Beamlet Deflection Research Articles

Observation of beamlet displacement and parallelism in NIO1

In the compact radiofrequency negative ion source NIO1 (Negative Ion Optimization phase 1), beamlet images are recorded from visible light monochrome cameras, for which several mounting positions are available. For two cameras, named CAM1 and CAM2, looking in directions perpendicular to each other and to the z axis of the beam drift tube, an extensive database of images is available, with methods and results of analysis discussed here. All NIO1 beamlets, arranged in a 3 × 3 matrix, are extracted, so CAM1 can record 3 beamlet projection groups and CAM2 also. Both cameras can be used to estimate the beam optics, depending on extracted beamlet currents, their uniformity and applied voltages; moreover CAM1 shows the filter current effects, while CAM2 images may give information on the deflection field (due to magnets inserted in the extraction grid EG and the post-acceleration grid PA). Light reflection is reduced by careful set-up, and by considering image central portion for analysis. Image luminosity can be simply fitted by Gaussian shapes, when the 3 projection groups are fairly separated. This analysis allows to estimate beamlet displacement and deflection. In general, optional algorithms for noise rejection and pre-smoothing for improving automatic recognizing of beamlet peaks is discussed, as well as the classes of available fits. Results for beamlet size, deflection and rms divergence are reported for selected datasets (within the 10 or 20 mrad goal). In some datasets, beamlet convergence was observed, indicating the need for further analysis and beam optics adjustments.

Three-dimensional analysis of RF-biased ion optics with misalignments of apertures

Accelerator grid hole shift is a critical reason for erosion failure of optic systems in ion thrusters, which may also cause an unexpected roll torque about the ion beam axis. A three-dimensional (3D) model of ion optics is developed based on a particle-in-cell Monte Carlo collision method to investigate the plasma dynamics and performance of radio frequency (RF) grid systems with misalignments of apertures, which are compared with those in the direct current (DC) grid system. For the benchmark case, the 3D model gives a better agreement with the experiments in the ion energy distribution function (IEDF) compared with the two-dimensional model from a previous publication, with 36.4% and 47.9% relative error reduction of the peak position and full width at half maximum (FWHM), respectively, indicating the effectiveness of the developed 3D model. Simulations show that in the RF grid system the ion beamlet is deflected in the direction opposite to the shift of the accelerator grid hole, while electrons move first in the hole shift direction, and then deflect in the opposite direction. The average ion beamlet deflection angle calculated is consistent with the predictions from linear optical theory in both the RF and DC grid system. The amplitude of beamlet deflection angle fluctuation with time decreases with the increase of RF frequency. When the grid holes shift, the ion beamlet will deflect with the divergence angle almost unchanged in the DC grid system, while the beamlet divergence angle increases in the RF grid system. When RF frequency is low, the big vortex-like structure in the electron velocity phase diagram breaks into small vortices, showing a reduced oscillation intensity. The hole shift also causes high-frequency oscillation in the shift direction. In terms of performance, the RF grid system is more sensitive to grid hole shift than the DC grid system.

Simulation of beamlet deflection and its compensation by aperture displacement for a NBI negative ion source prototype

A one-RF-driver prototype of the negative ion source for the NBI of CFETR is being tested and optimized at Southwest Institute of Physics, aiming for H− beam of 200 keV in 200 A/m2. For the NBI negative ion source, it's essential to have a good beam optics with small divergence and aiming trajectory. However, beamlet deflection is unavoidably caused by the magnets inserted in the extraction grid, and it results in the zig-zag beam profile. Measures must be taken to compensate the deflection. In this work, the beamlet deflection and its compensation using the aperture displacement method are studied for the one-RF-driver prototype with numerical simulation. The deflection angle of a single beamlet is calculated and the compensation scheme of displacing the aperture on the steering grid (SG) is designed. A 200 A/m2 uniform beamlet has a deflection angle of 8 mrad at the extraction/acceleration voltage 8 kV/192 kV, EG magnets’ flux peak ±45 mT. The angle can be fully compensated with 0.7 mm displacement of SG aperture. The compensation effect is analyzed for different conditions. The scheme's dependence on the voltage ratio, also the adaptiveness to the magnetic field and the beam property are learnt: For maintaining the compensation effect, a modification within 0.02 mm is needed when the acceleration voltage varies between 152 kV and 232 kV while keeping the extraction voltage unchanged. An increase of 0.1 mm of the displacement is needed when the magnetic field peak is enhanced 5 mT and the necessary increase is 0.15 mm when the non-uniformity is enhanced 10%. The compensation scheme is verified with multi-beamlet simulation in the last, taking the beamlet-beamlet interaction and the long distance transport into account.

3D magnetic field measurements and improvements at the negative ion source BATMAN Upgrade

BATMAN Upgrade is the testbed of the prototype radiofrequency-driven negative ion source, for the Heating Neutral Beams of ITER. Its extraction system corresponds roughly to one beamlet group of ITER (1/16th of ITER NBI extraction surface), from where negative ions are extracted together with undesired co extracted electrons. The latter are deflected out of the beam by a set of permanent magnets (Co-extracted Electron Suppression Magnets, CESMs) embedded in the second grid electrode. Two different configurations of CESMs are currently under investigation in the top and bottom halves of the grid system. The amount of co-extracted electrons can be reduced in the ion source by, among other means, applying a transversal magnetic filter field (MFF) to the plasma, created by either permanent magnets or a multi-kA current flowing vertically through the first grid electrode. A special device with five 3D Hall sensors has been developed and calibrated to measure the magnetic fields along each aperture axis in the grid system. The results have been compared with FEM simulations revealing very good agreement within the geometrical and material tolerances for the CESMs, but for the MFF a large discrepancy has been observed. The problem has been identified with a poor electric contact between pieces of the first grid electrode. The contact has been improved by setting annealed Cu washers as interlayer and the MFF matches the expected one. The poor electrical contact limited the maximum strength of the MFF but the results for ion source performance and beam optics are equivalent to those of the improved electrical contact. The effects of the MFF strength, its polarity and the MFF types on the ion source performance and single beamlet optics, regarding the vertical and horizontal beamlet deflection as well as the beamlet core divergence are discussed.

Target erosion process during broad ion beam sputtering using 3D modeling of ion trajectories

Understanding the distribution of particles sputtered from a target requires an appreciation of how ions impinge on the target. In pursuit of this goal, a fully three-dimensional model of the ion trajectories in a broad ion beam, assuming full space charge compensation, Gaussian emission characteristics of the beamlets, and beamlet deflection, was constructed. The modeled ion trajectories were used to simulate target erosion, enabling a comparison between the modeled erosion and the experimental erosion. The focus was on Ar and Xe ion species at ion energies in the range of 1.4–1.9 keV and on target materials, Si, Ta, and SiO2. Conclusions were drawn on the erosion process, the potential radial inhomogeneity of the plasma in the discharge chamber of the ion source, and on the opening angle of the emission characteristics of the beamlets. For the investigated process and an applied target tilt angle of 55°, the model verified that material-specific and angle-dependent ion–solid interaction mechanisms at the atomic level played only a minor role in the target’s macroscopic surface modification in the context of the qualitative distribution of the erosion profile. In contrast, the applied sputtering geometry played a significant role.

ITER-HNB plasma and extraction grids in BUG: Characterization of magnetic deflection correction

The BATMAN Upgrade test facility aims to extract H-/D- at high current densities. The inevitably co-extracted electrons are deflected out of the beamlet by permanent magnets before acceleration. These magnets induce a row-wise zig-zag deflection of the beamlets. In the new MITICA-like extraction system, this deflection is compensated by additional deflection correction magnets. IBSimu modeling studies indicate that the deflection correction system not only acts on the horizontal beamlet deflection, but also causes aberrations to the vertical angular distribution. Dependencies of the beamlet position and size are studied in several parameter scans with the available diagnostic tools (CFC tile calorimetry, Beam Emission Spectroscopy). The horizontal beamlet deflection is robustly compensated within the systematic uncertainty of the experiment. The triangular beamlet shape predicted on basis of the magnetic field structure is visible in the CFC calorimetry.

Computational design of magnetic beamlet deflection correction for NNBI

Coextracted electrons are inevitable for negative ion based NBI systems. To avoid wastefully accelerating these electrons to the full energy, they are magnetically deflected out of the beamlet onto the extraction grid. The deflection of the electrons creates an unwanted deflection of the ions, which is magnetically corrected in the ITER heating neutral beam. In order to gain experience with magnetic deflection correction, IPP has designed a magnetic deflection correction system in collaboration with the ITER organization, which will be characterized in the BATMAN Upgrade test facility. The ion-optics code IBSimu is used for the design of the magnetic deflection correction system. A comparison of the design candidates shows that the magnetic deflection correction system inherently leads to an increased divergence as result of the magnetic field structure. The divergence increase manifests itself as an increased fraction of a broader halo component.

Benchmark of beam acceleration codes on a high voltage negative ion accelerator for fusion with a new hypothesis on the beam meniscus

It is a widely recognized phenomenon that, in negative ion sources for NBI, the magnetic fields in the source cause an asymmetry of the current density at the meniscus, which affects the beam optics. In order to achieve a more realistic estimation of the negative ion beam optics, the ion current density profile at the beamlet meniscus is sometimes assumed to be non-symmetric with respect to the beamlet axis. The new hypothesis tested in this paper is an empirical law obtained by recent investigations on a similar Kamaboko ion source, which relates this asymmetry to the magnetic field strength at the meniscus and to the power injected in the ion source. For the first time this hypothesis is used to directly and correctly predict the value of the beamlet deflection.The MeV ion source Test Facility (MTF) is a high voltage negative ion beam accelerator dedicated to fusion experiments in QST, Naka, Ibaraki, Japan. MTF can be operated as a three- or five-stage multi-aperture accelerator with a configuration and beam energy comparable to the future ITER NBI. In 2019, experiments were conducted on MTF aiming at accelerating a H- beam with high energy and good optics for a long duration of the beam (around 100 s). These experiments allowed to measure the beamlet divergence and deflection as well as the heat loads due to particle impinging on the accelerator grids, over a wide range of operating parameters. The predictions of several beam simulation codes (Opera, COMSOL, SLACCAD, EAMCC3D) have been compared to the experimental measurements, which allows to obtain a good agreement in terms of beam optics and a fair agreement in terms of heat loads.

First direct comparison of whole beam and single beamlet divergences in a negative ion source with simultaneous BES and CFC tile calorimetry measurements

Neutral beam injection (NBI) systems are required for heating and current drive in the next generation fusion experiment ITER, and strict requirements are placed on the beamlet core divergence (<7 mrad) for transmission into the tokamak. The measurement of single beamlet divergence is challenging due to the multi-beamlet nature of the negative ion sources that are required for such systems; diagnostic systems compatible with large high power ion beams can only provide spatially averaged measurements, leading to mixing of beamlet signals within diagnostic results. To improve the understanding of this effect, a direct comparison has been made between the single beamlet and multi-beamlet divergence by a combination of both Beam Emission Spectroscopy (BES) and 1D carbon fiber composite tile calorimetry, in a joint campaign by IPP and Consorzio RFX. The measurements performed so far in this campaign at the BATMAN Upgrade Test Facility have led to two major results. First, an excellent agreement is found for single beamlet divergences from the two diagnostics, showing that the results from these diagnostic systems can be compared for single beamlets. Second, the contribution of beamlet deflection, caused by an alternating magnetic field at the extract grid, to the divergence as measured using BES has been quantified with up to a factor of 3 increase when compared with the single beamlet value. This demonstrates that further investigation is needed into how mixing of information from a beamlet affects diagnostic results with a combination of both simulation and experiment, which will be performed in a next step.

Design and first results of a retractable 1D-CFC beam target for BATMAN upgrade

BATMAN Upgrade (BUG) is a test facility for the production of negative ion beams from an RF driven plasma ion source devoted to supporting the development of the ITER Neutral Beam Injection (NBI). BUG consists of the IPP RF prototype source and a multi-aperture grid system corresponding roughly to a beamlet group of the ITER NBI grid system, i.e. an arrangement of 14 (vertical) ×5 (horizontal) Ø14 mm apertures, meaning the ion beam is comprised of 70 individual beamlets. The beams can be extracted with up to 10 kV and accelerated up to a total voltage of 45 kV for up to 10 s (steady state operation is underway). One of the goals of BUG is a detailed study of the ion beam optics. So far, the permanently installed beam diagnostic consisted of several lines of sight of Beam Emission Spectroscopy (BES) at two different positions and thermocouple measurements on the beam dump calorimeter. Resolving the divergence and deflection of single beamlets is technically exceptionally difficult with the existing diagnostic tools, therefore, a beam target made out of a one-directional carbon fiber composite material (1D-CFC) with dimensions 376×142×20 mm³ has been installed at a distance of 851 mm from the exit of the grid system. The thermal footprints of the beamlets are observed from the back side via infrared imaging with a high spatial resolution (<0.7 mm/pixel) that allows characterization of the beamlets at low divergence. The target can be rotated out of the beam to make it compatible with long pulses and the forthcoming steady state operation. The safety analysis of the target operation for different operational scenarios is presented together with an energy-based interlock. Finally, the accuracy of estimating the shape of the heat flux on the front of the target from the temperature profile at the back is assessed, based on FEM simulations of a single beamlet.

Experimental and Monte Carlo characterization of a dynamic collimation system prototype for pencil beam scanning proton therapy

There has been a growing interest in the development of energy-specific collimators for low-energy pencil beam scanning (PBS) to reduce the lateral penumbra. One particular device that has been the focus of several recent published works is the dynamic collimation system (DCS), which provides energy-specific collimation by intercepting the scanned proton beam as it nears to target edge with a set of orthogonal trimmer blades. While several computational studies have shown that this dynamic collimator can provide additional healthy tissue sparing, there has not been any rigorous experimental work to benchmark the theoretical models used in these initial studies. Therefore, it was the purpose of this work to demonstrate an experimental method that could integrate an experimental prototype with a clinical PBS system and benchmark the Monte Carlo methods that have been used to model the DCS. An experimental DCS prototype was designed and built in house to actively collimate individual proton beamlets during PBS within a well-characterized experimental setup. Monte Carlo methods were initially used to assess construction tolerances and later benchmarked against measurements, including integral depth dose and lateral asymmetric beamlet profiles. The experimental apparatus and measurement geometry were modeled using MCNP6 benchmarked from measurements performed at the Northwestern Chicago Proton Center. Gamma analysis tests were used to evaluate the agreement between the measured and simulated profiles with a strict 1mm/1% criteria and 5% dose threshold. Excellent agreement was observed between the simulated and measured profiles, which included 1mm/1% gamma analysis pass rates of at least 100% and 95% for the integral depth dose (IDD) profiles and lateral profiles, respectively. Differences in the relative profile shape were observed experimentally between beamlets collimated on- and off-axis, which was attributed to the partial transmission of the beam through an unfocused collimator. Exposure rates resulting from the activation of the device were monitored with survey meter measurements and were found to agree with Monte Carlo estimates of the exposure rate to within 20%. A DCS prototype was constructed and integrated into a clinical dose delivery system. While the results of this work are not exhaustive, they demonstrate the effects of beam source divergence, device activation, and beamlet deflection during scanning, which were found to be successfully modeled using Monte Carlo methods and experimentally benchmarked. Excellent agreement was achieved between the simulated and measured lateral spot profiles of collimated beamlets delivered on- and off-axis in PBS. The Monte Carlo models adequately predicted the measured elevated plateau region in the integral depth-dose profiles from the low-energy scatter off the collimators.

Experimental and numerical investigation on the asymmetry of the current density extracted through a plasma meniscus in negative ion accelerator

In multi-beamlet negative ion accelerators for neutral beam injectors, the transverse magnetic field necessary for suppressing the co-extracted electrons induces a deflection of the negative ion beamlets that must be corrected. For the design, particle-tracing simulation codes are used to compute ion trajectories and optical properties of the beamlets in the acceleration stage. In these codes, uniform boundary conditions are normally assumed for the ion current density distribution at the surface (called meniscus), where negative ions are extracted from the plasma and form beamlets, which are accelerated across the apertures of the accelerator grids. Recently, experimental campaigns dedicated to the accurate measurement of the beamlet deflection in the acceleration phase revealed higher deflection than foreseen by simulations. In this work, we demonstrate that an agreement with the experimental data can be obtained by incorporating in the numerical simulations a non-radially symmetric distribution of the ion current density extracted across the meniscus surface. In the first part, the asymmetry of the ion current density at the meniscus is studied in an empirical way, by analysing and fitting the experimental results obtained with different operating parameters. In the second part, we show that the ion current asymmetry estimated by this procedure is well consistent with the flow pattern of H− ions calculated in the meniscus zone using a detailed particle in cell (PIC) model of the ion source in the presence of transverse magnetic field.

Design of a focused collimator for proton therapy spot scanning using Monte Carlo methods.

When designing a collimation system for pencil beam spot scanning proton therapy, a decision must be made whether or not to rotate, or focus, the collimator to match beamlet deflection as a function of off-axis distance. If the collimator is not focused, the beamlet shape and fluence will vary as a function of off-axis distance due to partial transmission through the collimator. In this work, we quantify the magnitude of these effects and propose a focused dynamic collimation system (DCS) for use in proton therapy spot scanning. This study was done in silico using a model of the Miami Cancer Institute's (MCI) IBA Proteus Plus system created in Geant4-based TOPAS. The DCS utilizes rectangular nickel trimmers mounted on rotating sliders that move in synchrony with the pencil beam to provide focused collimation at the edge of the target. Using a simplified setup of the DCS, simulations were performed at various off-axis locations corresponding to beam deflection angles ranging from 0° to 2.5°. At each off-axis location, focused (trimmer rotated) and unfocused (trimmer not rotated) simulations were performed. In all simulations, a 4cm water equivalent thickness range shifter was placed upstream of the collimator, and a voxelized water phantom that scored dose was placed downstream, each with 4cm airgaps. Increasing the beam deflection angle for an unfocused trimmer caused the collimated edge of the beamlet profile to shift 0.08-0.61mm from the baseline 0° simulation. There was also an increase in low-dose regions on the collimated edge ranging from 14.6% to 192.4%. Lastly, the maximum dose, , was 0-5% higher for the unfocused simulations. With a focused trimmer design, the profile shift and dose increases were all eliminated. We have shown that focusing a collimator in spot scanning proton therapy reduces dose at the collimated edge compared to conventional, unfocused collimation devices and presented a simple, mechanical design for achieving focusing for a range of source-to-collimator distances.

Improved understanding of beamlet deflection in ITER-relevant negative ion beams through forward modelling of Beam Emission Spectroscopy

NBI systems for the ITER tokamak will require large (1 m × 2 m cross section) and powerful negative ion beams to achieve the required 16.5 MW per beamline. Such negative ion beams can only be created from the combination of many individual beamlets – 1280 per beam in the case of the ITER heating neutral beam (HNB). These beamlets are required to have a core divergence of less than 7 mrad. However in these large and powerful beams, individual beamlets cannot be measured, and divergence values can only be obtained for a mixture of multiple beamlets.To investigate this, experiments were performed at the BATMAN Upgrade (BUG) test facility, a negative ion source roughly 1/8 the size of the ITER HNB. Through Beam Emission Spectroscopy (BES) measurements, and synthetic diagnostic results from the code BBCNI, insights into the effects of beamlet mixing on experimental observations have been obtained. For a single beamlet, it is expected that BES measurements obtain a Doppler shifted Hα peak with a roughly Gaussian profile, the width of which is related to the beamlet divergence, and the central wavelength is a function of the beamlet energy and the BES observation angle. In experiments at BUG, it was observed that the amount of Doppler shift in some BES lines of sight depended on the ratio of voltages applied to the grid system, even though the total voltage remained the same.By combining diagnostic data from the experiment and forward modelling from BBCNI, it was found that the change in Doppler shift for the affected lines of sight was caused primarily by changes to the horizontal deflection of beamlets by uncompensated magnetic fields – termed ‘zig-zag’ deflection due to the alternating polarity by aperture row. The amount of Doppler shift was further modulated by the beamlet divergence, which affects the amount of beamlet mixing within the BES lines of sight.

Multi-beamlet investigation of the deflection compensation methods of SPIDER beamlets.

SPIDER (Source for Production of Ions of Deuterium Extracted from a Rf plasma) is an ion source test bed designed to extract and accelerate a negative ion current up to 40 A and 100 kV whose first beam is expected by the end of 2016. Two main effects perturb beamlet optics during the acceleration stage: space charge repulsion and the deflection induced by the permanent magnets (called co-extracted electron suppression magnets) embedded in the EG. The purpose of this work is to evaluate and compare benefits, collateral effects, and limitations of electrical and magnetic compensation methods for beamlet deflection. The study of these methods has been carried out by means of numerical modeling tools: multi-beamlet simulations have been performed for the first time.

Three-dimensional analysis of ion optics with misalignments of apertures

A three-dimensional computer model of ion optics is developed to analyze the focusing properties and lifetime characteristics of ion engines. The simulation model includes the following main parts: solution of the self-consistent problem with calculation of the potential and space charge distribution; calculation of rarefied gas flows in the free-molecule approximation; modeling of charge-exchange collisions; calculation of surface erosion rate; prediction of the ion optics lifetime. In the present study, manufacturing tolerances on the mutual alignment of the apertures are investigated. The modeling results are compared with predictions of the linear optical theory. It is shown that operating values of the perveance at an offset of the holes may be estimated using a two-dimensional axisymmetric model. According to the simulation results the beamlet deflection angle weakly depends on the ion beam current and agrees well with linear optical theory. The observed displacement of the erosion pattern on the acceleration grid can be a measure of the apertures misalignment in the hot operational state of the ion optics. The reasons of the observed asymmetry of the erosion pattern on the periphery of the ion-optical system, which may arise even at a perfect alignment of the apertures, are investigated.

Deflection compensation for multiaperture negative ion beam extraction: analytical and numerical investigations

Deflection of negative ion beamlets due to the magnets embedded in the first extraction electrode for the purpose of dumping the co-extracted electrons is a serious issue for multiaperture ion accelerators of neutral beam injectors. Several kinds of magnet arrays which offer the possibility of cancelling ion deflection, employing crossed rows of magnets or even more compact parallel row arrangements, are discussed. A general equation for beamlet deflection is presented here, and the interference of the magnetic deflection and the electrostatic lens steering is carefully calculated; this equation may also include beamlet–beamlet interactions and image charge effects. Analytical expressions are given for the field and the line integrals for the magnet arrays, and these are simplified for beam optics calculations, but still retain an excellent agreement with numerical values. Optimization formulas for the filling fraction xy of the magnets are given, for cancellation of deflection both after the first electrode or after the second accelerating electrode. The latter case is of direct interest for the design of small accelerators (e.g., NIO1), for which compact solutions are proposed, while the former case may approximate well the design of a large accelerator such as MITICA, with a predicted xy = 0.1015 against a numerical optimized value of 0.0975 ± 0.005 in normal conditions. The detailed comparison between simulation results and theory shows that thin lens models are suitable approximations for calculating beam steering. Stability of optimal xy prediction with respect to the first accelerating gap length is shown, and the variation of xy with the voltage is discussed.

Beam optics in a MeV-class multi-aperture multi-grid accelerator for the ITER neutral beam injector

In a multi-aperture multi-grid accelerator of the ITER neutral beam injector, the beamlets are deflected due to space charge repulsion between beamlets and beam groups, and also due to magnetic field. Moreover, the beamlet deflection is influenced by electric field distortion generated by grid support structure. Such complicated beamlet deflections and the compensations have been examined utilizing a three-dimensional beam analysis. The space charge repulsion and the influence by the grid support structure were studied in a 1∕4 model of the accelerator including 320 beamlets. Beamlet deflection due to the magnetic field was studied by a single beamlet model. As the results, compensation methods of the beamlet deflection were designed, so as to utilize a metal bar (so-called field shaping plate) of 1 mm thick beneath the electron suppression grid (ESG), and an aperture offset of 1 mm in the ESG.

Compensation of Beamlet Deflection by Mechanical Offset of Grid Apertures in the SPIDER Ion Source

The SPIDER experiment's main goal is to test the extraction of negative ions from an ITER-size ion source. It is designed to extract 1 280 negative ion beamlets and accelerate them up to a 100 kV potential. The negative ion beam at exit and the operating parameters will be carefully measured and optimized in order to match the ITER requirements for the Neutral Beam Injector (NBI) ion sources. Inside a negative ion accelerator, there are generally two main factors that can cause the deflection of the ion beamlets: the repulsion among beamlets and the electron suppression magnetic field. These two effects are both to be considered highly detrimental for the ITER NBI since they are expected to cause higher heat loads on the ITER NBI neutralizer and decrease the overall beam quality (in terms of aiming and divergence). Hence, they should also be considered and minimized for the SPIDER device, where it will be possible to precisely investigate the beamlet footprint using an instrumented calorimeter relatively close to the accelerator exit. This paper presents a design optimization process aiming at compensating the two described effects. To make this, a mechanical offset of the grounded grid apertures is considered. The OPERA-3-D code (Vector Fields Co. Ltd.) is used as the main tool for this optimization process because it can take into account beamlet repulsion and the interaction among the beamlets and grids. This is made by solving the electrostatic Poisson's equation with a finite element approach to calculate the particle trajectories of the negative ions under the influence of electrostatic fields, magnetic fields, and space charge.

IRES: A Code to Calculate the Beamlet–Beamlet Interaction for Multiaperture Electrostatic Accelerators

The beamlet-beamlet interaction is an important process which has a relevant impact on the design of the grids for a multiaperture electrostatic accelerator. Space-charge effect leads to beamlet deflection, increasing the divergence of the whole beamlet group. According to the beamlet deflection, the grid apertures have to be properly aligned in order to provide the correct aiming of the beamlets and to avoid excessive thermal load on the grids. A new tool called Ion Relativistic Equation Solver (IRES) has been developed in Matlab to simulate the 3-D trajectories of a whole group of beamlets by integrating the relativistic equation of motion; the benchmark between this simple code and the results calculated by other tools can be useful to address the electrostatic accelerator design toward a reliable solution. The IRES code starts from a 3-D map of magnetic and electric fields evaluated by other software packages (e.g., ANSYS or Comsol Multiphysics), and it determines iteratively the central particle trajectory of each beamlet. The field map is then updated by taking into account the effect of the spatial charge due to the negative-ion beamlets; the process is repeated until a self-consistent solution is reached both for the field maps and the trajectories. The code has been validated in the case of a simple beamlet-beamlet interaction by comparing the results with those obtained using an analytical formula. IRES has then been applied to study the trajectories of negative ions in the 1-MV ITER neutral-beam injector with a single-gap configuration. It is expected that the advantage of using IRES will be apparent when evaluating the beam divergence in the presence of a large number of beamlets, due to the 1-D approximation used in the code.