Characterization of bremsstrahlung radiations for 6 to 18 MeV electron beam from different Z elements: experimental and simulation approach

Transcription

1 Chapter 3. Characterization of bremsstrahlung radiations for 6 to 18 MeV electron beam from different Z elements: experimental and simulation approach This chapter deals with the study of bremsstrahlung spectra for 6 to 18 MeV electron beam from different materials such as low to high Z elements as an e - target. The simulation using FLKA involves the neutron, electron, positron and bremsstrahlung fluence determination at various angles. reover, the thickness of e - target has varied from thin to thick i.e from.1% to 15% of R CSDA. In addition, the reliability of FLKA simulation was confirmed by calculating the bremsstrahlung spectrum for the setup of experiments performed by other researchers and corresponding validation was done. The data generated in this chapter can be used as a right hand data for the researchers working in the field of medical, nuclear and accelerator physics. 47

2 Chapter 3. Characterization of bremsstrahlung radiation Importance and Objective Radiation therapy is a clinical modality dealing with the use of high doses of ionizing radiations in the treatment of patients mostly having malignant tumors. The aim of radiation therapy is to deliver a sufficiently high absorbed dose to a defined target volume resulting in the eradication of the tumor with as minimal a damage as possible to the surrounding healthy tissues. Radiotherapy with external high energy photon beams are the most common radiotherapy modality [1]. Electron beams are used either as the primary mode of radiation therapy or combined with photon beams. High energy electron and photon beams are typically produced by linear accelerators and also by Microtrons [2]. For a typical multi-energy medical linear accelerator, the accelerating potential spans between 4 and 25 MV. The mean energy of the photon beams varies between 1.5 and 7 MeV [3]. In external beam therapy, to optimize the dose distribution in a patient, the dose is typically delivered from different directions of modified shape and intensity of the beam. In radiation therapy with external radiation beams, the absorbed dose at the specific point in a patient should be known with an overall uncertainty of 3.5% [4 6]. The main reason for the requirement of high accuracy in dose delivery is typically narrow margin between the dose needed for tumor control and the dose causing complications for healthy tissues. The size of the dose margin depends on the biological characteristics of tissues, size and shape of the irradiated tissues, the quality of radiation as well as the dose fractionation regime. Due to individual nature of the dose margin, 3.5% uncertainty can be regarded as a general level accuracy requirement for dose delivery [4, 5]. sides an individual treatments, the high accuracy in dose delivery is essential to enable a reliable analysis and a comparison of results of different radiation therapy techniques and modalities [6]. The knowledge of the energy spectra and angular distribution of photon beams at the point of application is essential for accurate dose calculations [3]. Other applications requiring knowledge of the energy spectra include design of the treatment machine head, flattening filter and collimator. It is also

3 Chapter 3. Characterization of bremsstrahlung radiation 49 important to know the variation of energy spectrum as a function of radial distance from the beam axis. The bremsstrahlung energy spectrum in the central part of a photon beam is somewhat harder than in the region near edge of the beam. Consequently, the relative depth dose in tissue will vary as a function of distance from the beam axis. Variation of spectrum across the beam is also important when calculating transmission through a block or a compensating device [3]. Knowledge of the angular distribution of photons is useful when calculating dose near the beam boundaries. It is important to be able to evaluate reliably spectra of bremsstrahlung from electron accelerators as functions of photon energy and angle. As well as being required for fundamental reasons in photonuclear physics, quantitative evaluations of bremsstrahlung spectra are required for purposes such as predictions of γ ray radiation doses and dose rates, accelerator generated X- ray radiography exposures, radioisotope production rates, and source strengths in active γ-ray interrogation techniques [7]. so it is necessary to know the contamination of other particles like positron, neutron in bremsstrahlung beam, to minimize unwanted dose to the patient body. Therefore, to generate data for various energy and targets is very important as far as radiation therapy and radiography is concern Literature Survey The process of bremsstrahlung has been studied theoretically and experimentally for several decades. The theoretical status of the field in 1959 was reviewed by Koch and tz [8], who presented a compilation of theoretical formulae of various cross-sections, differentials in photon energy and photon scattering angle in thin targets and for a wide range of incident electron energies. The regimes of validity, in terms of incident energy, outgoing photon energy, angle and radiator atomic number, etc. are discussed and evaluated for thin targets. At a depth in a thick bremsstrahlung target, the intrinsic angular photon distribution for a thin target must be folded with the angular distribution of the electron produced by multiple scattering [9]. For semi-thin targets, Schiff [1]

4 Chapter 3. Characterization of bremsstrahlung radiation 5 derived a formula for the angular photon distribution. A review, including extensive tabulations of bremsstrahlung photon spectra, has been published by Seltzer and rger [11, 12]. A more recent review on various theoretical cross-sections that have been used in nte Carlo codes are described by Salvata [13]. Despite the relatively advanced state of the theory, few accurate, absolute measurements have been made of the spectrum of bremsstrahlung photons produced by high-energy electrons. A number of measurements have been performed for electrons of energies below 3 MeV: Faddegon et al. [14, 15] and the references therein. The thickness of the radiators generally used in these experiments complicates their comparison with theory, as multiple scattering and secondary processes become important. nte Carlo calculations, with the theoretical bremsstrahlung cross-sections as input, must be employed to account for the effects of radiator thickness and collimation on the photon spectrum and angular distribution. There has been much published on bremsstrahlung spectra over the past few decades. A wide range of techniques have been proposed to determine the bremsstrahlung: by early analytical modeling [1] and by elaborate nte Carlo simulations [16]. Additional analytical models exist in the literature which usually fit phase spaces obtained from nte Carlo simulations [17]. nfolding of empirical radiation data measured by spectrometry [14, 18] has also been attempted. Reconstruction from measured or calculated dosimetric data, usually transmission measurements or depthdose curves [19 25] is yet another popular means. hile each method offers different advantages and disadvantages, it is valuable to have an independent means to confirm the results of any given approach. ork on elementary bremsstrahlung cross sections [8, 11, 26] has been complemented by work on the practical computation of bremsstrahlung from radiators [27 33] in which different aspects of the bremsstrahlung spectrum are treated in different ways according to the intended application. A number of investigations on photon energy spectra have been reported in literature. But, to the best of our knowledge as for angular distributions from thick targets, there are very few researcher have published their work.

5 Chapter 3. Characterization of bremsstrahlung radiation 51 reover, the contamination of unwanted radiations such as e, e +, n have not been calculated and measured very often. Therefore, keeping the importance of bremsstrahlung in various fields mainly medical and industrial, the work on calculation on bremsstrahlung yield and spectra have been carried out. The process of bremsstrahlung production with other radiations is difficult to study theoretically even on the basis of correct experiments for different cases of thickness and materials of radiators (e γ target). Therefore, simulations using effective nte Carlo based FLKA has been carried out to generate bremsstrahlung radiations by bombarding 6 to 18 MeV electrons on low to high Z target (e γ ) of thickness varying from.1% to 15% of R CS DA at various angles. R CS DA is the range of the material for the incident electron energy. so, the simulation using FLKA involves the fluence determination of neutron, positron and secondary electrons. The data generated in this chapter will certainly help researchers working in the field of medical, nuclear and accelerator physics to take precise right hand data of flux and energies of bremsstrahlung radiations. This can be used for designing the various components of accelerator head of linear accelerator and to treat desire object in radiation therapy accurately. The reliability of FLKA simulation was also confirmed by validating the bremsstrahlung results with the results obtained in experiments performed by other researchers. 3.2 e γ rget The quality of the target to convert the electron energy into bremsstrahlung radiation is actually given by the ratio of energy loss due to radiation (de/dx) rad and ionisation, (de/dx) ion. It is therefore defined the conversion efficiency to produce bremsstrahlung radiation as the ratio between energy lost by the electrons due to the bremsstrahlung radiation and the initial electron energy [32]. This value, in particular depends on the Z of the target material and is proportional to energy of the electron. Basically, when high energy electrons having kinetic energy T e passes through a target, the radiative loss results in emission of the bremsstrahlung radiation whose energy is distributed in a continuum spectrum with end point equal to the electron energy. The energy spectrum of

6 Chapter 3. Characterization of bremsstrahlung radiation 52 bremsstrahlung can be evaluated as [8, 33, 34]. d 2 N γ dkdω (T e, k, w) = n i=1 η i (k, d i, w)τ i (T e, d i )N i dσ dk [(T e) i, k]b i (w) (3.1) This provides the spectrum in (photons sr 1 MeV 1 )/electron and is calculated by dividing the whole target material thickness in n layers and evaluating the bremss-trahlung production and diffusion in each layer. The terms appearing in Eq. (3.1) can be estimated as explained in [33, 34] and take into account all the parameters influencing the bremsstrahlung production such as target material, the electron energy loss, electron scattering inside the target material B i (w), the electron transmission coefficient τ(t e, d i ) and photon mass attenuation coefficient. η i (k, d i, w) is the coefficient of photon absorption in target material, N i is the number of atoms per unit cross section area in i th layer, dσ dk [(T e) i, k] is the elementary integral bremsstrahlung spectrum in the i th layer, k is the photon energy, w the observation angle with respect to beam axis and d i is the average depth of the i th slab. P Electron d e- target vacuum Figure 3.1: Geometry of e γ target for the generation of bremsstrahlung radiation. Consider a target in a vacuum as shown in Figure 3.1, irradiated by energetic electrons which generate bremsstrahlung radiations. The bremsstrahlung yield ds/dk is defined as the number of photons of energy k per unit energy from a target which would reach a given point P in the vacuum per unit solid angle per electron incident on the target. The solid angle dω, is defined from the point

7 Chapter 3. Characterization of bremsstrahlung radiation 53 of intersection of the beam axis with incident surface of the target to the point P. The bremsstrahlung yield is given by the following important relation, [14] ds dk = 1 N e d 2 N γ dk dω (3.2) here, (d 2 N γ /dk dω)dk is the number of photons with energy between k and k + dk which exit the target and reach point P per unit solid angle and N e is the number of electrons incident on the target. In principle, ds/dk depends on the distance of point P from the target, due to finite source size. The bremsstrahlung yield is defined for a target in a vaccum, thus for an air measurements consideration must be given to both attenuation and scatter in the air. The integrated bremsstrahlung yield S k is given by the following relation, [14] S k = kmax k ds dk dk = 1 (N γ ) k N e dω (3.3) where,(n γ ) k is the number of photons of energy greater than k which reach point P, k max is the maximum photon energy in the spectrum and is equal to the incident electron beam energy and k is the lowest transport limit of photon. The total bremsstrahlung yield is theoretically expressed by the the- Heitler equation and many approximation have been used to solve it for practical calculations. Seltzer and rger [11] published the results of electron-nucleus and electron-electron bremsstrahlung cross section, differential in photon energy and angle, for all elements up to 1 GeV. In FLKA the full set of Seltzer and rger cross section has been tabulated in an extended form [35]. In this work, the simulations were carried out using FLKA code to evaluate the materials and thicknesses to see highest bremsstrahlung yield. The bremsstrahlung fluence in term of (photon cm 2 MeV 1 )/electron is estimated from FLKA is defined by the ICR [36] and related to the bremsstrahlung yield by dφ dk = N ds e dk dω da (3.4)

8 Chapter 3. Characterization of bremsstrahlung radiation 54 where da is the cross-sectional area of the spehere at point P as shown in Figure 3.1. The mean energy of the bremsstrahlung beam is useful quality indicator [15]. E mean = 1 Emax E ds de (3.5) S E E de Strictly speaking, the whole spectrum should be used in the evaluations of the mean energy (E =). This would require knowledge of the spectral shape down to energies well below the turnover pint. In practice, this is difficult to achieve, especially for targets of low atomic number. It is therefore useful to define E mean with a low energy cutoff. 3.3 Validation of Bremsstrahlung production capabilities of FLKA The FLKA code was used to design the e γ targets and to simulate the configurations for the creation of bremsstrahlung beam. The reliability of our simulation was confirmed by calculating the spectra for the setup of the experiments performed by Faddegon et al. (1991) [15]. In his study, he used a 15 MeV electron beam incident on thick targets of various materials and measured the mean energy and energy spectrum with a sodium iodide detector placed 3 cm away from the target at different angles with respect to the incident electron beam. The simulation geometry was designed to match the experimental arrangement shown in Figure 3.2(a) as closely as possible. The 15 MeV electron beam was focused on Titanium exit window and subsequently the beam current was measured with silicon surface detector. Further, the beam was made to incident on the target passing through aluminum chamber. The targets were cylinders of (11.67 g/cm 2 thick, 6.72 g/cm 2 radius), (9.74 g/cm 2 thick, 9.81 g/cm 2 radius), (9.13 g/cm 2 thick, g/cm 2 radius). The height as well as radius of the respective target cylinder was kept approximately 11% of R CS DA such that the beam hit the target along the axis of the cylinder. though the thickness of 11% of R CS DA in the forward direction was kept, sufficient to achieve highest photon intensity with acceptable electron contamination. The exit window,

9 Chapter 3. Characterization of bremsstrahlung radiation 55 (a) (b) Figure 3.2: Experiment arrangement (a) used by Faddegon et al. [15] (b) used by Deshmukh et al. [37] for the measurement of Bremsstrahlung Yield. current monitor, target chamber (describe by Faddegon et al [15]), target, and the detector with shield was modeled in FLKA for estimation of bremsstrahlung yield at (i.e forward direction). The results measured and calculated by Faddegon et al [15] along with the results estimated using FLKA are shown in ble 3.1. It is observed that the results obtained using FLKA are comparable with the measured one by experimentally. ble 3.1: Integrated bremsstrahlung yield and mean energy of 15 MeV electron incident on thick,, and target the measurement and EGS4 calculations by Faddegaon et al. [15] and FLKA simulation(present). rget Bremsstrahlung Yield Mean Energy (1/Sr) (MeV) Measured Calculated FLKA Measured Calculated FLKA reover, the experimental results published by Deshmukh et al. [37] was also validated since the results were measured using 6 MeV Race-Track

10 Chapter 3. Characterization of bremsstrahlung radiation 56 Microtron at Pune niversity. Experimental setup used for the measurement of bremsstrahlung radiation is shown in Figure 3.2(b). In this study the author used 6 MeV electron beam to incident on the.12 cm thick lead as e γ target and produced bremsstrahlung radiations measured using scintillation detector. The same setup as in experimental conditions has been modeled in FLKA for simulating the results. The theoretical and experimental Bremsstrahlung spectrum for lead at 6 MeV electron energy is shown in Figure 3.3. From the Figure 3.3 it has been observed that the theoretical and experimental Bremsstrahlung spectra in the energy range.5 to 2 MeV show almost similar trend with marginal increase in the experimental case. However, in the energy range 2 6 MeV experimental value are lower than predicted, which may be due to absorption of photons in the target and air. In general, the experimentally obtained spectra are in good agreement with the respective theoretical spectra done by FLKA. 1xe 1 1xe 9 FLKA rve Experimental rve e 8 No. of Photons 1xe 7 1xe 6 1xe 5 e 4 1xe Photon Energy (MeV) Figure 3.3: Comparison of relative bremsstrahlung fluence measured by Deshmukh, et al [37] and calculated using FLKA simulation(present).

11 Chapter 3. Characterization of bremsstrahlung radiation Results The set of simulation was carried out to estimate the bremsstrahlung yield for (a) Electron Energy :- 6 MeV, 9 MeV, 12 MeV, 15 MeV, and 18 MeV (b) Materials used as e γ target (Z):- (4), (13), (14), (26), (29), (42), (47), (64), (73), (74), (79), (82), (92). (The materials having higher melting point were chosen for bremsstrahlung study.) (c) rget Thickness:- ranging from.1% to 15% of R CS DA The inputs for FLKA code are defined as the beam diameter.3 cm, beam direction along the Z axis and beam allowed to fall on the target perpendicularly. The cylindrical geometry was chosen and thickness of the cylinder was varied. The detector was kept at 1 cm from target along the Z direction for the measurement of bremsstrahlung fluence in term of (photon cm 2 MeV 1 /)e. An energy cut was set to be 1 kev for electron (E cut ) and photon (P cut ). reover, the to primary particles were used to run the system to minimise the statistical errors in the simulation. The estimated errors were found to be less than.1% in the bremsstrahlung case, it almost takes Hrs to complete the run on Xeon Quad core processor. The geometry used for the measurement of angular distribution of integrated bremsstrahlung fluence is shown in Figure 3.4. An electron beam is incident on the e γ target along Z direction and the generated radiations were estimated. Sphere of radius 1 cm has been divided by parallel planes along Z direction such that it can form.2 cm thick rings of sphere at various angles of to 18 with respect to the incident electron beam. The horizontal lines in the Figure 3.4 corresponds to the.2 cm thick rings for the measurement of particle fluence at various angles. The e γ conversion performances of several materials have been accurately studied by simulating the bremsstrahlung spectrum obtained for each material as a function of the converter thickness for different electron energies. hen high energy electron interacts with material, it produces bremss-

12 Chapter 3. Characterization of bremsstrahlung radiation 58 Z 1 The rings are detecting surface at various angles e target Electron beam 1, 1 X 1 Figure 3.4: A view of XZ plane geometry used for the measurement of angular distribution of bremsstrahlung radiation in FLKA simulation. trahlung radiation through the inelastic collision of electrons with nucleus. The variation in integrated bremsstrahlung fluence with e γ target thickness for 6, 9, 12, 15 and 18 MeV incident electron energy is shown in Figure 3.5(a), 3.5(b), 3.5(c), 3.5(d) and 3.5(e) respectively. From Figure 3.5 it is observed that as the e γ target thickness increases, the bremsstrahlung fluence also increases till certain thickness and then decreases with increase in the thickness of e γ target. It is observed from the figures that the bremsstrahlung fluence peak is shifted towards the lower thickness of the target with increase in the Z of the target. For higher density material the peak is found at lower thickness. This mainly attributes to the absorption of photon in the high density material itself. reover, the thickness which gives maximum bremsstrahlung fluence for e γ target is increases with the Z of the target and also with incident electron energy. The

13 Chapter 3. Characterization of bremsstrahlung radiation 59 Bremsstrahlung Fluence ((photon-cm -2 )/e _ ) (a) 6 MeV Bremsstrahlung Fluence ((photon-cm -2 )/e _ ) (b) 9 MeV Figure 3.5: Integrated bremsstrahlung fluence versus e γ target thickness for (a) 6 MeV and (b) 9 MeV energy electron incident on different materials. same trend is observed for 9, 12, 15 and 18 MeV electron energy case. It is also observed that ranium gives maximum bremsstrahlung fluence at the.8 cm, 1 cm, 1.2 cm, 1.4 cm and 1.5 cm thickness of target for 6, 9, 12, 15 and 18 MeV

14 Chapter 3. Characterization of bremsstrahlung radiation 6 Bremsstrahlung Fluence ((photon-cm -2 )/e _ ) (c) 12 MeV Bremsstrahlung Fluence ((photon-cm -2 )/e _ ) (d) 15 MeV Figure 3.5: Integrated bremsstrahlung fluence versus e γ target thickness for (c) 12 MeV and (d) 15 MeV energy electron incident on different materials. incident electron energy respectively and beryllium gives lowest bremsstrahlung fluence for all energies. Typical Photon fluence distribution in XY plane (7 cm 7 cm, 1 mm/bin)

15 Chapter 3. Characterization of bremsstrahlung radiation 61 Bremsstrahlung Fluence ((photon-cm -2 )/e _ ) (e) 18 MeV Figure 3.5: Integrated bremsstrahlung fluence versus e γ target thickness for (e) 18 MeV energy electron incident on different materials. Y (cm) X (cm).1.1 1e-5 1e-6 1e-7 Bremsstrahlung Fluence ((photon/mev-cm 2 )/electron) Figure 3.6: Photon fluence distribution in XY plane (7 cm 7 cm, 1mm/bin) for 6 MeV electron incident on.8 cm thick tungsten target. is shown in Figure 3.6 for 6 MeV electron incident on.8 cm thick tungsten target. Figure 3.6 shows that the maximum photon fluence is in the forward

16 Chapter 3. Characterization of bremsstrahlung radiation 62 direction which is at center and it drops radially. The photon fluence is.1 (photon MeV 1 cm 2 )/e at the center and drops to 1 7 at the edge. The angular distribution of the relative bremsstrahlung fluence for each material at thickness equal to the range of respective energy of electron are shown in Figure 3.7(a), 3.7(b), 3.7(c), 3.7(d), and 3.7(e), respectively for 6, 9, 12, 15, and 18 MeV electrons. It is observed from Figure 3.7 that the relative bremsstrahlung radiations produced in the forward direction i.e. at is more and decreases exponentially with increase in the angle. In addition, the relative bremsstrahlung fluence decays very slowly for low Z materials and slowly for high Z materials with increase in angle. However, till 8 to 9 the fluence converges for all the materials. This is because de/dx for electrons in the initial few angstrom layers of the target is same and further increases in angle, the electron see long path and have observed more statistical fluctuations in the de/dx. Relative Bremsstrahlung Fluence Angle (degree) (a) 6 MeV 2.8 mm 13.6 mm 15.2 mm 4.9 mm 4.4 mm 3.9 mm 3.8 mm 5.3 mm 2.5 mm 2.2 mm 2.1 mm 3.7 mm 2.2 mm Figure 3.7: Angular distribution of bremsstrahlung fluence for (a) 6 MeV energy electron incident on e γ target of thickness equal to the range of electrons. The angle at which bremsstrahlung intensity drops to half of the maximum bremsstrahlung intensity is calculated for each thickness of the e γ target. Half and tenth value is defined as the angles where the photon intensity drops

17 Chapter 3. Characterization of bremsstrahlung radiation 63 Relative Bremsstrahlung Fluence Angle (degree) (b) 9 MeV 3.8 mm 19.7 mm 22. mm 7. mm 6.3 mm 5.5 mm 5.3 mm 7.2 mm 3.4 mm 2.9 mm 2.9 mm 5. mm 3. mm Relative Bremsstrahlung Fluence Angle (degree) (c) 12 MeV 4.5 mm 25.4 mm 28.3 mm 8.9 mm 7.9 mm 6.8 mm 6.6 mm 8.9 mm 4.2 mm 3.6 mm 3.5 mm 6. mm 3.6 mm Figure 3.7: Angular distribution of bremsstrahlung fluence for (b) 9 MeV and (c) 12 MeV energy electron incident on e γ target of thickness equal to the range of electrons. to 1 2 and 1 1 of the maximum intensity. The half angle explains about the beam divergence, more the half angle value more the beam spread, therefore intensity is distributed. The variation in bremsstrahlung half angle value with thickness of

18 Chapter 3. Characterization of bremsstrahlung radiation 64 Relative Bremsstrahlung Fluence Angle (degree) (d) 15 MeV 49.8 mm 3.8 mm 34.3 mm 1.6 mm 9.4 mm 8. mm 7.7 mm 1.3 mm 4.8 mm 4.1 mm 4.1 mm 7. mm 4.1 mm Relative Bremsstrahlung Fluence Angle (degree) (e) 18 MeV 59. mm 35.9 mm 39.8 mm 12.1 mm 1.7 mm 9.1 mm 8.7 mm 11.5 mm 5.4 mm 4.6 mm 4.6 mm 7.7 mm 4.6 mm Figure 3.7: Angular distribution of bremsstrahlung fluence for (d) 15 MeV and (e) 18 MeV energy electron incident on e γ target of thickness equal to the range of electrons. e γ target are shown in Figure 3.8(a), 3.8(b), 3.8(c), 3.8(d) and 3.8(e) respectively for 6, 9, 12, 15 and 18 MeV electron energy. It is observed from Figure 3.8 that as the e γ target thickness increases, the bremsstrahlung half angle value

19 Chapter 3. Characterization of bremsstrahlung radiation 65 Bremsstrahlung half angle value (degree) (a) 6 MeV Bremsstrahlung half angle value (degree) (b) 9 MeV Figure 3.8: Angle at which maximum bremsstrahlung intensity becomes half versus the e γ target thickness for (a) 6 MeV and (b) 9 MeV energy electron incident on different materials. increases slowly for low Z materials i.e for beryllium and increases very sharply for high Z material i.e. uranium. This means that the bremsstrahlung radiations

20 Chapter 3. Characterization of bremsstrahlung radiation 66 Bremsstrahlung half angle value (degree) (c) 12 MeV Bremsstrahlung half angle value (degree) (d) 15 MeV Figure 3.8: Angle at which maximum bremsstrahlung intensity becomes half versus the e γ target thickness for (c) 12 MeV and (d) 15 MeV energy electron incident on different materials. spread out more as increases in thickness and Z of the material. It is also observed that the bremsstrahlung half angle value is higher for high Z materials. Mean energy of the bremsstrahlung radiations coming out from e γ

21 Chapter 3. Characterization of bremsstrahlung radiation 67 Bremsstrahlung half angle angle (degree) (e) 18 MeV Figure 3.8: Angle at which maximum bremsstrahlung intensity becomes half versus the e γ target thickness for (e)18 MeV energy electron incident on different materials. target for 6, 9, 12, 15, and 18 MeV energy incident electrons are shown in Figure 3.9(a), 3.9(b), 3.9(c), 3.9(d) and 3.9(e) respectively. It is observed from Figure 3.9 that the mean energy of the bremsstrahlung spectrum decreases with angle. The forward direction ( ) bremsstrahlung spectrum is found to be more harden than the orthogonal (9 ) and backward direction (18 ). It is also seen form the figure that mean energy is found to be more in case of high Z () material than low Z material (). It is important to note in this regard that as the energy of the electron beam increases the bremsstrahlung spectrum found to be more harden i.e. the mean energy of bremsstrahlung increases with energy. Typically, for beryllium, it is varied from.9 MeV to 2 MeV with increasing electron beam energy from 6 to 18 MeV at the forward direction ( ). The bremsstrahlung energy spectrum generated in e γ target of thickness equal to the range of the incident electron of energy 6, 9, 12, 15 and 18 MeV are shown in Figure 3.1(a), 3.1(b), 3.1(c), 3.1(d) and 3.1(e) respectively. In general, for the bremsstrahlung energy spectra, the fluence increases with decreasing photon energy until the turnover point of the spectrum is reached. This

22 Chapter 3. Characterization of bremsstrahlung radiation 68 Mean energy of bremsstrahlung (MeV) mm 13.6 mm 15.2 mm 4.9 mm 4.4 mm 3.9 mm 3.8 mm 5.3 mm 2.5 mm 2.2 mm 2.1 mm 3.7 mm 2.2 mm Angle (degree) (a) 6 MeV Mean energy of bremsstrahlung (MeV) mm 19.7 mm 22. mm 7. mm 6.3 mm 5.5 mm 5.3 mm 7.2 mm 3.4 mm 2.9 mm 2.9 mm 5. mm 3. mm Angle (degree) (b) 9 MeV Figure 3.9: Angular distribution of bremsstrahlung mean energy for (a) 6 MeV and (b) 9 MeV energy electron incident on e γ target of thickness equal to the range of electron.

23 Chapter 3. Characterization of bremsstrahlung radiation 69 Mean energy of bremsstrahlung (MeV) mm 25.4 mm 28.3 mm 8.9 mm 7.9 mm 6.8 mm 6.6 mm 8.9 mm 4.2 mm 3.6 mm 3.5 mm 6. mm 3.6 mm Angle (degree) (c) 12 MeV Mean energy of bremsstrahlung (MeV) mm 3.8 mm 34.3 mm 1.6 mm 9.4 mm 8. mm 7.7 mm 1.3 mm 4.8 mm 4.1 mm 4.1 mm 7. mm 4.1 mm Angle (degree) (d) 15 MeV Figure 3.9: Angular distribution of bremsstrahlung mean energy for (c) 12 MeV and (d) 15 MeV energy electron incident on e γ target of thickness equal to the range of electron. is the point at which the bremsstrahlung beam begins to be strongly attenuated in the target. Typically, the turnover point is varies between 5 to 6 kev energy for 6 to 18 MeV incident electron on lead target.

24 Chapter 3. Characterization of bremsstrahlung radiation 7 Mean energy of bremsstrahlung (MeV) mm 35.9 mm 39.8 mm 12.1 mm 1.7 mm 9.1 mm 8.7 mm 11.5 mm 5.4 mm 4.6 mm 4.6 mm 7.7 mm 4.6 mm Angle (degree) (e) 18 MeV Figure 3.9: Angular distribution of bremsstrahlung mean energy for (e) 18 MeV energy electron incident on e γ target of thickness equal to the range of electron. Bremsstrahlung Fluence ((photon-cm -2 -MeV -1 )/e _ ) Bremsstrahlung Energy (MeV) (a) 6 MeV 2.8 mm 13.6 mm 15.2 mm 4.9 mm 4.4 mm 3.9 mm 3.8 mm 5.3 mm 2.5 mm 2.2 mm 2.1 mm 3.7 mm 2.2 mm Figure 3.1: Energy spectra of bremsstrahlung radiations from e γ target of thickness equal to the range of the electron bombarded with (a) 6 MeV electron energy for different materials.

25 Chapter 3. Characterization of bremsstrahlung radiation 71 Bremsstrahlung Fluence ((photon-cm -2 -MeV -1 )/e _ ) Bremsstrahlung Energy (MeV) (b) 9 MeV 3.8 mm 19.7 mm 22. mm 7. mm 6.3 mm 5.5 mm 5.3 mm 7.2 mm 3.4 mm 2.9 mm 2.9 mm 5. mm 3. mm Bremsstrahlung Fluence ((photon-cm -2 -MeV -1 )/e _ ) Bremsstrahlung Energy (MeV) (c) 12 MeV 4.5 mm 25.4 mm 28.3 mm 8.9 mm 7.9 mm 6.8 mm 6.6 mm 8.9 mm 4.2 mm 3.6 mm 3.5 mm 6. mm 3.6 mm Figure 3.1: Energy spectra of bremsstrahlung radiations from e γ target of thickness equal to the range of the electron bombarded with (b) 9 MeV and (c) 12 MeV electron energy for different materials. Typical results for 6 MeV electron energy, the variation in transmitted electron fluence as function of e γ target thickness for different materials is shown in Figure yond the target, there is contribution of secondary

26 Chapter 3. Characterization of bremsstrahlung radiation 72 Bremsstrahlung Fluence ((photon-cm -2 -MeV -1 )/e _ ) Bremsstrahlung Energy (MeV) (d) 15 MeV 49.8 mm 3.8 mm 34.3 mm 1.6 mm 9.4 mm 8. mm 7.7 mm 1.3 mm 4.8 mm 4.1 mm 4.1 mm 7. mm 4.1 mm Bremsstrahlung Fluence ((photon-cm -2 -MeV -1 )/e _ ) Bremsstrahlung Energy (MeV) (e) 18 MeV 59. mm 35.9 mm 39.8 mm 12.1 mm 1.7 mm 9.1 mm 8.7 mm 11.5 mm 5.4 mm 4.6 mm 4.6 mm 7.7 mm 4.6 mm Figure 3.1: Energy spectra of bremsstrahlung radiations from e γ target of thickness equal to the range of the electron bombarded with (d) 15 MeV and (e) 18 MeV electron energy for different materials. and direct transmitted electrons in the photon beam. Figure 3.11 shows only the contribution of direct transmitted electrons in photon beam. It is found that the e γ target thickness increases, more the electrons get absorbed in the target

27 Chapter 3. Characterization of bremsstrahlung radiation 73 Electron Fluence ((electron-cm -2 )/e _ ) Figure 3.11: Variation in transmitted electron fluence as a function of e γ target thickness of different materials for 6 MeV electron. which results into more bremsstrahlung and less contribution of electrons beyond the target. Larger thickness is required to stop the incident electrons inside the e γ target for low Z material, while smaller thickness is sufficient to stop the incident electron in high Z material. The variation in integrated positron fluence as a function of e γ target thickness for 6, 9, 12, 15 and 18 MeV incident electron energy is shown in Figure 3.12(a), 3.12(b), 3.12(c), 3.12(d) and 3.12(e) respectively.

28 Chapter 3. Characterization of bremsstrahlung radiation 74 Positron Fluence ((positron-cm -2 )/e _ ) e-5 1e-6 1e-7 1e (a) 6 MeV Positron Fluence ((positron-cm -2 )/e _ ) e-5 1e-6 1e-7 1e (b) 9 MeV Figure 3.12: Integrated positron fluence versus e γ target thickness for (a) 6 MeV and (b) 9 MeV incident electron energy on different materials. The contribution of positron is also estimated in the forward direction which found to be 3 to 4 order less than the bremsstrahlung intensity as shown in Figure The e γ target produces positrons through the pair production process

29 Chapter 3. Characterization of bremsstrahlung radiation 75 Positron Fluence ((positron-cm -2 )/e _ ) e-5 1e-6 1e-7 1e (c) 12 MeV Positron Fluence ((positron-cm -2 )/e _ ) e-5 1e-6 1e-7 1e (d) 15 MeV Figure 3.12: Integrated positron fluence versus e γ target thickness for (c) 12 MeV and (d) 15 MeV incident electron energy on different materials. and which has more cross section for higher energy of bremsstrahlung radiation. re number of positrons are produced in high Z targets since the cross section for pair production is directly proportional to Z 2 of the element. It is

30 Chapter 3. Characterization of bremsstrahlung radiation 76 Positron Fluence ((positron-cm -2 )/e _ ) e-5 1e-6 1e-7 1e (e) 18 MeV Figure 3.12: Integrated positron fluence versus e γ target thickness for (e) 18 MeV incident electron energy on different materials. observed from the figure that as the e γ target thickness increases the positron contribution also increases till a certain thickness and beyond that the positron contribution falls. This is due to the absorption of positron in the e γ target itself. If the photonuclear reaction threshold of the e γ target is less than the incident electron energy, then neutrons can be produced in the e γ target. The photo nuclear reaction threshold for the,,,,,,,,,,, and is 1.67, 13.6, 17.18, 11.2, 1.85, 8 9, 9.54, 8.5, 7.58, 7.2, 8.7, 7.37 and 5.3 MeV respectively. (The threshold values taken from Atlas of Giant Dipole Resonance). The mentioned threshold energies are for the isotope which having highest abundance in nature. The other isotopes of the element have different thresholds. For the case of 6 MeV electron energy, beryllium and uranium produces neutrons through photo nuclear and fission process which is shown in Figure 3.13(a). For 9 MeV electron energy, produces highest neutron fluence because of higher cross section and fission in the target which is shown in Figure 3.13(b). reover, the materials such as,,,,

31 Chapter 3. Characterization of bremsstrahlung radiation 77 Neutron Fluence ((neutron-cm -2 )/e _ ) 1e-6 1e-7 1e-8 1e-9 1e-1 1e-11 1e-12 1e (a) 6 MeV Neutron Fluence ((neutron-cm -2 )/e _ ) 1e-5 1e-6 1e-7 1e-8 1e-9 1e-1 1e-11 1e (b) 9 MeV Figure 3.13: Integrated neutron fluence versus e γ target thickness for (a) 6 MeV and (b) 9 MeV incident electron energy on different materials. also produces negligible contribution of neurons in bremsstrahlung beam. It is observed from the Figure 3.13(c) that the is giving maximum neutron fluence,

32 Chapter 3. Characterization of bremsstrahlung radiation 78 Neutron Fluence ((neutron-cm -2 )/e _ ).1 1e-5 1e-6 1e-7 1e-8 1e-9 1e-1 1e-11 1e-12 1e (c) 12 MeV Neutron Fluence ((neutron-cm -2 )/e _ ).1.1 1e-5 1e-6 1e-7 1e-8 1e-9 1e-1 1e-11 1e (d) 15 MeV Figure 3.13: Integrated neutron fluence versus e γ target thickness for (c) 12 MeV and (d) 15 MeV incident electron energy on different materials. while is not producing neutron in the target. However, is having lowest contribution of neutrons seen for 12 MeV energy electrons incident on e γ target. hereas, for the case of 15 MeV incident electron energy, the neutron produced

33 Chapter 3. Characterization of bremsstrahlung radiation 79 Neutron Fluence ((neutron-cm -2 )/e _ ).1.1 1e-5 1e-6 1e-7 1e-8 1e-9 1e-1 1e-11 1e (e) 18 MeV Figure 3.13: Integrated neutron fluence versus e γ target thickness for (e) 18 MeV incident electron energy on different materials. in the e γ target is shown in Figure 3.13(d). It is observed that all the materials having photonuclear reaction threshold lower than the 15 MeV electron energy, shows neutrons for e γ target. Out of this is giving maximum neutron fluence because of its higher cross section and fission. The neutron fluence contribution in and material found to be negligible. reover, the threshold energy for is lower than other materials, but it produces less neutrons because of lower cross section value. However, the materials such as,, almost produces same amount of neutron fluence. Variation of neutron fluence produced in e γ target bombard by 18 MeV electron is shown in Figure 3.13(e), which shows that high Z elements produces maximum neutron fluence while for low Z electron produces minimum neutron fluence. It is also observed from all the Figure 3.13 that the neutron fluence increases till certain thickness and then further decrease with increases in the e γ target thickness.

34 Chapter 3. Characterization of bremsstrahlung radiation 8 Figure 3.14(a) shows the variation in bremsstrahlung fluence with atomic number of e γ target for 6 to 18 MeV electron energies. It is observed from the figure that the usually bremsstrahlung fluence increases with Z of the e γ target except gadolinium and lead where bremsstrahlung fluence found to be less. This attributes mainly due to the fall in the density of the respective material. Variation in mean energy of bremsstrahlung radiation with atomic number of e γ target is shown in Figure 3.14(b). From this figure it is seen that for 6 MeV energy electron the mean energy increases continuously with Z, whereas for 18 MeV incident electron there is fluctuations in the mean energy of bremsstrahlung radiation for,,,, due to there respective variations in the absorption cross section for bremsstrahlung radiation. Variation in the contribution of positron fluence with atomic number of e γ target is shown in Figure 3.14(c). From this figure it is also observed that the positron fluence increases with atomic number except and for which it is found less. This is because of the lower density for the respective target as compared to others. Variation in the neutron fluence with atomic number of e γ target for 6-18 MeV electron energy is shown in Bremsstrahlung Fluence ((photon-cm -2 )/e _ ) MeV Electron 9 MeV Electron 12 MeV Electron 15 MeV Electron 18 MeV Electron Atomic Number of e-γ target (a) Figure 3.14: (a) Variation in bremsstrahlung fluence with respect to the atomic number of e γ target for 6 18 MeV incident electron energies.

35 Chapter 3. Characterization of bremsstrahlung radiation 81 3 Bremsstrahlung Mean Energy (MeV) Atomic Number of e-γ target (b) 6 MeV Electron 9 MeV Electron 12 MeV Electron 15 MeV Electron 18 MeV Electron Figure 3.14: (b) Variation in mean energy of bremsstrahlung with respect to the atomic number of e γ target for 6 18 MeV incident electron energies. Positron Fluence ((positron-cm -2 )/e _ ) MeV Electron 9 MeV Electron 12 MeV Electron 15 MeV Electron 18 MeV Electron Atomic Number of e-γ target (c) Figure 3.14: (c) Variation in positron fluence with respect to the atomic number of e γ target for 6 18 MeV incident electron energies.

36 Chapter 3. Characterization of bremsstrahlung radiation Neutron Fluence ((neutron-cm -2 )/e _ ) 1e-5 1e-6 1e-7 1e-8 1e-9 1e-1 1e-11 1e-12 6 MeV Electron 9 MeV Electron 12 MeV Electron 15 MeV Electron 18 MeV Electron Atomic Number of e-γ target (d) Figure 3.14: (d) Variation in neutron fluence with respect to the atomic number of e γ target for 6 18 MeV incident electron energies. Figure 3.14(d). It is observed from figure that the neutron fluence increases with atomic number and mainly depending on the respective cross section of the targets. Overall, the variation of bremsstrahlung fluence, mean bremsstrahlung energy, positron fluence and neutron fluence with incident electron energy for different targets are shown in Figure 3.15(a), 3.15(b), 3.15(c) and 3.15(d) respectively. In all the cases it is observed that as energy of the incident electron increases the bremsstrahlung fluence, mean energy, positron fluence, neutron fluence increases. hereas, the contribution of each fluence of bremsstrahlung, positron, neutron and mean energy increases with the Z of the target materials. reover, it is observed that the contribution of positron and neutron is depending on the intensity of bremsstrahlung radiations generated in the target.

37 Chapter 3. Characterization of bremsstrahlung radiation 83 Bremsstrahlung Fluence ((photon-cm -2 )/e _ ) Electron Energy (MeV) (a) Figure 3.15: (a) Variation in bremsstrahlung fluence with respect to the incident electron energy on different atomic number of e γ target. 3 Bremsstrahlung Mean Energy (MeV) Electron Energy (MeV) (b) Mean energy of bremsstrahlung Figure 3.15: (b) Variation in mean energy of bremsstrahlung with respect to the incident electron energy on different atomic number of e γ target.

38 Chapter 3. Characterization of bremsstrahlung radiation 84.1 Positron Fluence ((positron-cm -2 )/e _ ) e-5 1e Electron Energy (MeV) (c) Figure 3.15: (c) Variation in positron fluence with respect to the incident electron energy on different atomic number of e γ target..1.1 Neutron Fluence ((neutron-cm -2 )/e _ ) 1e-5 1e-6 1e-7 1e-8 1e-9 1e-1 1e-11 1e Electron Energy (MeV) (d) Neutron fluence Figure 3.15: (d) Variation in neutron fluence with respect to the incident electron energy on different atomic number of e γ target.

39 Chapter 3. Characterization of bremsstrahlung radiation Conclusion The data of bremsstrahlung radiations generated in various target for different energy of electron from 6 to 18 MeV are summarized and concluded below, Maximum bremsstrahlung fluence is obtained for high Z material () and higher incident electron energy (18 MeV). The mean energy of bremsstrahlung radiation for high Z target is observed more. The bremsstrahlung fluence is maximum in the forward direction and it decreases sharply with angle. High Z targets produce higher neutron fluence for energies greater than 12 MeV electron. The contribution of direct transmitted electrons beyond the range of electron in the target is negligible. The contribution of positron in the bremsstrahlung beam is negligible. 3.6 Future Scope The study shown here only considers the individual targets. Based on the results further studies can be carried out using multilayer targets. The multilayer target can be formed with the combinations of materials such that the maximum bremsstrahlung radiations can be obtained with marginal contribution of electron, positron and neutron.

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