Beam Distribution Research Articles

Change in coherence properties of ovally Gaussian Schell-model vortex beam in non-Kolmogorov turbulence along an uplink path

Analytical expressions are obtained for the cross-spectral density (CSD) matrix elements of an ovally Gaussian Schell-model vortex (OGSMV) beam propagating in non-Kolmogorov turbulence along uplink path based on the extended Huygens-Fresnel principle, and its coherence properties such as spectral degree of coherence (SDOC), phase distributions and coherence vortices are investigated in detail. Results indicate that the profile of the SDOC of OGSMV beam in turbulence gradually degrades into a Gaussian-like profile, and OGSMV beam with smaller ovality, larger topological charge number and initial coherence lengths will slow down this process. Interestingly, it is clearer to observe the coherence rings of the SDOC for OGSMV beam by reducing the initial auto-correlation lengths. Furthermore, one also finds that the number of elliptical edge dislocation for phase distribution of OGSMV beam is equal to topological charge number. They can provide two effectively ways for measuring topological charge number. Lastly, we used the phase screen simulation to verify our theoretical predictions. Theoretical outcomes are in good agreement with the simulations. Our results will be of important reference for optical communication.

Generation of the flat-top beam using convolutional neural networks and Gerchberg-Saxton algorithm

Abstract Laser technology has made rapid progress in recent years and has been widely used in various fields such as medicine, biology, military, and materials science. However, the limitations of traditional Gaussian intensity distribution of the laser beams in applications have prompted the emergence and development of flat-top beam shaping technology, which has received widespread attention. Here, we introduce a new method for generating flat-top beams that combines the traditional Gerchberg-Saxton algorithm with convolutional neural networks, using spatial light modulators to achieve flat-top beam shaping. A comparative analysis was conducted by comparing the root mean square error and diffraction efficiency of the generated flat-top beam with the results obtained using only the traditional Gerchberg-Saxton algorithm. Compared with the traditional Gerchberg-Saxton algorithm, the method proposed in this paper can generate a flat-top beam with smaller differences from the target light intensity and higher energy utilization, providing new possibilities for the application of laser technology.

Propagation properties of two types of sinc Schell-model beams in oceanic turbulence

Abstract The evolution of two types of sinc Schell-model (SSM) beams, each considered with both circular and rectangular symmetries, is investigated during their propagation in oceanic turbulence. The expressions for the spectral intensity and spectral coherence of the transmitted optical field are derived using the extended Huygens-Fresnel principle. Based on these expressions, numerical simulations are carried out to explore how source and turbulence parameters influence the transmitted field. The results demonstrate that the spectral intensity distribution of the SSM1 beam evolves from an initial Gaussian profile into a circular or rectangular flat-topped shape during propagation, while the SSM2 beam develops into a ring-shaped or array-like pattern. As the dissipation rate of turbulent kinetic energy decreases, or the mean square temperature dissipation rate and the strength of temperature and salinity fluctuations increase, the energy of these beams disperses from its concentrated regions to the surrounding areas, causing the characteristic intensity distributions to become blurred. Additionally, the coherence of these beams exhibits oscillatory distributions, with the SSM2 beam showing stronger oscillations compared to the SSM1 beam and displaying greater sensitivity to changes in turbulence parameters. The intensity and coherence distributions are also affected by source parameters, which play a dominant role at shorter propagation distances. However, as the distance increases, turbulence parameters gradually become the primary influence. The results presented here may be applied to oceanic optical communication and remote sensing.

Propagation characteristics of a circular Airyprime Gaussian beam in a gradient refractive index medium

In this paper, the focusing characteristics of a circular Airyprime Gaussian beam (CAPGB) propagating in a gradient refractive index (GRIN) medium is studied for the first time, to the best of our knowledge, and some interesting features are observed. We find that the CAPGB exhibits periodic focus–defocus behavior and completes a period propagation process with two focal points within a half variation period L/2 of the GRIN medium. Meanwhile, the CAPGB has singularity at the positions of z=(2j+1)L/4 on the optical axis. The focal lengths of bifocal points, the distance between two focal points, the focal intensity, and the focusing ability can be manipulated by beam parameters and the GRIN factor. It is noteworthy that the number (one or two) of focal points in one focusing period, and the focusing period or frequency of the CAPGB in the GRIN medium could be controlled by the beam distribution factor and GRIN factor, respectively. Moreover, the focusing ability of the CAPGB is much higher than that of a circular Airy Gaussian beam in the GRIN medium.

Proton Cyclotron Waves and Pickup Ion Ring Distribution Instabilities Upstream of Mars

AbstractProton cyclotron waves (PCWs) upstream of Mars are thought to be associated with the instabilities of pickup ions. The instabilities of pickup ions of ring distributions have larger maximum growth rates compared with beam distributions. However, observations revealed a notably‐reduced occurrence rate of PCWs for pickup ions of ring distributions. Linear instability analysis and a corresponding two‐dimensional particle‐in‐cell (PIC) simulation are performed to investigate the instabilities of pickup ion ring distributions upstream of Mars. Linear instability analysis indicates that a pickup ion ring distribution is unstable to the ion cyclotron, ion Bernstein, and mirror instabilities. The corresponding PIC simulation confirms the linear analysis results and further demonstrates that the pickup ions are scattered toward an isotropic shell distribution by the waves excited. Interestingly, the saturation energy of the waves is much lower than that driven by a corresponding pickup ion beam distribution, and mirror waves eventually dominate the system.

Composite underwater optical wireless channel modeling based on the electric field Monte Carlo method

In this study, we propose a simulation method to investigate the scattering characteristics of beams with specific phase structures in waters containing micrometer-scale particles and bubbles. This method is based on the electric field Monte Carlo (EMC) algorithm and utilizes the Mie theory and ray tracing method. We simulate the propagation of orbital angular momentum (OAM) beams in a composite underwater channel using the proposed method and analyze the impact of bubble density on the spiral phase distribution of the OAM beams. We also design an underwater experiment in a water tank to simulate the propagation of OAM beams in the composite channel. The results reveal that the power of the desired mode of the OAM beam decreases as the bubble density increases, which is consistent with the simulation results. This method facilitates a realistic simulation of structured light beam propagation in waters containing particles and bubbles and can provide reference data for studying the scattering characteristics of structured beams in composite underwater channels.

Supression of shielding effect of large area field emitter cathode in radio frequency gun environment

Abstract Utilisation of large area field emitters (LAFE) cathodes for rf gun injector hold promise for delivering compact, high power and high brightness electron beam for advanced accelerator technologies. LAFEs subjected to DC electric fields posses significant challenges due to the shielding effect which restricts emission from central emitters and decreases the overall current density. Mitigating the shielding effect of LAFE in rf gun environment is essential for meeting the desired beam quality requirement in an accelerator. The current distribution of LAFE under DC conditions depend on its various geometrical parameters such as emitter height, inter-emitter distance, aspect ratio, number of emitters. Additionally, in rf gunsetup, LAFEs are subjected to variable macroscopic electric field at different emitter position which can potentially alter the current distribution compared to DC fields. In this work, we have systematically studied the shielding effect properties of LAFE in rf gun environment under the influence of various LAFE parameters. A semi-analytical approachhas been adopted to estimate the current distribution which combines the analytically calculated field enhancement factor (γ) and numerically calculated applied rf field values. This new methodology was first validated using COMSOL simulation and then employed for field emission performance estimation of a LAFE cathode integrated in a½ cell S-band (2856 MHz) rf gun. The simulation results reveals that under favourable conditions, a Gaussian spatial distribution of beam can be obtained from LAFE thus countering the shielding effect typical in DC fields. By optimizing the LAFE parameters, the desired current and beam distribution pattern can be achieved. This study highlights the adoption of a promising approach for designing LAFE cathodes suitable for rf gun which can lead to advancement of field emission technologies for accelerator-related applications.

Assessing the robustness of dose distributions in carbon ion prostate radiotherapy using a fast dose evaluation system.

We developed a software program for swiftly calculating dose distributions for carbon ion beams. This study aims to evaluate the accuracy of dose calculations using this software and assess the robustness of dose distribution in treating prostate cancer. At the Osaka Heavy Ion Therapy Center, markers are inserted into the prostate gland and used for position verification. To account for geometric changes along the beam path due to marker translation, a beam-specific planning target volume (bsPTV) is set for each beam. To validate the accuracy of the dose calculations using the developed software, dose distributions for prostate and sarcoma cases were calculated and compared with the treatment planning system. To assess the robustness of the dose distribution, position verification data from 346 cases were utilized to reproduce dose distributions for three matching methods: bone matching, widely adopted in most particle therapy centers; marker translation, which involves direct translation to markers without bone matching; and marker translation after bone matching. The coverage of the target (D99 of clinical target volume (CTV)) was assessed to evaluate the robustness of the dose distribution. Additionally, statistical analyses were conducted for the dose distributions of each matching method. The dose calculation for a single condition can be completed very quickly. Statistical analysis revealed significant differences among dose distributions considering the three matching methods. When irradiation was performed with bone matching only, the D99 was reduced by more than 10% in approximately 7.5% of cases, making it as the poorest among the three matching methods. However, there was no significant reduction in target coverage with the other two methods. We have demonstrated the accuracy of the developed software for rapidly calculating dose distributions for carbon ion beams and confirmed the robustness of the dose distributions based on the bsPTV.

Comparison of elastic properties of periodic and aperiodic porous structures produced by additive methods

The aim of this work was to design, print, and examine elastic properties of porous structures with various parameters and beam distributions. These structures, generated using an algorithm, featured three types of lattices: octet, cubic, and Voronoi diagram-based, with different porosities (40 %, 60 %, 80 %) and beam sizes (0.45 mm, 0.66 mm). They were printed using Direct Light Processing and examined using X-ray computed microtomography. Compression tests were conducted to determine the Young’s modulus. The results were compared with computer simulations performed using Abaqus. The tools used, such as 3D printing and X-ray computed microtomography, were described, and the results and conclusions of the tests were presented. As a result, comparable outcomes were obtained for structures with higher beam diameter, while significantly different results were observed for structures with lower beam diameter.

Real-time measurement of two-dimensional LET distributions of proton beams using scintillators.


The linear energy transfer (LET) of proton therapy beams increases rapidly from the Bragg peak to the end of the beam. Although the LET can be determined using analytical or computational methods, a technique for efficiently measuring its spatial distribution has not yet been established. Thus, the purpose of this study is to develop a technique to measure the two-dimensional LET distribution in proton therapy in real time using a combination of multiple scintillators with different quenching. Inorganic and organic scintillator sheets were layered and irradiated with proton beams. Two-color signals of the CMOS sensor were obtained from the scintillation light and calibration curves were generated using LET. LET was calculated using Monte Carlo simulations as LETt and LETd weighted by fluence and dose, respectively. The accuracy of the calibration curve was evaluated by comparing the calculated and measured LET values for the 200 MeV monoenergetic and spread-out Bragg peak (SOBP) beams. LET distributions were obtained from the calibration curves.
Main results:
The deviation between the calculated and measured LET values was evaluated. For both LETt and LETd, the deviation in the plateau region of the monoenergetic and SOBP beams tended to be larger than those in the peak region. The deviation was smaller for LETd. In the obtained LETd distribution, the deviation between the calculated and measured values agreed within 3% in the peak region, while the deviation was larger in other regions. The LET distribution can be measured with a single irradiation using two scintillator sheets. This method may be effective for verifying LET in daily clinical practice and for quality control.&#xD.

Vibration analysis of functionally graded saturated porous beams using radiative energy transfer method

An energy flow model based on the radiative energy transfer method (RETM) is established for the high-frequency response prediction of finite functionally graded saturated porous beams. The Timoshenko beam theory and the Biot thoery are applied to derive the motion governing equations of the beam. The response of the beam loaded by a high-frequency point force is described by vibrational energy density and intensity. The energy response of the beam is contributed by the rays emitted from the actual source set at load point and then reflected through the fictitious sources at the boundaries. Fictitious sources are determined by the energy balance equations at the boundaries. Numerical examples show that the energy distributions of the saturated porous beams are well predicted by the proposed approach.

Joint phase control in metasurfaces for optical convolution operations

Combining the propagation and geometric phases in a metasurface facilitates the independent control of multiple parameters of the light field. However, the geometric phase often displays a random distribution, making it difficult to observe directly. We introduce a frequency-dependent phase response: at frequency f1, there is a superposition of the geometric and propagation phases, whereas at frequency f2, the propagation phase remains constant, and only the geometric phase is applied. The superposition can be interpreted as a convolution process in far-field Fraunhofer diffraction, enabling convolution metasurface devices to generate complex orbital angular momentum beams array and patterned array. Notably, the geometric phase aligns with the characteristic distribution of orbital angular momentum beams, allowing direct observation of the loaded geometric phase. These findings open what we believe to be new avenues for manipulating and calculating complex vector optical fields, optical information coding, controlling light-matter interactions, and enhancing optical communication.

Spoke-Type Structures in an Ion Diode with Magnetic Insulation of Electrons

The article presents the results concerning the cross-sectional energy density distribution of a pulsed ion beam for two types of diodes with electron open drift: with external magnetic insulation (250 kV, 80 ns, 0.6 T) and with self-magnetic insulation of electrons (250–300 kV, 120 ns, 0.8 T). Anode plasma is formed using a breakdown along the surface of the anode dielectric coating (single-pulse mode) or explosive electron emission (with double opposite-polarity pulses). It was found that, when the energy density of the ion beam exceeds ≈0.4 J/cm2, periodic spoke-type structures with a step of 3–6 cm in the beam cross section are formed. The processes of formation of such a structure—nonuniform density of anode plasma and self-organization of anode and/or cathode plasma in crossed electric and magnetic fields—are analyzed. It is shown that the formation of local plasma regions in the anode–cathode gap of an ion diode can cause the formation of a periodic structure of the cross-sectional energy density distribution.

An upgrade of the radial probes for HIRFL-SFC

SFC (Sector Focusing Cyclotron) is essential to the Heavy Ion Research Facility in Lanzhou (HIRFL). Its beam extraction efficiency is directly related to the overall operational efficiency of the accelerator. The original radial probes of the SFC, due to its outdated equipment, no longer meet the requirements for beam tuning in terms of mechanical precision, vacuum level, and local noise. Three new sets of radial probes have been developed in phases. These devices were installed at the accelerator site during annual maintenance, providing axial and radial beam distribution during acceleration. Since 2020, the system has been operating without any failures, providing corresponding beam parameters for the accelerator's operation and ensuring the normal functioning of the accelerator.

Reduction of the Downward Energy Flux of Nonthermal Electrons in the Solar Flare Corona due to Cospatial Return-current Losses

High-energy electrons carry much of a solar flare’s energy. Therefore, understanding changes in electron beam distributions during their propagation is crucial. A key focus of this paper is how the cospatial return current reduces the energy flux carried by these accelerated electrons. We systematically compute this reduction for various beam and plasma parameters relevant to solar flares. Our 1D model accounts for collisions between beam and plasma electrons, return-current electric-field deceleration, thermalization in a warm target approximation, and runaway electron contributions. The results focus on the classical (Spitzer) regime, offering a valuable benchmark for energy flux reduction and its extent. Return-current losses are only negligible for the lowest nonthermal fluxes. We calculate the conditions for return-current losses to become significant and estimate the extent of the modification to the beam’s energy flux density. We also calculate two additional conditions that occur for higher injected fluxes: (1) where runaway electrons become significant, and (2) where current-driven instabilities might become significant, requiring a model that self-consistently accounts for them. Condition 2 is relaxed and the energy flux losses are reduced in the presence of runaway electrons. All results are dependent on beam and cospatial plasma parameters. We also examine the importance of the reflection of beam electrons by the return-current electric field. We show that the interpretation of a number of flares needs to be reviewed to account for the effects of return currents.

Enhancing Time-of-Flight Diffraction (TOFD) Inspection through an Innovative Curved-Sole Probe Design

Time-of-Flight Diffraction (TOFD) is a method of ultrasonic testing (UT) that is widely established as a non-destructive technique (NDT) mainly used for the inspection of welds. In contrast to other established UT techniques, TOFD is capable of identifying discontinuities regardless of their orientation. This paper proposes a redesign of the typical TOFD transducers, featuring an innovative curved sole aimed at enhancing their defect detection capabilities. This design is particularly beneficial for thick-walled samples, as it allows for deeper inspections without compromising the resolution near the surface area. During this research, an evaluation consisting in simulations of the ultrasonic beam distribution and experimental tests on a component with artificially manufactured defects at varying depths has been performed to validate the new design. The results demonstrate a 30 to 50% higher beam distribution area as well as an improvement in the signal-to-noise ratio (SNR) resulting in a 24% enhancement in the capability of defect detection compared to the traditional approach.

A Method of Realizing Adaptive Uniform Illumination by Pyramid Prism for PA-LiDAR

In this paper, we propose a simple method to generate the uniform illumination using a pyramid prism for Plane Array Laser Imaging Detection and Ranging (PA-LiDAR). The principle of the pyramid prism shaping the Gaussian beam to form a uniform beam was analyzed theoretically. By changing the parameters of the pyramid prism and laser beam, the profile distribution of the output beam can be easily adjusted. Based on the operation mode and illumination requirements of PA-LiDAR, we have developed a set of LiDAR prototypes using a pyramid prism and carried out experimental research on these prototypes. The simulation and experimental results demonstrated that this method can achieve a uniform illumination beam with excellent propagation properties for meeting the technical requirements of PA-LiDAR. This method of uniform illumination has the advantages of being simple, flexible, easily adjustable and convenient to operate.

Revealing the propagation dynamic of a Laguerre-Gaussian beam with two Bohm-like theories

By employing x-Bohm theory and p-Bohm theory, we construct the position and momentum trajectories of single-mode and superposed-mode Laguerre-Gaussian (LG) beams. The dependence of divergence velocity and rotation velocity on the initial position and propagation distance is quantified, indicating that LG beams exhibit subluminal effects, even in free space. Additionally, we clarify the formation of the petal-shaped intensity distribution of the superposed-mode LG beam in terms of motion trajectory, where the particle-like trajectory and wave-like interference are “simultaneously” observed. Our work provides an intuitive way to visualize the propagation characteristics of LG beams and deepen the comprehension of Bohm-like theory.

Efficient six-dimensional phase space reconstructions from experimental measurements using generative machine learning

Next-generation accelerator concepts, which hinge on the precise shaping of beam distributions, demand equally precise diagnostic methods capable of reconstructing beam distributions within six-dimensional position-momentum spaces. However, the characterization of intricate features within six-dimensional beam distributions using current diagnostic techniques necessitates a substantial number of measurements, using many hours of valuable beam time. Novel phase space reconstruction techniques are needed to reduce the number of measurements required to reconstruct detailed, high-dimensional beam features in order to resolve complex beam phenomena and as a feedback in precision beam shaping applications. In this study, we present a novel approach to reconstructing detailed six-dimensional phase space distributions from experimental measurements using generative machine learning and differentiable beam dynamics simulations. We demonstrate that this approach can be used to resolve six-dimensional phase space distributions from scratch, using basic beam manipulations and as few as 20 two-dimensional measurements of the beam profile. We also demonstrate an application of the reconstruction method in an experimental setting at the Argonne Wakefield Accelerator, where it is able to reconstruct the beam distribution and accurately predict previously unseen measurements 75× faster than previous methods. Published by the American Physical Society 2024

Study on the Improvement of Theoretical and Electric Field Simulation Methods for the Accurate Prediction of FEEP Thruster Performance

In this study, we investigate and propose an improved theoretical method to more accurately predict the performance of a field-emission electric propulsion (FEEP) thruster with its complex configuration. We identify critical flaws in the previous theoretical methods and derive corrected equations. Additionally, we define and implement the overall half angle of the Taylor cone to account for variations in the Taylor cone’s half angle depending on the applied voltage. Next, we also establish an improved method of the electric filed simulation in a three-dimensional domain to accurately predict a trajectory of extracted ions and a resulting spatial beam distribution of the FEEP thruster by incorporating a configuration of the Taylor cone with the estimated overall half angle from the results of the present theoretical method. Through comparison with the experimental measurements, we found that the present improved methods for theoretical and electric field simulations can yield more accurate predictions than those of the previous methods, especially for higher V and Iem regimes, which correspond to the actual operating conditions of the FEEP thruster. Consequently, we anticipate that the proposed methods can enhance the reliability and efficiency of the design process by accurately predicting performance when developing the new FEEP thruster with its non-symmetric complex configuration to match specific thrust or spatial beam requirements.