Initial Beam Parameters Research Articles

A method for determination of parameters of the initial electron beam hitting the target in linac

Detailed characteristics of the electron beam incident on the target of the Linac are almost impossible to be measured. With Monte Carlo technique it is possible to simulate the transport of radiation through the accelerator head and find out the initial beam parameters. These parameters, such as energy spectrum and spatial distribution can be ascertained by matching the simulated dose distributions with the measured dose distributions using trial and error. In this work, a Monte Carlo modeling of the HPD Siemens Primus linear accelerator in 6 MV photon beams at Dong Nai general hospital was performed. The simulated Percent depth doses (PDD) and beam profiles (OCR) were then compared with the measured ones. Excellent agreements were obtained between simulations and measurements with an average difference of 0.7% for PDD less than 2% for OCR. The percentage gamma passing rate is 100% with 1% dose difference and 1 mm distance to agreement as acceptance criteria. The best suited energy and radius of the electron beam incident on the target were found at 6.04 MeV and at FWHM = 1.2 mm respectively.

Propagation Properties of the Rectangular Multi-Gaussian Schell-Model Beams in Uniaxial Crystals Orthogonal to the Optical Axis

A stochastic beam generated by a recently introduced source of Schell type with rectangular multi-Gaussian spectral degree of coherence is shown to posses interesting novel features on propagation in uniaxial crystals. The analytical expression for the cross-spectral density function of the rectangular multi-Gaussian Schell-model (RMGSM) beams propagating in uniaxial crystals orthogonal to the optical axis is derived. With the help of the derived formula, the evolution properties of the spectral density, the effective beam width, and the spectral degree of coherence of the RMGSM beams in a uniaxial crystal are investigated in detail. It is shown that the evolution properties of an RMGSM beam in uniaxial crystal are much different from its evolution properties in free space, and the propagation properties of the RMGSM beams in uniaxial crystals are closely related to the initial beam parameters (beam index M and spatial coherence length) and the parameters of the uniaxial crystals (the ratio of extraordinary and ordinary refractive indices). The results demonstrate the potential of uniaxial crystals for modulating the properties of the RMGSM beams.

An amplitude-preserved adaptive focused beam seismic migration method

Gaussian beam migration (GBM) is an effective and robust depth seismic imaging method, which overcomes the disadvantage of Kirchhoff migration in imaging multiple arrivals and has no steep-dip limitation of one-way wave equation migration. However, its imaging quality depends on the initial beam parameters, which can make the beam width increase and wave-front spread with the propagation of the central ray, resulting in poor migration accuracy at depth, especially for exploration areas with complex geological structures. To address this problem, we present an adaptive focused beam method for shot-domain prestack depth migration. Using the information of the input smooth velocity field, we first derive an adaptive focused parameter, which makes a seismic beam focused along the whole central ray to enhance the wave-field construction accuracy in both the shallow and deep regions. Then we introduce this parameter into the GBM, which not only improves imaging quality of deep reflectors but also makes the shallow small-scale geological structures well-defined. As well, using the amplitude-preserved extrapolation operator and deconvolution imaging condition, the concept of amplitude-preserved imaging has been included in our method. Typical numerical examples and the field data processing results demonstrate the validity and adaptability of our method.

A geometrical model for the Monte Carlo simulation of the TrueBeam linac

Monte Carlo simulation of linear accelerators (linacs) depends on the accurate geometrical description of the linac head. The geometry of the Varian TrueBeam linac is not available to researchers. Instead, the company distributes phase-space files of the flattening-filter-free (FFF) beams tallied at a plane located just upstream of the jaws. Yet, Monte Carlo simulations based on third-party tallied phase spaces are subject to limitations. In this work, an experimentally based geometry developed for the simulation of the FFF beams of the Varian TrueBeam linac is presented. The Monte Carlo geometrical model of the TrueBeam linac uses information provided by Varian that reveals large similarities between the TrueBeam machine and the Clinac 2100 downstream of the jaws. Thus, the upper part of the TrueBeam linac was modeled by introducing modifications to the Varian Clinac 2100 linac geometry. The most important of these modifications is the replacement of the standard flattening filters by ad hoc thin filters. These filters were modeled by comparing dose measurements and simulations. The experimental dose profiles for the 6 MV and 10 MV FFF beams were obtained from the Varian Golden Data Set and from in-house measurements performed with a diode detector for radiation fields ranging from 3 × 3 to 40 × 40 cm2 at depths of maximum dose of 5 and 10 cm. Indicators of agreement between the experimental data and the simulation results obtained with the proposed geometrical model were the dose differences, the root-mean-square error and the gamma index. The same comparisons were performed for dose profiles obtained from Monte Carlo simulations using the phase-space files distributed by Varian for the TrueBeam linac as the sources of particles. Results of comparisons show a good agreement of the dose for the ansatz geometry similar to that obtained for the simulations with the TrueBeam phase-space files for all fields and depths considered, except for the 40 × 40 cm2 field where the ansatz geometry was able to reproduce the measured dose more accurately. Our approach overcomes some of the limitations of using the Varian phase-space files. It makes it possible to: (i) adapt the initial beam parameters to match measured dose profiles; (ii) reduce the statistical uncertainty to arbitrarily low values; and (iii) assess systematic uncertainties (type B) by using different Monte Carlo codes. One limitation of using phase-space files that is retained in our model is the impossibility of performing accurate absolute dosimetry simulations because the geometrical description of the TrueBeam ionization chamber remains unknown.

Propagation of a Laguerre–Gaussian correlated Schell-model beam beyond the paraxial approximation

Recently, Laguerre–Gaussian correlated Schell-model (LGCSM) beam was introduced theoretically [Mei and Korotkova, Opt. Lett. 38(2), (2013), 91–93] and generated experimentally [Wang et al., Opt. Lett. 38(11), (2013), 1814–1816]. In this paper, we treat the propagation of a LGCSM beam beyond the paraxial approximation. Based on the generalized Rayleigh–Sommerfeld diffraction integral, analytical expressions for the intensity and spectral degree of coherence of a nonparaxial LGCSM beam propagating in free space are obtained, and the corresponding results of a paraxial LGCSM beam are also derived as a special case. Our numerical results show that the nonparaxial propagation properties of a LGCSM beam are closely related to the initial beam parameters, such as the beam waist width, the coherence width and the mode order. Furthermore, in the far field, flat-topped, hollow intensity profiles can be formed through varying the initial beam parameters, which is different from that of a nonparaxial Gaussian Schell-model beam.

Evolution properties of a Laguerre-Gaussian correlated Schell-model beam propagating in uniaxial crystals orthogonal to the optical axis.

Analytical expressions for the cross-spectral density function and the second-order moments of a Laguerre-Gaussian correlated Schell-model (LGCSM) beam propagating in uniaxial crystals orthogonal to the optical axis are derived. Based on the formulas derived, we study the propagation properties, such as beam irradiance, beam diameters, and the spectral degree of coherence, of a LGCSM beam inside uniaxial crystals in detail. The effect of the initial beam parameters (mode order and spatial coherence length) and the parameters of the uniaxial crystals on the evolution properties of a LGCSM beam is revealed through numerical examples. The uniaxial crystals provide one way to modulate the properties of a LGCSM beam.

Degree of polarization of a tightly focused, partially coherent anomalous hollow beam.

By using the Richards-Wolf vector diffraction theory, the formulas of the propagation of a linearly polarized, partially coherent anomalous hollow beam (AHB) through a high numerical aperture (NA) thin lens are derived. The tight focusing properties of a partially coherent AHB, including the degree of polarization, the intensity distribution, and the degree of coherence, are studied in detail. It is found that the focusing properties of a partially coherent AHB are closely determined by the initial coherence, initial beam parameters, and NA of the thin lens. However, no matter how high the value of eccentricity, the initial beam will reduce to a Gaussian beam of quasi-circular symmetry at the focal plane. No matter the value of NA, the size of the beam will remain invariant, which is an interesting phenomenon, and the beam has good stability. The results may find application in optical trapping with a partially coherent field.

Nonparaxial propagation of elliptical Gaussian vortex beams in uniaxial crystal orthogonal to the optical axis.

Analytical expressions for the three components of nonparaxial propagation of a polarized elliptical Gaussian vortex beam in uniaxial crystal orthogonal to the optical axis are derived. Intensity and phase distributions of the three components of a polarized elliptical Gaussian vortex beam propagating in a uniaxial crystal orthogonal to the optical axis are illustrated by numerical examples. The influences of the initial beam's parameters and the parameters of the uniaxial crystal on the evolution of the beam's intensity and phase distributions in the uniaxial crystal are examined in detail. Results show that the statistical properties of an elliptical Gaussian vortex beam nonparaxially propagating in uniaxial crystal orthogonal to the optical axis are closely determined by the initial beam's parameters and the parameters of the crystal. The beam waist width ω0 not only affects the size of the beam profile in uniaxial crystal but also determines the nonparaxial effect of an elliptical Gaussian vortex beam. The profile of an elliptical Gaussian vortex beam in the uniaxial crystal becomes twisted and tilted, whether the elliptical factor α is greater or smaller than unity. The beam profile is tilted to the left in positive crystal. In contrast, it is inclined to the right in negative crystal. The results indicate that uniaxial crystal provides a convenient method to modulate the intensity and phase distributions of an elliptical Gaussian vortex beam, which is beneficial to optical manipulation of microscopic particles and nonlinear optics involving a specific beam profile and phase.

Characterizing a proton beam with two different methods in beam halo experiments

In beam halo experiments, it is very important to correctly characterize the RFQ output proton beam. In order to simulate the beam dynamics properly, we must first know the correct initial beam parameters. We have used two different methods, quadrupole scans and multi-wire scanners to determine the transverse phase-space properties of the proton beam. The experimental data were analyzed by fitting to the 3-D nonlinear simulation code IMPACT. For the quadrupole scan method, we found that the RMS beam radius and the measured beam-core profiles agreed very well with the simulations. For the multi-wire scanner method, we choose the case of a matched beam. By fitting the IMPACT simulation results to the measured data, we obtained the Courant-Snyder parameters and the emittance of the beam. The difference between the two methods is about eight percent, which is acceptable in our experiments.

Nonparaxial propagation of Lorentz–Gauss beams in uniaxial crystal orthogonal to the optical axis

Analytical expressions for the three components of nonparaxial propagation of a polarized Lorentz-Gauss beam in uniaxial crystal orthogonal to the optical axis are derived and used to investigate its propagation properties in uniaxial crystal. The influences of the initial beam parameters and the parameters of the uniaxial crystal on the evolution of the beam-intensity distribution in the uniaxial crystal are examined in detail. Results show that the statistical properties of a nonparaxial Lorentz-Gauss beam in a uniaxial crystal orthogonal to the optical axis are closely determined by the initial beam's parameters and the parameters of the crystal: the beam waist sizes-w(0), w(0x), and w(0y)-not only affect the size and shape of the beam profile in uniaxial crystal but also determine the nonparaxial effect of a Lorentz-Gauss beam; the beam profile of a Lorentz-Gauss beam in uniaxial crystal is elongated in the x or y direction, which is determined by the ratio of the extraordinary refractive index to the ordinary refractive index; with increasing deviation of the ratio from unity, the extension of the beam profile augments. The results indicate that uniaxial crystal provides an effective and convenient method for modulating the Lorentz-Gauss beams. Our results may be valuable in some fields, such as optical trapping and nonlinear optics, where a light beam with a special profile and polarization is required.

Second-order moments of an electromagnetic Gaussian Schell-model beam in a uniaxial crystal

We derive the analytical expressions for the second-order moments of an electromagnetic Gaussian Schell-model (EGSM) beam propagating in a uniaxial crystal. With the help of the derived formulas, we study the evolution properties of the propagation factor, the effective radius of curvature and the Rayleigh range of an EGSM beam in a uniaxial crystal. It is found that the evolution properties of an EGSM beam in a uniaxial crystal are much different from its evolution properties in free space and are closely determined by the initial beam parameters and the parameters of the uniaxial crystal. The uniaxial crystal provides one way for modulating the properties of an EGSM beam.

Multi-Gaussian Schell-model vortex beam

Abstract Multi-Gaussian Schell-model (MGSM) beam was introduced recently (Sahin and Korotkova, 2012 [34] , and Korotkova et al., 2012 [35] ). In this paper, multi-Gaussian Schell-model vortex (MGSMV) beam is introduced as a natural extension of MGSM beam. The explicit expression for the cross-spectral density of a MGSMV beam propagating through a stigmatic ABCD optical system is derived and the focusing properties of a MGSMV beam are studied in detail. It is found that we can shape the focused beam profile by varying the initial beam parameters, which will be useful in material thermal processing and particle trapping.

State of polarization and propagation factor of a stochastic electromagnetic beam in a gradient-index fiber

With the help of a tensor method, we investigate the evolution properties of the state of polarization of an electromagnetic Gaussian Schell-model beam propagating through a gradient-index (GRIN) fiber. We find that the Stokes parameters and the polarization ellipse exhibit periodicity. The initial beam parameters affect the values of the Stokes parameters and the parameters of the polarization ellipse. Furthermore, based on the second-order moments of the Wigner distribution function, the explicit expression for the propagation factor (known as the M(2) factor) in the GRIN fiber is derived. It is shown that the M(2) factor remains invariant on propagation and is determined only by the initial beam parameters.

Propagation properties of a radial phased-locked partially coherent anomalous hollow beam array in turbulent atmosphere

Abstract The propagation properties of a phase-locked partially coherent anomalous hollow beam (AHB) array in turbulent atmosphere is investigated in detail. The analytical expressions for the average intensity of a radial phase-locked partially coherent AHB array in turbulent atmosphere are derived based on the extended Huygens–Fresnel principle. By using the analytical expressions, the average intensity distribution and spreading properties of a radial phase-locked partially coherent AHB array in turbulent atmosphere and in free space are numerically studied. The results show that the propagation properties of a radial phase-locked partially coherent AHB array in turbulent atmosphere are significantly affected by initial beam parameters and the structure constant of turbulent atmosphere.

Average intensity and spectral shifts of a partially coherent standard or elegant Laguerre-Gaussian beam beyond paraxial approximation

With the help of the Rayleigh-Sommerfeld diffraction integral, an analytical formula for the spectral density of a nonparaxial polychromatic partially coherent (NPPC) standard or elegant Laguerre-Gaussian (LG) beam propagating through free space is derived. The evolution properties of the intensity distribution of a NPPC standard or elegant LG beam are studied numerically. It is found that the behavior of the intensity distribution of the NPPC standard or elegant LG beam is determined by the initial beam parameters (i.e., beam waist size, spatial coherence width and beam orders). Furthermore, we also study the influence of the initial beam parameters on the spectral change of a NPPC standard or elegant LG beam upon propagation in free space. It is shown that the on-axis spectral shift of a NPPC standard LG beam is almost the same with that of a NPPC elegant LG beam when the initial beam parameters of two type beams are identical. However, the difference between the off-axis spectral shift between a NPPC standard LG beam and a NPPC elegant LG beam is enhanced with the decrease of beam waist size or with the increase of spatial coherence width and beam mode orders.

Statistical properties of a cylindrical vector partially coherent beam in turbulent atmosphere

Cylindrical vector (CV) partially coherent beam was introduced (Dong et al. Opt Express 19:5979–5992, 2011) and generated (Wang et al. Appl Phys Lett 100:051108, 2012) recently. In this paper, we derive the realizability conditions for a CV partially coherent beam, and we derive the analytical formula for the cross-spectral density matrix of a CV partially coherent beam propagating in turbulent atmosphere based on the extended Huygens-Fresnel formula. The statistical properties, such as the average intensity, the complex degree of coherence and the degree of polarization of a CV partially coherent beam in turbulent atmosphere are studied in detail and compared with those in free space. It is found that the statistical properties of a CV partially coherent beam in turbulent atmosphere are much different from those in free space, and are affected by the initial beam parameters.

Spectral shift of a partially coherent standard or elegant Laguerre–Gaussian beam in turbulent atmosphere

Spectral changes of a partially coherent standard or elegant Laguerre–Gaussian (LG) beam propagating in turbulent atmosphere were studied numerically. Our results show that the spectral changes of a partially coherent standard or elegant LG beam in turbulent atmosphere are determined by both the structure constant of the turbulent atmosphere and the initial beam parameters. Furthermore, it is found that a partially coherent elegant LG beam is less affected by the turbulent atmosphere than a partially coherent standard LG beam from the aspect of the on-axis spectral shift, and this advantage is enhanced for small structure constant, small beam waist size, large mode orders, and large transverse coherence length. Our results will be useful in long-distance free-space optical communications.

Uncertainty and sensitivity analysis of the effect of the mean energy and FWHM of the initial electron fluence on the Bremsstrahlung photon spectra of linear accelerators

A calculation of the correct dose in radiation therapy requires an accurate description of the radiation source because uncertainties in characterization of the linac photon spectrum are propagated through the dose calculations. Unfortunately, detailed knowledge of the initial electron beam parameters is not readily available, and many researchers adjust the initial electron fluence values by trial-and-error methods. The main goal of this work was to develop a methodology to characterize the fluence of initial electrons before they hit the tungsten target of an Elekta Precise medical linear accelerator. To this end, we used a Monte Carlo technique to analyze the influence of the characteristics of the initial electron beam on the distribution of absorbed dose from a 6MV linac photon beam in a water phantom. The technique is based on calculations with Software for Uncertainty and Sensitivity Analysis (SUSA) and Monte Carlo simulations with the MCNP5 transport code. The free parameters used in the SUSA calculations were the mean energy and full-width-at-half-maximum (FWHM) of the initial electron distribution. A total of 93 combinations of these parameters gave initial electron fluence configurations. The electron spectra thus obtained were used in a simulation of the electron transport through the target of the linear accelerator, which produced different photon (Bremsstrahlung) spectra. The simulated photon spectra were compared with the 6-MV photon spectrum provided by the linac manufacturer (Elekta). This comparison revealed how the mean energy and FWHM of the initial electron fluence affect the spectrum of the generated photons. This study has made it possible to fine-tune the examined electron beam parameters to obtain the resulted absorbed doses with acceptable accuracy (error <1%).

Evolution properties of the complex degree of coherence of a partially coherent Laguerre–Gaussian beam in turbulent atmosphere

Evolution properties of the complex degree of coherence of a partially coherent Laguerre–Gaussian beam (LGB) on propagation in free space and turbulent atmosphere are studied comparatively with the help of the general propagation formula for such beam. It is found that the behavior of the complex degree of coherence of a partially coherent LGB on propagation in turbulent atmosphere is much different from that in free space and is closely related to the initial beam parameters and the structure constant of the turbulent atmosphere. The distribution of the modulus of the complex degree of coherence of the partially coherent LGB finally becomes of Gaussian distribution at long propagation distance in turbulent atmosphere, and it becomes of Gaussian distribution more slowly with the increase of the mode orders, beam width and wavelength. Our results will be useful in long-distance free-space optical communications.

Statistical properties of a nonparaxial Gaussian Schell-model beam in a uniaxial crystal

Nonparaxial propagation theory of coherent beams in a uniaxial crystal is extended to the partially coherent case. An analytical formula for the 3×3 cross-spectral density matrix of a nonparaxial Gaussian Schell-model (GSM) beam propagating in a uniaxial crystal orthogonal to the optical axis is derived. Statistical properties, such as the spectral intensity and the degree of polarization, of a nonparaxial GSM beam in a uniaxial crystal are studied numerically. It is found that the statistical properties of a nonparaxial GSM beam are closely determined by its initial beam parameters and the parameters of the crystal. Uniaxial crystal can be used to modulate the spectral density and degree of polarization of a nonparaxial partially coherent beam. Our results may be useful in some applications, such as optical trapping and nonlinear optics, where a light beam with special beam profile and polarization is required.