2A.Electron Ranges in Flame Retardant Polyethylene InsulationThe normalized ranges (thickness x density in g/sqcm) can be obtained by multiplying the ranges in cm,as given above, by the volume density of the flameretardant insulation, which has been calculated tobe 1.614 g/cu cm. Materials with different volumedensities tend to have similar normalized ranges,which can also be called areal or area densities.The areal density of a flat sheet can be measured bydividing its weight by its area. (Thickness x density =weight / area in g/sq cm). The areal density is a usefulquantity for comparing electron ranges in materialswith different compositions and volume densities [34-36].Table 2B.Electron Ranges in Flame Retardant Polyethylene InsulationIn addition to specifying the average dose needed tocrosslink the insulation, knowing the absorbed dosedistribution within the wire or cable insulation canprovide more assurance that the electron energy issufficient. The absorbed dose distribution depends onthe thickness, density and atomic composition of theinsulation as well as the diameter and compositionof the metallic conductor. Because of the cylindricalgeometry and the shielding and backscattering effectsof the conductor, accurate calculations of the dosedistribution are not simple, but they can be done withsuitable Monte Carlo probability codes. Several codesare available, but most of them are not very userfriendly[37, 38]. IBA Industrial, Inc. can provide adviceregarding these types of calculations [35].Temperature RiseThe thermal capacity of polymeric insulating materialis typically about half that of water, e.g. about 2 joulesper gram per degree Celcius. With this value, a doseof 100 kGy absorbed quickly in a single pass of thewire through the electron beam would cause thetemperature of the insulation to rise about 50 degreesCelcius. However, with a multiple-pass underbeamfixture which could have more than 100 passes, thedose per pass would be less than 1 kGy and thetemperature rise per pass would be less than halfa degree Celcius. The multiple-pass method allowsmuch of this heat to dissipate between passes.Processing RateThe results of Monte Carlo calculations of electronenergy depositions can also be used to estimate theline speed of an electron beam treatment process.The absorbed dose is proportional to the numberof energetic electrons injected per unit area of theprocessed material, while the beam current is ameasure of the number of electrons emitted per unittime. Therefore, the processing rate or line speed ofthe wire or cable within the electron beam increaseswith the beam current and the number of passesand decreases with increasing beam width and doseaccording to the following equation:S = 6.0 D(e) I N / (W D)where S is the line speed in meters per minute andD(e) is the energy deposition per electron in MeV perunit areal density (thickness times volume density).This quantity can be calculated with a suitableMonte Carlo code. I is the electron beam current inmilliamperes, N is the number of passes through thebeam, W is the width of the scanning beam in metersand D is the total dose in kGy [34-36].4