Angular Distribution Of Bremsstrahlung Research Articles

BREMS: Partial-wave calculation of spectra and angular distributions of electron-atom bremsstrahlung at electron energies less than 30 MeV (New Version Announcement)

BREMS: Partial-wave calculation of spectra and angular distributions of electron-atom bremsstrahlung at electron energies less than 30 MeV (New Version Announcement)

A model for the energy and angular distribution of x rays emitted from an x-ray tube. Part I. Bremsstrahlung production.

To develop an analytical model for bremsstrahlung production in a thick x-ray target (i.e., the x-ray tube anode) that takes into account the intrinsic bremsstrahlung angular distribution. X-ray spectrum models developed from theoretical principles have traditionally treated the angular distribution of the bremsstrahlung production as spherically uniform. This assumption stems from the rationale that electrons promptly attain a diffuse directional distribution in an x-ray target due to multiple scattering, thereby effectively masking the intrinsic bremsstrahlung angular distribution. In this work, a model that explicitly accounts for the angular distribution of the bremsstrahlung production is presented. The model combines Monte Carlo-calculated depth, energy, and angular distributions of electrons penetrating the x-ray target, and incorporates theoretical results for the differential bremsstrahlung cross section. The effects of using different simplified model assumptions for the electron penetration and the intrinsic bremsstrahlung angular distribution are analyzed for tungsten and molybdenum targets in the energy range 20-300keV. Typical assumptions of previous models are shown to introduce errors in calculated spectra. Particularly, it is shown that predictions of fluence and air kerma free-in-air can be overestimated by 15-30% (2-3% in aluminum half-value layer thickness) for clinically relevant beam qualities. The present model is able to reproduce comprehensive Monte Carlo calculations of the bremsstrahlung production generally to within 1%. The bremsstrahlung model developed in this work is an improvement over previous models in that the main features of the electron penetration and the resulting bremsstrahlung are considered in detail. The model can be used for more accurate predictions of the energy and angular distribution of x rays emitted from an x-ray tube.

Performance of different theories for the angular distribution of bremsstrahlung produced by keV electrons incident upon a target

Different theories of the intrinsic bremsstrahlung angular distribution (i.e., the shape function) have been evaluated using Monte Carlo calculations for various target materials and incident electron energies between 20 keV and 300 keV. The shape functions considered were the plane-wave first Born approximation cross sections (i) 2BS [high-energy result, screened nucleus], (ii) 2BN [general result, bare nucleus], (iii) KM [2BS modified to emulate 2BN], and (iv) SIM [leading term of 2BN]; (v) expression based on partial-waves expansion, KQP; and (vi) a uniform spherical distribution, UNI [a common approximation in certain analytical models]. The shape function was found to have an important impact on the bremsstrahlung emerging from thin foil targets in which the incident electrons undergo few elastic scatterings before exiting the target material. For thick transmission and reflection targets the type of shape function had less importance, as the intrinsic bremsstrahlung angular distribution was masked by the diffuse directional distribution of multiple scattered electrons. Predictions made using the 2BN and KQP theories were generally in good agreement, suggesting that the effect of screening and the constraints of the Born approximation on the intrinsic angular distribution may be acceptable. The KM and SIM shape functions deviated notably from KQP for low electron energies (< 50 keV), while 2BS and UNI performed poorly over most of the energy range considered; the 2BS shape function was found to be too forward-focused in emission, while UNI was not forward-focused enough. The results obtained emphasize the importance of the intrinsic bremsstrahlung angular distribution for theoretical predictions of x-ray emission, which is relevant in various applied disciplines, including x-ray crystallography, electron-probe microanalysis, security and industrial inspection, medical imaging, as well as low- and medium (orthovoltage) energy radiotherapy.

Generation of X rays at the grazing incidence of 18-MeV electrons on a thin Si crystal in a betatron chamber

The generation of X rays at the grazing incidence of 18-MeV electrons with a 50-μm-thick Si crystal 4 mm in length along the electron beam has been studied. The crystal has been placed in a goniometer inside the chamber of a B-18 betatron. The results exhibit strong changes in the angular distribution of bremsstrahlung at the variation of the orientation of the crystal. This effect is not observed in the case of the normal incidence of electrons on the surface of a thin crystal where the channeling of electrons, which occurs at certain orientation of the crystal, is absent. Images of a reference microstructure have been obtained with a high resolution of details of the microstructure owing to the smallness of the source of radiation. The dependence of the contrast of an image on the position of the microstructure in the radiation cone has been demonstrated.

Gas bremsstrahlung studies for medium energy electron storage rings using FLUKA Monte Carlo code

Abstract Gas bremsstrahlung is generated due to the interaction of the stored electron beam with residual gas molecules of the vacuum chamber in a storage ring. As the opening angle of the bremsstrahlung is very small, the scoring area used in Monte Carlo simulation plays a dominant role in evaluating the absorbed dose. In the present work gas bremsstrahlung angular distribution and absorbed dose for the energies ranging from 1 to 5 GeV electron storage rings are studied using the Monte Carlo code, FLUKA. From the study, an empirical formula for gas bremsstrahlung dose estimation was deduced. The results were compared with the data obtained from reported experimental values. The results obtained from simulations are found to be in very good agreement with the reported experimental data. The results obtained are applied in estimating the gas bremsstrahlung dose for 2.5 GeV synchrotron radiation source, Indus-2 at Raja Ramanna Centre for Advanced Technology, India. The paper discusses the details of the simulation and the results obtained.

Angular Distribution of Bremsstrahlung from Copper and Tungsten Targets Bombarded by 18, 28, and 38MeV Electrons

We measured the angular distribution of bremsstrahlung photons between 0 and 120 degrees from copper and tungstentargets bombarded by 18, 28, and 38MeV electrons at the electron linac of Hokkaido University. Activation detectors and two types of dosimeters were applied for the measurement. The measured results were compared with those calculated with the Monte Carlo code MCNP5 to verify the calculated results. The calculated results of both the reaction rates and ambient dose equivalent rates gave good agreement with the measured ones in the case of 18MeV electrons. A good agreement between the measurement and calculation was also observed for relative angular distributions of dose rates from 38MeV electrons; however, the calculation overestimated the measured data by a factor of 1.2 to 2.0. To achieve further accuracy of calculation, improvement of photonuclear reaction data and absorbed dose measurement are necessary for bremsstrahlung radiation dosimetry.

SU‐FF‐T‐48: A Study of the Impact of X‐Ray Energy and Angular Distributions Produced From 6‐ and 18‐MV Medical Linear Accelerators On Non‐Target Exposures

Purpose: Recently two AAPM task groups have identified the need for more detailed data on the energy and angular distribution of bremsstrahlung X‐ray photons produced from the target of medical linear accelerators. Previous studies had focused on primary photon beam toward the patient. On the other hand, X‐ray photons produced at large angles are responsible for neutron activations in the surrounding of the accelerator head and for the secondary radiation dose to the patient outside the treatment volume. This paper presents our effort to create a database on angular X‐ray energy and fluence distributions from a medical linear accelerator outside the primary beam direction. Method and Materials: Parameters for a Varian Clinac 2100C operated in 6‐ and 18‐MV were modeled using the MCNPX code. Energy and 360° angular distributions of photons and electrons emanating from radiotherapy targets were determined using MCNPX. A tally sphere was placed around the target in order to characterize the full 4π emittance of these particles from the target. The tallies were binned according to energy and the directional cosine from a fixed vector pointing perpendicular to the target face. Results: Both the 6‐ and 18‐MV photon beams are mostly emitted in forward direction and are predominately in low energies. A low energy peak in the backward direction is also seen in the 6‐MV distribution. The electron distribution emanating from the target for the 6‐MV platform is highly backward directed, while the electron distribution from the 18‐MV platform is mostly low energy and has a forward and backward directed contribution. Conclusion: The results in these studies are consistent with data from previous studies. A detailed database on angular X‐ray energy and fluence distributions from medical linear accelerator outside the primary beam direction will allow the sources of the secondary photonuclear interactions to be located and mapped.

Energy Spectra and Angular Distribution of Bremsstrahlung Emitted from a Thick Tungsten Target by 11.8 MeV Electrons

Energy Spectra and Angular Distribution of Bremsstrahlung Emitted from a Thick Tungsten Target by 11.8 MeV Electrons

Angular distributions of fast electrons, ions, and Bremsstrahlung x/gamma-rays in intense laser interaction with solid targets.

We study the angular distributions of fast electrons, ions, and bremsstrahlung x/ gamma-rays generated during the interaction of an ultrashort intense laser pulse with solid targets. A relation is found on the angular directions for fast electrons and ions as a function of the particle's kinetic energy, experienced Coulomb potential changes, and the incident angle of the laser pulse. It is valid independent of the acceleration mechanisms and the polarization of the laser pulse, as confirmed by particle-in-cell simulations. The angular distribution of bremsstrahlung x/gamma-rays is presented to show explicitly its correlation with the corresponding angular distributions of electrons.

Observation of multiple passes of electrons through thin internal targets of a betatron

We present observations of the radiation produced by electrons making multiple passes through thin targets in a betatron. We show the influence of multiple passes on the distribution of electrons and on the angular distribution of bremsstrahlung. Measurements of electron-beam spots and bremsstrahlung distributions have been performed for 15–33 MeV electrons and target thicknesses of 10 −5–3.5×10 −3 radiation lengths. Estimates of the number of passes were obtained for thin targets by comparing them with 1.3 mm thick W and 1.5 mm thick Cu targets, through which electrons pass only once. The numbers of 33 MeV electron passes observed were 460 for 3 μm Mylar, 200 for 20 μm Be, 171 for 5 μm Cu and 30 for 15 μm Cu foils. The multiple pass effect can be useful in the future for increasing the efficiency of novel X-ray sources, such as transition and parametric radiators.

Simulation of a high-brightness, hard X-ray source based on high-intensity interaction of ultra-short laser pulses with high-Z targets

The results of numerical simulations of fast electrons interaction with matter, calculated yield and angular distribution of bremsstrahlung and fluorescence K-α X-ray radiation and generation of electromagnetic fields, carried out by ERA, PM2D, and PRIZMA codes for the state of experiments on interaction of ultra-short laser pulses with high-Z targets at intensity of 1016−1018 W/cm2 are presented. Spherical targets with conical hollows and conical targets of high-Z matter are proposed for experiments with picosecond lasers to increase the brightness of hard X-ray sources.

New developments in the theory of bremsstrahlung

We discuss new progress in bremsstrahlung, beyond the predictions previously available. A relativistic code for the calculation of bremsstrahlung in a screened central potential, utilizing an expansion in electron partial waves and photon multipoles, was developed some time ago by Tseng and Pratt [Phys. Rev. A 3 (1971) 100]. For electron bremsstrahlung, unlike for bremsstrahlung in ion-atom collisions, this potential bremsstrahlung contribution generally dominates the atomic or polarizational bremsstrahlung contribution associated with atomic structure, except for radiation of energies comparable to transition energies [M.Y. Amusia and R.H. Pratt, Commun. At. Mol. Phys. 28 (1992) 247]. Predictions from the potential bremsstrahlung calculations are in reasonably good agreement with experiment [R.H. Pratt and I.-J. Feng, in: Atomic Inner Shell Physics, ed. B. Crasemann (Plenum, New York, 1985) p.]. Tabulations are available for both the spectrum and the bremsstrahlung angular distribution [R.H. Pratt, Atom. Data Nucl. Data Tables 20 (1977) 175; L.D. Kissel et al., ibid. 28 (1983) 381]. A major shortcoming has been that the code only obtains the doubly differential cross section, summing over all states of the outgoing scattered electron. No adequate predictions have been available to compare with experimental results for the triply differential cross section, which show substantial disagreement with simpler theory [W. Nakel, in press, 1994]. This problem has recently been remedied [X.M. Tong, C.D. Shaffer and R.H. Pratt, to be published], directly summing numerically the partial wave contributions to the matrix element. In the first cases studied good agreement has been achieved with the experiments. A second shortcoming of the code was its inability to deal with incident electron energies below about 1 keV, needed to study the transition between classical and quantum behavior [L. Kim and R.H. Pratt, Phys. Rev. A 36 (1987) 45]. We discuss recent results in this classical domain. We also review new developments in polarizational bremsstrahlung and two photon bremsstrahlung.

Comparisons of thick-target bremsstrahlung calculations by EGS4/PRESTA and ITS version 2.1

Two Monte Carlo codes, EGS4/PRESTA and ITS version 2.1, have been used to calculate spectral distributions of bremsstrahlung and annihilation quanta in 10–30 MV beams from thick targets of Be, Al, and Pb. Spectra are absolute (photons per incident electron) and calculated in 44 annular regions of 1° widths, covering all angles. It was found necessary to do ITS calculations using shortened sub-step sizes for electrons near the target surface to remove a 30–40% error in the angular distribution of bremsstrahlung at small angles that occurs when using default sub-step sizes. The EGS calculations were done using the enhancement which randomly samples the bremsstrahlung angle from an appropriate distribution and giving due consideration to K-shell X-rays. A survey is done of the remaining discrepencies in the spectral distributions of fluence, the total fluence and the mean energies of each spectrum. In general, EGS and ITS agree to ±20% for fluence and ±5% for mean energy. Results are compared to a set of high-precision measurements of absolute thick-target bremsstrahlung spectra used previously to show that EGS is reliable to ±10% for fluence and ±2% for mean energy. The measurements did not clearly identify a strong preferance towards either EGS or ITS.

New analytic forms for the classical bremsstrahlung angular distributions in the Coulomb case

The authors reconsider the analytic expression of classical electrodynamics for the bremsstrahlung intensity component Iy in the case of a Coulomb field. They show that Iy, known in the literature as a parametric integral, can be expressed compactly with a Hankel function and its derivatives with respect to variable and order or, alternatively, with hypergeometric functions. The authors express the total intensity It in the same manner. The new analytic expressions of Iy and It are used for precise tabulations of the spectrum sigma and the particle parameter a2, the two quantities relevant for classical dipole approximation of the bremsstrahlung angular distributions. Two simple analytic approximate formulae are found to satisfactorily describe the majority of the angular distributions. A comparison with the quantum results is also presented.

Angular distribution of particle-induced X-ray emission

The angular distribution of the continuum radiation in the energy range 2–15 keV for angles 30–160° has been investigated, both experimentally for 1.5, 2, 3, and 4 MeV protons on Al, and theoretically for secondary electron bremsstrahlung, emphasizing the electron bremsstrahlung angular distributions. The limitations imposed alone by the electron bremsstrahlung are mentioned. There is a reduction in the continuum at backward angles relative to that at 90° which is measured at the characteristic radiation energy T m to be a factor 1.6 in 135° and 2.6 in 160°, rising for higher radiation energies to a factor 3 to 4.

High-current-density relativistic electron beams in conical diodes

Current densities of 20 MA/cm2 are obtained in the focus of a modest (450 kV, 60 kA) beam in a conical ’’parapotential’’ diode. The electron flow in the diode is studied using pinhole photography and bremsstrahlung angular distribution measurements.

Electron bremsstrahlung angular distributions in the 1-500 keV energy range

Predictions of bremsstrahlung angular distributions from incident electrons of kinetic energy 1-500 keV are examined using numerical data obtained from a numerical calculation in partial waves, under the assumption that the process is described as a single-electron transition in an atomic central potential. For low-$Z$ elements the Born approximation or the Elwert-Haug approach, modified with form-factor screening, give good predictions for the shape of the angular distributions, except at forward and backward angles. That is, the results are good in the main region which contributes to the energy spectrum. For high-$Z$ elements such predictions are accurate within about 15%. Analytic properties of the shape of the angular distribution from simpler theories suggest a simple way to parametrize the results.

Angular distributions of bremsstrahlung from 12?22 MeV electrons as a function of target thickness

Angular distributions of bremsstrahlung from 12?22 MeV electrons as a function of target thickness

Low-energy angular distribution of bremsstrahlung from thick targets (T/E)

Low-energy angular distribution of bremsstrahlung from thick targets (T/E)

Koinzidenzexperimente zum Elementarprozeß der Bremsstrahlungserzeugung

By using a coincidence method, the angular distribution of bremsstrahlung has been measured for definite energy loss and definite angle of the outgoing electron. The incident electron energy was 300 keV. With a magnetic spectrometer, outgoing electrons with an energy of 170 keV and scattering angles of 0°, 5° and 10° were selected. The electrons and photons were both detected in scintillation counters. A gold foil of 250 A thickness served as the target.