Non-ideal Beam Research Articles

Accuracy of linear transformations performed on a nonideal Mach–Zehnder interferometer

We consider a mathematical model of a planar Mach–Zehnder interferometer with nonideal beam splitters. For this model, we obtain two fidelity estimates of the matrix–vector multiplication in the form of dependences of the multiplication error on the beam splitting error in directional couplers. The first estimate is obtained as a measure of the difference between the transfer matrices implemented by interferometers and is presented in the form of the norm of the difference between two unitary matrices corresponding to ideal and non-ideal interferometers. The second estimate is obtained as a measure of the difference in output intensities. It is shown that in the latter case the fidelity depends both on the beam splitter error and on the parameters of the input signals. We verified the second estimate using computer simulations of MZI in COMSOL Multiphysics.

Proposal and design of 81.25 MHz heavy ion drift tube linacs for BISOL

Based on the design requirements proposed by the Beijing On-Line Isotope Separation project (BISOL), four Sn22+-based, 81.25 MHz continuous wave (CW) drift tube linac (DTL) cavities have been designed. These DTLs are capable of accelerating Sn22+ of 0.1 pmA from 0.5 MeV/u to 1.8 MeV/u over a length of 7 m, with an output longitudinal normalized RMS emittance of 0.35π·mm·mrad, and transmission efficiency higher than 95%. The dynamics design adopted the KONUS (Kombinierte Null Grad Struktur Combined 0° Structure) scheme. Comprehensive error study implies that these DTLs can accommodate a wide range of non-ideal beams and cavity alignment errors while maintaining high transmission efficiency. The electromagnetic design employed a Cross-bar H-mode (CH) structure for superior water-cooling characteristics, and a detailed tuning analysis was conducted to derive an optimal tuning scheme. The results of the multiple-physics analysis indicate that the frequency shift of each cavity is within an acceptable range. Comparing the dynamics requirements with the RF design results, similar particle output phase distribution, equivalent energy gain and consistent emittance growth are observed. Detailed designs will be presented in this manuscript.

Effect of Non-Ideal Electron Beam Characteristics on the Performance of a Megawatt-Power Gyrotron with an External Monochromatic Signal

Effect of Non-Ideal Electron Beam Characteristics on the Performance of a Megawatt-Power Gyrotron with an External Monochromatic Signal

Astigmatic electron beam propagation

An astigmatic electron beam with an ellipticity ratio of approximately 2:1 was examined using the Enhanced Modified Faraday Cup (EMFC) diagnostic to measure its properties and show how the power density distribution varies near the beam waist. Results show that the beam has two power density peaks, one on either side of the beam crossover point, resulting from different focal distances of the major and minor axes of the elliptical beam shape. Quantification of the beam properties was used to establish a depth-of-field where the beam diameter and peak power densities are relatively constant. For the 1 kW beam studied here, the depth-of-field measured approximately ±5 mm from the beam crossover point, illustrating how electron beam diagnostics can be used to identify process control limits for repeatable and reliable welds under non-ideal electron beam power density distribution conditions.

A Volterra-PEM approach for random vibration spectrum analysis of nonlinear systems

In this paper, the Volterra series and the pseudo-excitation method (PEM) are combined to establish a frequency domain method for the power spectral density (PSD) analysis of random vibration of nonlinear systems. The explicit expression of the multi-dimensional power spectral density (MPSD) of the random vibration response is derived analytically. Furthermore, a fast calculation strategy from MPSD to physical PSD is given. The PSD characteristics analysis of the random vibration response of nonlinear systems is effectively achieved. First, within the framework of Volterra series theory, an improved PEM is established for MPSD analysis of nonlinear systems. As a generalized PEM for nonlinear random vibration analysis, the Volterra-PEM is used to analyse the response MPSD, which also has a very concise expression. Second, in the case of computation difficulties with multi-dimensional integration from MPSD to PSD, the computational efficiency is improved by converting the multi-dimensional integral into a matrix operation. Finally, as numerical examples, the Volterra-PEM is used to estimate the response PSD for stationary random vibration of a nonlinear spring-damped oscillator and a non-ideal boundary beam with geometrical nonlinearity. Compared with Monte Carlo simulation, the results show that by constructing generalized pseudo-excitation and matrix operation methods, Volterra-PEM can be used for input PSD with arbitrary energy distribution, not only restricted to broadband white noise excitation, and accurately predict the secondary resonance phenomenon of the random vibration response of nonlinear systems in the frequency domain.

How Far is the Difference Between Mechanical Behavior of Ideal and Non-Ideal FG-GPLRC Beams?

This study explored the disparities in bending, buckling, and vibration results of ideal and non-ideal functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) beams. The smooth and continuous profiles of material distributions of ideal FG-GPLRC beams were modified for making the controlling tracks to produce two different forms of non-ideal FG-GPLRC beams which had in-and out-stepwise distributions of material constituents across the beam’s thickness. The Halpin–Tsai model and the rule of mixture were used to predict the effective material properties of the nanocomposite beams. The closed-form solution possessing less time of computation was provided for predicting the mechanical behavior of the beams, and it was validated for accuracy by comparing with the results of the Ritz method. The study’s results suggest that non-ideal beams with an out-stepwise distribution of material constituents have a better dispersion of reinforcing nanomaterials than in-stepwise distribution. Therefore, the results of the beams with an out-stepwise distribution are closer to those of ideal beams than with in-stepwise distribution.

Effect of Electron Beam Properties on a Second Harmonic Gyrotron

In harmonic gyrotrons, the narrow operating region of the harmonic mode is significantly restricted by the severe mode competition from the fundamental parasitic modes, which makes it important to study the nonlinear effects of beam-wave interaction in the case of a nonideal electron beam. In this article, the effect of the electron velocity spread and the beam radius spread on the mode excitation, interaction efficiency as well as mode competition are analyzed for the desired harmonic mode and the parasitic fundamental mode operating far from the cut-off frequency. The effect of velocity spread is interpreted via the electron cyclotron resonance condition as well as the electron beam susceptibility with respect to the resonator field. The results show that the velocity spread can greatly broaden the effective operating region of the harmonic mode and the efficiency degradation can be contained at a reasonable level by proper design consideration of the interaction circuit. Whereas, the beam radius spread is the main factor that accounts for the efficiency degradation and can aggregate the mode competition. The results are referential to the design and analysis of harmonic gyrotrons as well as continuously frequency tunable gyrotrons.

Design of a CW BISOL RFQ for Three Kinds of High-Charge-State Ions Simultaneous Acceleration

Based on the latest design requirements proposed by the Beijing On-Line Isotope Separation (BISOL) project, a new Sn22+-based, 81.25 MHz CW radio frequency quadrupole (RFQ) with external bunching has been designed. This RFQ can accelerate Sn22+ to 0.5 MeV/u with an output longitudinal-normalized rms emittance of 0.20 keV/u·ns over a length of 5.6 m. The tolerance and error analysis results indicate that this RFQ can handle a wide range of non-ideal beams while maintaining relatively lower longitudinal emittance growth and higher transmission efficiency. To maintain the beam intensity, the RFQ will simultaneously accelerate three kinds of high-charge-state mixed ions (132Sn21+, 132Sn22+ and 132Sn23+), the simulation results given by Impact-T show that the RFQ can achieve high transmission of the mixed beam. Compared with the previous Sn21+-based internal bunching RFQ scheme, this RFQ has a shorter length and smaller output emittance, which is beneficial to the designs of subsequent Medium-energy Beam Transport (MEBT) and Drift Tube Linac (DTL). In electromagnetic design, a four-vane structure with 48 tuners and 16 π-mode stabilizers (PSLs) were chosen. The results of the multi-physics analysis show that the maximum temperature rise and the maximum deformation of the cavity are 13.6 K and 40.3 µm, respectively. The results simulated with CST Microwave Studio (CST) and HFSS software were consistent.

Volume averaging effect in nonlinear processes of focused laser fields.

We report theoretical derivations and experimental results on the volume averaging effect of nonlinear processes in focused laser fields. This effect is considered detrimental in revealing the intensity dependence of a nonlinear process, caused by the intensity variation across the sampled volume of a focused laser. Following the treatment in the literature, we prove that if the signal dependence can be expressed as a simple power function of the laser intensity and if the detection region encompasses effectively the whole volume, volume average does not affect the final conclusion on the derived exponent. However, to reveal the detailed saturation effect of a multi-photon process, intensity selective scans involving spatial filters and displacement of the laser focus (z-scan) are required. Moreover, to fully capture the dependence of the signal on the variation of the laser intensity, the degree of spatial discrimination and the corresponding range of the z-scan need to be modeled carefully. Limitations in the dynamic range of the detector or the laser power, however, can thwart the desired scan range, resulting in erroneous fitting exponents. Using our nanosecond laser with a non-ideal Gaussian beam profile based on multiphoton ionization of argon atoms from a collimated molecular beam and from ambient argon gas, we report experimental measurements of the beam waist and Rayleigh range and compare the experimental intensity dependence of Ar+ with theoretical values. Agreements between theory and experiment are remarkable.

CW RFQ design and investigation for multi-charge-state acceleration of radioactive beams from BISOL

A continuous-wave (CW) heavy-ion radio frequency quadrupole (RFQ) has been designed to accelerate radioactive beams from the Beijing Isotope Separation On-Line (BISOL) facility. This RFQ will accelerate high-charge-state ions such as 132Sn21+ from 3 keV/u to 300 keV/u with a vane length of 3.77 m at a frequency of 81.25 MHz. The transmission efficiency reached 98.1% in simulation. The output longitudinal normalized rms emittance is 0.31 keV/u⋅ns. Tolerance analysis shows that this RFQ can handle a wide range of non-ideal beams while retaining a relatively high transmission efficiency and low longitudinal emittance. In order to increase the intensity of the radioactive ion beams (RIB), this RFQ will accelerate multi-charge-state beams simultaneously. In the case of the tin beam (Sn), we have studied the transmission of adjacent charge state beams and multi-charge-state beams in this RFQ. The transmission efficiency and output transverse beam quality of the multi-charge-state beams are close to the results of the single-charge-state beam, but the output longitudinal emittance is larger. For the radio frequency (RF) structural design, we have compared different types of RFQ, including an IH RFQ, a 4-rod RFQ and a 4-vane RFQ. We have selected a 4-vane RFQ design with dipole stablizer rods, due to the considerations of power consumption, the flatness of electric field, cooling convenience and machining efficiency. We have performed full 3D simulations with multi-physics analysis.

Shading correction assisted iterative cone-beam CT reconstruction

Recent advances in total variation (TV) technology enable accurate CT image reconstruction from highly under-sampled and noisy projection data. The standard iterative reconstruction algorithms, which work well in conventional CT imaging, fail to perform as expected in cone beam CT (CBCT) applications, wherein the non-ideal physics issues, including scatter and beam hardening, are more severe. These physics issues result in large areas of shading artifacts and cause deterioration to the piecewise constant property assumed in reconstructed images. To overcome this obstacle, we incorporate a shading correction scheme into low-dose CBCT reconstruction and propose a clinically acceptable and stable three-dimensional iterative reconstruction method that is referred to as the shading correction assisted iterative reconstruction. In the proposed method, we modify the TV regularization term by adding a shading compensation image to the reconstructed image to compensate for the shading artifacts while leaving the data fidelity term intact. This compensation image is generated empirically, using image segmentation and low-pass filtering, and updated in the iterative process whenever necessary. When the compensation image is determined, the objective function is minimized using the fast iterative shrinkage-thresholding algorithm accelerated on a graphic processing unit. The proposed method is evaluated using CBCT projection data of the Catphan© 600 phantom and two pelvis patients. Compared with the iterative reconstruction without shading correction, the proposed method reduces the overall CT number error from around 200 HU to be around 25 HU and increases the spatial uniformity by a factor of 20 percent, given the same number of sparsely sampled projections. A clinically acceptable and stable iterative reconstruction algorithm for CBCT is proposed in this paper. Differing from the existing algorithms, this algorithm incorporates a shading correction scheme into the low-dose CBCT reconstruction and achieves more stable optimization path and more clinically acceptable reconstructed image. The method proposed by us does not rely on prior information and thus is practically attractive to the applications of low-dose CBCT imaging in the clinic.

The Experimental Verification of Gaussian Beam Coupling for ECH Transmission Line at 400 GHz

We design a quasi-optical transmission line system for a 400 GHz gyrotron beam. The 400GHz Gaussian beam is injected to a corrugated waveguide bounced from a quasi-optical mirror. From detailed 2D field patterns of the output beam emitted from the corrugated waveguide, we analyze the mode contents and the source of non-ideal beam expansion

Relaxation Process of Interacting Two-mode System Influenced by Markovian Thermal Reservoirs

Two different models of a relaxation process are considered for a linearly interacting two-mode system under the influence of independent Markovian thermal reservoirs. One is to describe the relaxation process of bare particles and the other is to describe the one of quasi particles which are derived from bare particles by the Bogoliubov transformation. The difference is that the former does not includes the effect of the inter-mode interaction on the damping operator while the latter does. The equations of motion are solved algebraically by making use of non-equilibrium thermo field dynamics. The relaxation processes in the two models are investigated in detail. The results are applied for investigating a non-ideal beam splitter with photon loss and noise addition.

Compensation of non-ideal beam splitter polarization distortion effect in Michelson interferometer

A composite optical structure consisting of two quarter-wave plates and a single half-wave plate is proposed for compensating for the polarization distortion induced by a non-ideal beam splitter in a Michelson interferometer. In the proposed approach, the optimal orientations of the optical components within the polarization compensator are determined using a genetic algorithm (GA) such that the beam splitter can be treated as a free-space medium and modeled using a unit Mueller matrix accordingly. Two implementations of the proposed polarization controller are presented. In the first case, the compensator is placed in the output arm of Michelson interferometer such that the state of polarization of the interfered output light is equal to that of the input light. However, in this configuration, the polarization effects induced by the beam splitter in the two arms of the interferometer structure cannot be separately addressed. Consequently, in the second case, compensator structures are placed in the Michelson interferometer for compensation on both the scanning and reference beams. The practical feasibility of the proposed approach is introduced by considering a Mueller polarization-sensitive (PS) optical coherence tomography (OCT) structure with three polarization controllers in the input, reference and sample arms, respectively. In general, the results presented in this study show that the proposed polarization controller provides an effective and experimentally-straightforward means of compensating for the polarization distortion effects induced by the non-ideal beam splitters in Michelson interferometers and Mueller PS-OCT structures.

Comparison of silicon and 4H silicon carbide patterning using focused ion beams

In this work, focused ion beam (FIB) milling of different structures is studied and compared for two different electronic materials, i.e., silicon (Si) and silicon carbide (SiC). Results show that the same processing parameters yield different trench cross sections for Si and SiC, even when the different material removal rates (MRR) are taken into account. In order to investigate more complex structures, nanocone arrays were fabricated in Si and SiC. The difference in the shape of the trench cross section and complex structures can be mainly explained by the significant difference in the angle dependent MRR for both materials. Other effects which occur during FIB irradiation by the non-ideal beam shape such as swelling and damage outside of the purposely processed region are emulated and sensitively studied by scanning probe microscopy techniques such as atomic force microscopy (in-line and off-line) and scanning spreading resistance microscopy, respectively, for SiC and the results are compared with those for Si.

Characteristics of a W-band sixth-harmonic peniotron with a nonideal electron beam

A calculation code for a self-consistent nonlinear large signal of peniotrons has been developed in this study. A PIC simulation of a W-band sixth harmonic peniotron with an ideal electron beam has shown 30 kW output power and conversion efficiency of up to 40%, which agree well with the results obtained under the peniotron self-consistent nonlinear large-signal calculation code. Thus, the code can be used to study peniotron performance when effects such as electron velocity spread and guiding center deviation exist. Calculated results show that a 10 kW microwave output power and a conversion efficiency of 17% can always be obtained if the peniotron guiding center deviation and longitudinal velocity spread are no more than 8%. These results help determine the minimum requirements of the electron beam quality in W-band practical peniotrons.

Propagation properties of a nonideal semi-Gaussian laser beam through a nonlinear medium material: Numerical experiment

The nonideal semi-Gaussian beam generated in our work has a certain ascent border width. Due to its asymmetry, the propagation properties of a nonideal semi-Gaussian laser beam in nonlinear materials have some unique characters. In our work, the propagation properties of a nonideal semi-Gaussian laser beam with a small ascent border width through a ZnSe nonlinear crystal is theoretically studied, and the relations of the propagation properties and the various parameters of the nonlinear medium and the semi-Gaussian beams are also analyzed theoretically in detail.

Self-amplified spontaneous emission free electron laser devices and nonideal electron beam transport

We have developed, at the SPARC test facility, a procedure for a real time self-amplified spontaneous emission free electron laser (FEL) device performance control. We describe an actual FEL, including electron and optical beam transport, through a set of analytical formulas, allowing a fast and reliable on-line ``simulation'' of the experiment. The system is designed in such a way that the characteristics of the transport elements and the laser intensity are measured and adjusted, via a real time computation, during the experimental run, to obtain an on-line feedback of the laser performances. The detail of the procedure and the relevant experimental results are discussed.

Numerical study of beam propagation and plasma properties in the neutralizer and the E-RID of the ITER Neutral Beam Injector

Non-ohmic heating will be used in the experimental nuclear fusion reactor ITER to reach thermonuclear temperatures. Two heating mechanism will be implemented, i.e. microwaves resonant with ion and electron cyclotron frequencies and energetic neutral beam injection, which contributes also to the current drive. Each one of the two neutral beam injector planned for ITER will deliver 16 MW of 1 MeV D0 beam. In the injector, negative ions D− coming from a 40 A negative ion source are electrostatically accelerated to 1 MeV, and stripped of their extra electron by collision with a target gas in a structure known as the neutralizer. Residual charged particles are deflected after the neutralizer in an electrostatic ion dump (E-RID). The ionization of the deuterium buffer gas filling the neutralizer induced by the D− beam creates a rarefied plasma which is expected to efficiently screens the Coulomb repulsion of the beam. Moreover, this plasma can eventually escape from the neutralizer and move back in the accelerator, towards the accelerating grids and the negative ion source. The transport of the beam through the neutralizer and the RID and the related plasma properties were studied using a 3D electrostatic particle-in-cell code called OBI-3 (Orsay Beam Injector 3 dimensional). Particle–particle and particle–wall collisions are treated using the Monte Carlo collision approach. Simulations show that the secondary plasma effectively screens the beam space charge preventing beam transverse expansion. Plasma ions created in the neutralizer form an upstream current with a magnitude of ∼0.5% of the negative ion current. Gas breakdown leading to arc formation in the RID was not observed. Finally, results for the propagation of non-ideal beams coming from simulations of the extraction and consecutive acceleration taken from Revel et al 2013 Nucl. Fusion 53 073027 are presented.

Fluence scan: an unexplored property of a laser beam

We present an extended theoretical background of so-called fluence scan (f-scan or F-scan) method, which is frequently being used for offline characterization of focused short-wavelength (EUV, soft X-ray, and hard X-ray) laser beams [J. Chalupský et al., Opt. Express 18, 27836 (2010)]. The method exploits ablative imprints in various solids to visualize iso-fluence beam contours at different fluence and/or clip levels. An f-scan curve (clip level as a function of the corresponding iso-fluence contour area) can be generated for a general non-Gaussian beam. As shown in this paper, fluence scan encompasses important information about energy distribution within the beam profile, which may play an essential role in laser-matter interaction research employing intense non-ideal beams. Here we for the first time discuss fundamental properties of the f-scan function and its inverse counterpart (if-scan). Furthermore, we extensively elucidate how it is related to the effective beam area, energy distribution, and to the so called Liu's dependence [J. M. Liu, Opt. Lett. 7, 196 (1982)]. A new method of the effective area evaluation based on weighted inverse f-scan fit is introduced and applied to real data obtained at the SCSS (SPring-8 Compact SASE Source) facility.