ASNT

matter, an effective energy (keV eff ) may be used. The effective energy of the spectrum will depend on the object material, material thickness, and kilovolt- age peak, but is usually in the range of one-half to one-third of the kilovoltage peak value. ELECTRON BACKSCATTER Electrons that strike the target can also backscatter from the target surface, lose energy, and therefore not generate meaningful amounts of X-radiation. The efficiency, η , of this backscatter is parameter- ized as Equation 1: where f is the angle from the normal for the bombarding electrons and Z = 74 for tungsten for incident electron energies 10 keV to 100 keV (Reimer 1998). At normal incidence, nearly half the incident electrons backscatter. At significant angles away from normal, as f increases, the efficiency drops. This means that less heat is delivered to the target, but it also means that fewer X-rays are generated. Most radiographic inspection tubes employ normal incidence electron beams to maximize X-ray generation. Angular Distribution of Emerging X-Rays The bremsstrahlung portion of X-radiation generated in thick-target X-ray sources is the large fraction of the total radiation emitted. In the tens to hundreds keV range of energy, characteristic X-rays comprise a fraction of the total, depending upon electron energy and target material. At lower energies, below the tens keV range, low-target Z characteristics supply a significantly higher fraction (Behling 2016). This feature and filters made of thin coatings of materials can be used to produce nearly monochromatic sources (keV to tens keV wide). The nearly isotropic distribution of X-rays emerging is affected noticeably by the absorption for long-path X-ray trajectories at small angles with respect to the target surface as shown in Figure 6 (CASINO n.d.). The effect can be a few percent to more than 10% over 10º to 20º target angle, depending upon incident electron energy and target material. This is less severe for industrial (Eq. 1) η Z , φ ( ) = 1 + cos φ ( ) − 9/ Z 1 2

inspection tubes that use 45° target angles where the effect of absorption is small; departure from isotropic angular distribution becomes more evident at emission angles that are much larger than normal angles. In the realm of higher-energy radiography, 1 to 10 MeV, drop-off at the edge of radiation fields is due to the forward-peaked radiation pattern discussed previously. Characteristic X-rays emerge from the atom once the electron has interacted. The atom’s mass is Z × m proton / m electron times larger than the electron, so it remains relatively motionless following the process. The emerging X-rays are nearly isotropic. In electron nucleus interactions giving rise to bremsstrahlung radiation of an accelerated charged particle due to the coulomb electric field of the nucleus, the radiating particle is the electron. Analysis of this shows that the electron radiates in the classical manner of a dipole radiation field and the power as a function of forward angle, θ , to a distant observer at r , given by Equation 2. where ε 0 is permittivity of free space, c is speed of light, e the charge of the electron, and X is the position vector of the charge (Jackson 1975 and Behling 2016). The direction of radiation is maximum in a direction perpendicular to the accelerated motion of the electron. For higher electron energies incident on targets for radiographic inspection, a relativistic treatment is necessary and results in a factor (1- β cos θ ) 6 in the denominator and β = v / c for the electron. At highly relativistic energies for the electron, the distribu- tion of power is forward peaked; high-energy X-ray sources take advantage of this by using transmis- sion mode targets. So 1 to 10 MeV X-rays created from accelerated electron beams are distributed in a forward-peaked pattern that is an advantage for imaging thick, dense objects — most of the radiation is going toward the object, not elsewhere where expensive, thick shielding might be required to lower the dose to personnel and ancillary equipment. (Eq. 2) P θ , r ( ) = c 16 π 2 ε 0 rc 2 ( ) d 2 X e dt 2 ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 2 sin 2 θ

CHAPTER 2

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Part 2