Performance assessment of a newly developed non-invasive 2D beam profile monitor for high-intensity accelerators

In high-intensity accelerators, minimizing beam loss is paramount to avoid damages and activation of accelerator components. To achieve this, a reliable beam profile monitor is essential for assessing the beam center and spread. Additionally, the beam profile can be used to steer the beam during regular operation, thus reducing beam loss. In cases of irregular events, the monitor can initiate beam profile recording to identify and address any issues promptly. In this manuscript, we present a detailed description of a non-invasive 2D beam profile monitor, focusing on its components, operation, and most importantly, its reliability and failure modes. From operation experience, failure modes of the system and its effects were identified. Fault tree analysis was carried out. Failure rate of sheet generator was estimated using response surface method. Failure rates of components were used to estimate the failure rate of the system. From the target reliability, the required maximum repair time of the system was calculated.


Introduction
High-intensity proton accelerators are crucial components in accelerator-driven sub-critical systems (ADS, which are designed for various applications, including nuclear waste transmutation and neutron production.ADS is a sub-critical reactor which is driven by a spallation neutron source) [1,2].The additional neutrons required by the sub-critical reactor to continue operation is generated by the interaction of a high energy (∼ 1 GeV) proton beam produced by a high intensity (typically currents of 10s of mA [2]) particle accelerator with a suitable target (typically Pb-Bi eutectic target [2]) and are called spallation neutrons.One of the challenges in ADS is the requirement of a reliable particle accelerator that provides a high intensity proton beam.Disruption in the beam can lead to reactor down time.It can also cause thermal stress in the components of the reactor [3].
A 1 GeV 10 mA proton accelerator, being developed for the Indian ADS program, will consist of number of energy stages [2].The current plan of the 1 GeV accelerator program is shown in figure 1.The proton beam is first generated in an ion source and transported to multiple accelerator components.The transport sections consist of diagnostic and control instruments that guide and match the beam from one accelerating section output to the next stage.These instruments also ensure that the high power beam does not interact with the beamline material as it can cause thermal damage and radio-activation [4,5].The entire beam path is also maintained in ultra high vacuum to ensure minimise beam loss due to interaction with molecules in the path.
A beam profile monitor can provide essential information about the beam's centre and spread, enabling operators to make real-time adjustments to reduce beam loss during regular operation.

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Furthermore, it can be programmed to trigger profile recording during irregular events, allowing for the rapid identification and resolution of issues.In this manuscript, we introduce a non-invasive 2D beam profile monitor designed for high-intensity accelerators [4] and evaluate its performance for ADS like requirements.The reliability requirement of ADS accelerator is less than 50 trips per year of > 5 min each which is ∼ 99.43% reliability [3].We have therefore set the target for the performance evaluation of the beam profile monitor as 99.9% reliability for this study.

Description of the gas sheet beam profile monitor 2.1 Overview
The gas sheet beam profile monitor is a non-invasive instrument as the beam-gas interaction used to image the beam profile leads to less than 0.2% beam loss [5].The instrument generates a gas sheet in the beam line at the location where the profile is to be measured as shown in figure 2. The beam interacts with the gas sheet and excites the gas molecules leading to production of fluorescence photons.Nitrogen was the chosen gas for the current study [4].A camera positioned on the viewport of the main vacuum chamber captures the emitted photons, allowing for the visualization of the beam profile.

Sheet generation
The core component of the beam profile monitor is the sheet generator, which consists of two generators positioned on either side of the beam, as illustrated in figure 3.These generators use the positional beaming effect observed in molecular flow domains when gas passed through a long conduit to produce a directional flow in the gas at the exit [6].A small gap between two steel plates forms a reservoir and a long, thin slit.The sheet is generated at the exit of this slit called slit 1.The generated gas sheet passes through a differential vacuum chamber that connects to the main vacuum chamber through -2 -  a thicker slit called slit 2, which effectively skims the gas sheet, as depicted in figure 4. Two turbo molecular pumps (Pump 1 and Pump 2) with maximum capacity of 700 and 900 L s −1 were connected to the main chamber during earlier experiments to maintain the necessary vacuum conditions.Both differential chambers of the sheet generators were also connected to a turbo molecular pump (Sheet generator pump) with maximum capacity of 700 L s −1 via a vacuum manifold.These pumps were connected to individual backing pumps and had independent gate valves and display/control units.Gas from a nitrogen gas source is introduced into the reservoir of both sheet generators through vacuum valves, ensuring a constant gas supply.More details of this system can be found in [4].

Gas sheet overlap
The gas sheets generated by both sheet generators overlap within the main vacuum chamber, producing a uniform density gas sheet positioned at around 45-degree angle to the beam axis.This configuration allows for optimal interaction between the beam and the gas sheet, leading to the emission of photons that can be used to generate the beam profile.

Imaging and beam line integration
The beam profile monitor is equipped with a camera that is mounted on a view port within the main vacuum chamber, enabling the imaging of beam induced fluorescence of the gas sheet.The monitor is seamlessly integrated into the accelerator's beam line, as depicted in figure 5, ensuring that it can be used to monitor the beam profile in real time.

Parts of the beam profile monitor
The main vacuum chamber houses the gas sheet generators, camera, and all associated components.Figure 5 shows the block diagram of the beam profile monitor.The chamber is designed, fabricated and tested for required ultra high vacuum condition.It has number of ports to connect to the beam line, high capacity vacuum pumps, gas inlet, pressure sensors and additional sensors.It also includes four viewports with camera mount.Vacuum pumps are used to maintain the required ultra high vacuum conditions within the sheet generators and the main vacuum chamber.There are three vacuum pumping systems consisting of a gate valve, a turbo molecular pump and a backing pump connected via vacuum bellows.A nitrogen gas source provides the gas needed to generate the gas sheets.The gas must be pure (99.99%) with low water content.Filters are required to avoid dust from entering the flow.These vacuum valves control the flow of gas from the source to the reservoirs of the gas sheet generators to achieve the required gas sheet pressure for imaging the beam profile.Sheet Generators are the core components responsible for generating the gas sheets using the molecular beaming effect [6].A camera captures the emitted photons to generate the beam profile.Vacuum gauges are integrated into the system to monitor vacuum conditions and ensure proper operation.For an inlet pressure of ∼ 750 Pa the measured chamber wall pressure was 2 × 10 −3 Pa [4].

Performance assessment
Assessing the performance of the beam profile monitor is essential to maintain the safety and efficiency of high-intensity accelerators.This section outlines the key considerations for evaluating the performance of the monitor and explores potential failure modes.
In regular operation, beam profile monitor is used for steering and focusing beam.Wrong measurements from noisy profile images could lead to steering/defocusing the beam to hit the beamline components which should ultimately lead to a trip by the Machine Protection System.
In case of irregular events, the beam profile monitor is used to capture the event details.Wrong measurements can lead to misinterpretations, which may not help resolve the issue before restarting.
To ensure the reliability of the beam profile monitor, several factors must be taken into account.Some of the factors are external to the beam profile monitor system such as: the properties of the beam, the vacuum leaks and dust entry in the nearby sections of the beamline, the power supplies, functioning of control systems and control signals, the quality and pressure of the gas from the gas source, EMI in the environment and stray light sources from adjacent system that may affect the profile imaging.For performance evaluation of the beam profile system, we assume that there are no faults in these external factors.We have limited the scope of study to the failures within the system such as mismatch in the two sheet generators due to manufacturing tolerances, fluctuations in the chamber pumps and chamber outgassing rates, blockages in the gas flow within the system and vacuum leaks within the system.

Operational experiences
In our operational experience in the test bench, most of the failures were due to external factors which can be resolved in actual accelerator design.Among the internal factors, the most prominent failure was due to a mixture of grease and dust blocking the gas flow in the thin (100 micron) section of slit 1.The original manufacturer had applied vacuum grease on the vacuum gasket of slit 1.This was completely cleaned and vacuum tested.We found the grease unnecessary for achieving the required vacuum.We also introduced a filter at the gas inlet to the sheet generator to prevent dust from entering.We also used nitrogen flushing of the chamber whenever we opened the vacuum ports for modifications in the system -5 - to keep the chamber clean.We have not observed any blockage after these steps were ensured.Another issue we faced was due to stray light sources making it difficult for the camera to detect the faint glow from beam induced fluorescence.A glow from the ion vacuum gauge was removed by repositioning it and the glow from the ion-source plasma was managed by changing the camera viewport to the opposite side.

Failure Modes and Effects Analysis (FMEA)
We identified the possible failure modes of each component in the gas sheet generator system.We analysed the effect of these failures on the system and the global effect on the particle accelerator facility of which this system is a part.The results are tabulated in table 1.This method of analysing the reliability of a system is known as FMEA [7].
Variation in gas sheet pressure, uniformity and ambient vacuum can result in inaccurate beam profiles.The variation may be due to fluctuations in the gas source pressure or changes in the flow path.Water vapour, dust, oil and dirt may also enter the vacuum chambers along with the nitrogen gas or through other ports connected to adjacent systems in the beamline.This can clog the gas flow.The 10 cm long, 5 cm wide, 0.1 mm thin gas sheet generator slit is the most vulnerable to flow blocks.Over time, vacuum parts such as connectors, adapters, valves and pump components may degrade or wear out.Increased outgassing and leaks through various ports or from nearby connected systems in the beam line can affect the vacuum level in the vacuum chambers, even introducing vacuum fluctuations and thereby affect performance of the system.Camera malfunctions may also hinder beam profile imaging.

Fault analysis
In this section, we use the method of fault tree analysis [8] to identify possible the modes of failure of the beam profile measurement system and their possible causes.We analyse the cause to trace the possible component level failures that leads to failures of the system.The fault tree is shown in figure 6.
In the previous section we have identified that the failure of the system can cause two global effects namely: beam profile not captured and deviation in beam profile measurement.Assuming that a beam with parameters within the operating range of the profile monitor is present at the input, if a beam profile distribution signal above the background noise is not obtained, then we assume it to be a deviation from the requirement.

Component failure probability estimation
In section 3, various parts of the gas sheet beam profile monitoring systems were described.For studying the reliability of the system, we require estimating the failure probability of its components.Most of the components in the system such as vacuum components and imaging components are generic in nature.Their failure probabilities were obtained from literature.The gas sheet generator being a newly designed component of this system, the response surface method was used to estimate its failure probability.The workflow of this method is shown in figure 7.

Generic Data
Ultra high vacuum generation and maintenance technologies have matured to standard products and quality assurance procedures for numerous research, industrial and medical applications.
Failure probabilities of generic components are listed in table 2. Failure probability of standard vacuum components were taken from [9,10] and optical systems were taken from [11].
Table 2. Failure probability of generic components of the gas sheet beam profile monitor.

Gas sheet generator failure probability estimation
The sheet generator being a newly designed system, we needed to compute its failure probability.For this we used the Molflow+ [12] simulation model of the system.The simulation setup is shown in figure 8.The sheet pressure is measured using meshed pressure measurement surfaces in the simulation which are transparent to the gas flow [4].
. Uncertain parameters.The input parameters of the model are listed in table 3.
Sensitivity studies.We carried out sensitivity analysis on the sheet pressure and sheet uniformity by varying all the input parameters to the model by 10%.We observed that the uniformity of the gas sheet deteriorated more easily on changing these parameters.
The chamber dimensions varied only by < 0.1% of the total value, hence these do not affect the system significantly.The chamber outgassing can be affected by the vacuum conditioning of the chamber as well as by the gas flow to and from adjacent systems connected.Hence, this has a significant on the system.The effective pump capacity of the main chamber may vary with gas inlet.The reservoir width and depth had 1% tolerance in dimensions and this does not have significant effect on the system.The slit 1 thickness and slit 2 thickness had significant tolerances (10% and 17% respectively).The gap between the slits also had significant tolerance (4%).The slit 1 length did not have significant tolerance in dimensions (0.5%).The sheet generator pump capacity is minimum -10 - Effective pumps capacity calculated from the pump datasheets and the conductance of connecting pipes and flanges.The gas pressure can vary the pump throughput and conductance of pipes.At higher gas loads, the pump controllers may also ramp down the pumps.
Gas inlet flow rate 0.13 Pa L s −1 cm −2 The inlet flow rate was calculated to match the inlet pressure obtained from actual system.This parameter is controlled to achieve desired intensity of beam profile.Variation in inlet flow is assumed to be an external failure and not part of the sheet generator failure calculations.
Reservoir width 2 cm manufacturing tolerance of 0. The effective pumps capacity was calculated from the pump and the conductance of connecting pipes and flanges assuming molecular flow domain [4].The actual pressure in this region is higher and hence the conductance of the pipe is higher.Thus, this will be the minimum pumping capacity at the differential pressure region of the sheet generators.
5 L s −1 .This is the minimum calculated pump capacity and it was found from sensitivity study that higher pumping rate did not significantly affect the output of the system.
We also carried out simulation to study affect of blockage of a flow at the output end of slit 1 of one of the sheet generators.We observed that a 50% blockage resulted in 8.47% non-uniformity of gas sheet.A 50% blockage is a significant blockage and did not increase the non-uniformity significantly.

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Significant parameters.Table 4 lists the significant parameters of the model.Response surface method.Response surface methodology (RSM) [13] is useful for analyzing the system, which has number of independent input parameters.Here, we used Central Composite Design (CCD) [14] to design experiments to estimate the coefficients of a second order equation that approximates the response of the system to five of the significant input parameters identified in the previous section.We used this equation to carry out Monte Carlo simulations to estimate the failure probability.

Design of experiments.
For the second-order fit, we employed a Central Composite Design (CCD) in selecting experimental points, strategically covering the targeted range of inputs.This approach involved including data points featuring the nominal values for all inputs, as well as sets where one variable was adjusted to its upper and lower limits.Additionally, we incorporated sets comprising all possible combinations of inputs, encompassing both upper and lower limit values.Diagram representing these for three variables are shown in figure 9. Total number of data points,  is given by  = 1 + 2 ×  + 2  , where  is the number of input parameters.Total points for 5 variables were 1 + 2 × 5 + 2 5 = 43.The data points for response surface generation are given in table 5.
-12 - Where: 1 is the capacity of a main chamber pump in litre per second,  2 is the outgassing from one side of the cylinder approximated by a decagon cross-section in ×10 −6 Pa L s −1 cm −2 ,  3 is the gap of slit 1 in mm,  4 is the gap of slit 2 in mm and  5 is the axial distance between slit 1 and slit 2. Monte Carlo simulations.We conducted 10,000 Monte Carlo simulations using this equation.The failure criteria was chosen as non-uniformity in the gas sheet above 15%.The sum of experiments which met the failure criteria divided by the total number of experiments gives the failure probability of the gas sheet generator.

Result and discussion
We carried out reliability study of the system.From FMEA we were able to identify failure modes of the system components and their effect on the system as well as the global effects on the accelerator facility.A failure of the components can cause failure in obtaining the beam profile that may result in improper operation of the system.Vacuum failures can also lead to beam losses.
In fault tree analysis, we identified the two major system failures: no image and image not providing beam profile data as per the requirement.From the analysis we found that the vacuum gauge at the gas inlet was most prone to failures.The effective failure rate of the system was found to be 2.3970 × 10 −4 per hour.
-14 - For an availability of 99.9%, we calculated the required mean time to repair (MTTR).The MTTR should be within 4 hours.Therefore, it should be ensured that any repair in the system should be carried out within 7 hours.We also calculated the system failure rate required to obtain an MTTR of 72 hours with 99.9% availability.It was found to be 1.39028 × 10 −5 per hour.
We obtained the component failure probability of generic parts of the system from literature.For the newly designed part, the sheet generator, we conducted sensitivity analysis for all the input parameters.The response surface method was used to compute the coefficients of an approximate second order equation that gave the gas non-uniformity in percentage,  as: The response surface is plotted in figure 10.As there are 5 inputs, the plots were generated by keeping 3 inputs as constant values chosen such that the failure regions are visible on the surface.
The experiments were chosen using Central Composite Design.Monte Carlo simulations were carried out to calculate the failure probability.From calculations, 15% linear variation in a Gaussian profile of 2 mm Gaussian width resulted in 20% error in FWHM measurement.The failure criteria was set to be above 15% non-uniformity in the gas sheet and the failure probability obtained was 1 × 10 −4 .

Conclusion
The performance evaluation of a gas sheet beam profile monitor was carried out for use in a high intensity proton accelerator that requires to meet the reliability requirements for applications like ADS.The operational experience and failure analysis of the system has been reported in this manuscript.From the fault tree analysis, we computed that the repair time for the system components must be less than 7 hours to achieve the required reliability.We computed the failure probability of the custom designed part in the system, the sheet generator, using RSM method to be 1 × 10 −4 .For generic components we have compiled the reliability data from literature for the analysis.

Figure 1 .
Figure 1.The accelerator development program for Indian ADS.

Figure 2 .
Figure 2. Schematic diagram showing the positioning of gas sheet generator for beam profiling by beam induced fluorescence.Reprinted from [4], Copyright (2024), with permission from Elsevier.

Figure 3 .
Figure 3. 3D model of the gas sheet generator showing internal parts including the gas feed and vacuum manifold connected to the two sheet generators mounted above and below the beam path mounted on rails hanging from the upper rotatable flange.Reprinted from [4], Copyright (2024), with permission from Elsevier.

Figure 4 .
Figure 4. Parts of the gas sheet generator, the left is exploded view and right is the sectional diagram of the assembly.Reprinted from [4], Copyright (2024), with permission from Elsevier.

Figure 5 .
Figure 5. Parts of the beam profile monitor.

Figure 6 .
Figure 6.Fault tree of gas sheet beam profile monitor system.

Figure 6 .
Figure 6.Fault tree of gas sheet beam profile monitor system (cont.).

Figure 7 .
Figure 7. Workflow for failure probability estimation of Gas sheet generator.

Figure 9 .
Figure 9. Design experiments chosen for three variables using CCD.

Figure 10 .
Figure 10.Response surface plots.Failure regions on the surface is marked in red colour.

Table 1 .
FMEA of the functional Modules of the system.

Table 3 .
Model input parameters and uncertainty.

Table 4 .
The significant parameters along with their nominal values and range.

Table 6 .
Calculated coefficients of the response surface.