Skip to main content
NCBI home page
Scientific Reports logoLink to Scientific Reports
. 2026 May 6;16:20939. doi: 10.1038/s41598-026-42751-1

Carbon ion stripper for NSTRI tandem accelerator

M Mohseni Kejani 1,2, F Ghasemi 2,✉, F Abbasi Davani 1, Sh Sanaye Hajari 2, M Lamehi Rachti 2
PMCID: PMC13338403  PMID: 42091928

Abstract

The tandem accelerator project at the Nuclear Science and Technology Research Institute (NSTRI) aims to design and construction a 1.7 MV accelerator for AMS applications. Alongside the design and construction of the high voltage power supply for the intended accelerator, the accelerating tube including the low-energy section, the stripper section, and the high-energy section is also being developed. This paper focuses specifically on the design of the stripper section for a carbon ion beam. In the design of this section, by excluding interactions involving charge states of (q, q–2) and (q, q + 2), a total of 14 interactions between charge states (q, q + 1) and (q, q–1) have been considered. After deriving the interaction cross-sections at the desired energy, the optimal geometry was introduced, and the charge exchange efficiency was calculated for different gas throughputs. At a gas throughput of 9 Standard Cubic Centimeter per Minute (SCCM), an equilibrium thickness of 2.3 × 1016 cm−2 was achieved, which ensures charge exchange equilibrium for the formation of various carbon charge states within the designed geometry. Results indicate that for charge states 1+, 2+, and 3+, the 14C/12C stripping ratios are 1.22, 1.01, and 0.89 respectively, while the corresponding ratios for 14C/13C are 1.52, 1.09, and 0.76. These variations highlight the importance of considering isotopic mass effect on stripping efficiency in AMS-based radiocarbon measurements. The optimized geometry of the stripper section was constructed and experimentally tested. Pressure measurements taken in different regions showed excellent agreement with the gas-flow simulation results, validating the accuracy of the simulation. Furthermore, the calculated carbon charge-state fractions were validated with experimental measurements from another reference at 1.7 MeV in nitrogen under equilibrium-thickness conditions. The results reveal a close match between the calculated fractions in this study and the experimental data, further supporting the reliability of the model and the credibility of the results. The results demonstrate that this optimized geometry and structure are capable of achieving the required atomic density for reaching the equilibrium thickness of the carbon beam, while the overall length is reduced to approximately one-third of that in conventional stripper designs.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-42751-1.

Keywords: radiocarbon dating, tandem technique, charge exchange interaction, gas stripper, equilibrium thickness

Subject terms: Energy science and technology, Engineering, Physics

Introduction

Archaeology is an interdisciplinary science focused on reconstructing past lifestyles, social structures, and technologies through the study of material remains. A key challenge is accurately dating these findings, which is essential for understanding historical and cultural developments. Dating methods, including Optically Stimulated Luminescence (OSL)1–10, dendrochronology11–14, and radiocarbon (14C) dating11–14, help estimate artifact ages and provide insights into past environmental and climatic changes10,15. Radiocarbon dating, for example, enables age estimation up to about 55,000 years by analyzing the decay of carbon-14 isotopes, which are absorbed by living organisms16. When an organism dies, carbon exchange ceases, and 14C decays with a half-life of approximately 5,700 years. To enhance accuracy, corrections such as calibration17–19 and isotopic fractionation20–23 are applied. Radiocarbon dating methods, including beta counting24–27, gas proportional counting28–30, and Accelerator Mass Spectrometry (AMS)26,31–34, measure the ratio of 14C to stable carbon isotopes. AMS, offering high sensitivity for small samples and ancient ages, is the preferred method for radiocarbon dating but requires a tandem accelerator35.

The tandem accelerator is a type of electrostatic accelerators36. Electrostatic accelerators are the simplest type of ion accelerators37. This kind of accelerators provide the ability to achieve beams with very good energy resolution (typically in the range of 10−438, which is why they are among the most widely used accelerators in research fields, particularly in analysis. The ion source, high-voltage power supply, and accelerating tube are the main components of electrostatic accelerators.

In a tandem accelerator, unlike single-stage accelerators, high-voltage terminals are used twice to achieve higher energy for ions39. One of the key features of this type of accelerator is the placement of its ion source outside the high-voltage section, allowing for easy replacement of the ion beam produced from different samples for the analysis of various specimens39. In the ion source suitable for this type of accelerator, negative ions are generated. These ions are accelerated by the high-voltage potential as they pass through the low-energy section of the accelerating tube. When these ions pass through the charge exchange cell and reach the high-voltage terminal, they lose their electrons and become positive ions. The positive ions then accelerate toward the zero potential39.

The most important difference between a tandem accelerator and other single-stage electrostatic accelerators is the stripper section. This section is located in the middle of the accelerating tube, between the low-energy and high-energy sections, and is responsible for converting negative ions to positive ions36. For the stripper section of the tandem accelerator, there are two main options: using a carbon foil-based stripping system40–43 or a gas-based stripping system44–48. If stable beam transfer and achieving higher current are prioritized, the gas-based stripping system is more commonly used36. On the other hand, if achieving higher charge state and consequently higher beam energy is the priority, the carbon foil-based stripping system is used36. The main challenge with the gas-based stripping system is the leakage of gas to the sides of the accelerating tube, which disrupts the vacuum needed for particle acceleration. Meanwhile, the primary challenge with the carbon foil system is the short lifespan of the foil when using heavy ions and the reduction in beam current after stripping36.

Archaeology in Iran is very important due to its ancient history, diversity, and richness of archaeological artifacts. Physics and Accelerators Research School (PARS) at Nuclear Science and Technology Research Institute (NSTRI) is active in the development of both radiofrequency49–52 and electrostatic accelerators53,54. Also, numerous analyses have been carried out at NSTRI in the field of archaeology55–67. These analyses were mainly conducted using the single-stage accelerator available at NSTRI. However, given the applications of the tandem accelerator, which allows for precise and rapid dating of small samples, the design and construction of a tandem accelerator at the NSTRI, in collaboration with Shahid Beheshti University (SBU), has been initiated. This accelerator, which will be used for accelerating hydrogen and carbon ion beams, will have applications in element identification analysis or ion implantation using hydrogen ion beam, and radiocarbon dating. The power supply for this accelerator has been built and is capable of producing a voltage of 1.7 MV53. This power supply, based on a capacitive parallel-fed Cockcroft-Walton design, consists of 34 cascade stages which is housed within an insulated gas tank as shown in.

Figure 153. It is capable of providing the necessary power for ion acceleration in both.

Fig. 1.

Fig. 1

Open in a new tab

Capacitive parallel-fed Cockcroft-Walton power supply constructed at NSTRI.

single-stage and tandem modes.

The final specifications of the NSTRI tandem accelerator project are presented in Table 1, and a layout of NSTRI tandem accelerator is shown in Fig. 2. This paper presents the design of the stripper system for carbon ions in the NSTRI tandem accelerator project.

Table 1.

specifications of the NSTRI tandem accelerator project.

Ion source H− and C−
Hydrogen Beam current 20 µA
Carbon Beam current 50 µA
Stripper gas Nitrogen (N2)
HV power supply range 0.3–1.7 MV
HV power supply ripple 500 V
HV insulation gas type CO2+N2
Number of cascade stages 34
Open in a new tab

Fig. 2.

Fig. 2

Open in a new tab

Layout of NSTRI tandem accelerator: (1) Carbon ion source, (2) Hydrogen ion source, (3) Injection magnet, (4) Low-energy section of accelerating tube, (5) stripper section, (6) High-energy section of accelerating tube, (7) Switching magnet, (8) Beam lines, (9) High-Voltage power supply.

Carbon stripping and cross-section of interactions

As the C⁻ ion beam passes through the nitrogen gas environment, the carbon negative ions collide with the gas molecules and the charge exchange (Ch. Ex.) process begins. In this process, the carbon ions can convert from one charge state to others, including negative ions, neutrals, and positive ions. These continuous charge state changes are influenced by various interactions, such as electron capture, electron detachment, and ion recombination.

In tandem accelerators with applications in radiocarbon dating, efficient conversion of the negative carbon beam to positive ones is essential for entering the acceleration section. Therefore, all potential interactions occurring in the stripper section must be carefully considered. This consideration includes calculating the interaction rates and determining the final distribution of ions produced after passing through the stripper section. The number of each interaction leading to charge state changes from q to q′ (Nqq΄) can be calculated by Eq. (1).

graphic file with name d33e500.gif 1

In Eq. (1), the variables q and q′ represent the initial and final charge states of the carbon ions in the charge exchange process, the parameter ngas​ denotes the gas number density in cm−3 within the stripper section (which determines the probability of collisions between carbon ions and gas molecules), σqq′ is the interaction cross-section in cm2 (which determines the probability of a charge change occurring between the specific states q and q′) and x is defined as the interaction length in cm.

The first step in calculating the charge exchange interaction rate for each charge state is to determine the interaction cross-section at an energy of 1.7 MeV. A scheme of general interactions along with their corresponding cross-section indices is provided in Fig. 3. Additionally, more detailed information regarding the types of interactions, along with their cross-section’s indices, is reported in Table 2.

Fig. 3.

Fig. 3

Open in a new tab

General interactions.

Table 2.

List of general interactions in stripper sections.

No. Interaction Type Cross Section Index
1 Cq−1+N2→Cq Single Electron Detachment of Cq−1 σq−1,q
2 Cq+1+N2→Cq Single Electron Capture of Cq+1 σq+1,q
3 Cq+N2→Cq−1 Single Electron Capture of Cq σq, q−1
4 Cq+N2→Cq+1 Single Electron Detachment of Cq σq, q+1
5 Cq−2+N2→Cq Double Electron Detachment of Cq−2 σq−2,q
6 Cq+2+N2→Cq Double Electron Capture of Cq+2 σq+2,q
7 Cq+N2→Cq−2 Double Electron Capture of Cq σq, q−2
8 Cq+N2→Cq+2 Double Electron Detachment of Cq σq, q+2
Open in a new tab

As shown in Fig. 3; Table 2, carbon ions with charge state q can undergo multiple interaction during the charge exchange process. Each of these interactions is dependent on its specific cross-section at a given energy. For accurate simulation of the charge exchange process, precise values of the cross-sections for each interaction at the desired energy (1.7 MeV) must be considered. Various references were reviewed to obtain the interaction cross-sections; however, no measured or calculated values were found at the desired energy of 1.7 MeV. On the other hand, among the interactions listed in Table 2, the cross-section of interactions 5, 6, 7, and 8 were found to be negligible and thus were excluded from the calculations. Table 3 presents a complete list of most probable interactions, along with the interaction type, cross-section index, and the references used.

Table 3.

list of most probable interactions in stripper sections.

Interaction Type Cross Section Index References
1 C−+N2→C0 Single Electron Detachment of C0 σ−10 68–70
2 C0+N2→C+ Single Electron Detachment of C+ σ01 69,71,72
3 C++N2→C2+ Single Electron Detachment of C2+ σ12 68,71
4 C2++N2→C3+ Single Electron Detachment of C3+ σ23 68,73
5 C3++N2→C4+ Single Electron Detachment of C4+ σ34 73,74
6 C4++N2→C5+ Single Electron Detachment of C5+ σ45 73,75,76
7 C5++N2→C6+ Single Electron Detachment of C6+ σ56 75–78
8 C6++N2→C5+ Single Electron Capture of C6+ σ65 75–77
9 C5++N2→C4+ Single Electron Capture of C5+ σ54 73,77,78
10 C4++N2→C3+ Single Electron Capture of C4+ σ43 77,79,80
11 C3++N2→C2+ Single Electron Capture of C3+ σ32 73,77,79
12 C2++N2→C+ Single Electron Capture of C2+ σ21 69,73
13 C++N2→C0 Single Electron Capture of C+ σ10 69,73,81–84
14 C0+N2→C− Single Electron Capture of C0 σ0−1 68–70
Open in a new tab

s

To estimate the cross sections of the interactions listed in Table 3, data were gathered from various references covering a wide energy range (10−3 to 102 MeV/amu), and a fitted curve was generated based on these datasets, yielding an R-squared value exceeding 0.92. Figure 4 presents the obtained curves. After extracting the cross-section values, these data were used for simulation of interactions in charge exchange cell.

Fig. 4.

Fig. 4

Open in a new tab

Cross section of carbon charge exchange interactions: (a) σ (q, q+1), (b) σ (q, q-1).

As shown in Fig. 4, the energy values in these plots are expressed in units of MeV per amu (atomic mass unit). This implies that the cross-section values differ for various carbon isotopes due to their mass differences. The resulting variation is significant and must be taken into account in the calculations.

According to Eq. (1), the amount of charge exchange is directly influenced by the gas number density (ngas) and the interaction path length (x). In the early stages, as these two parameters increase, the probability of collisions between the carbon ions and gas molecules increases, and as a result, the charge exchange rate also rises. However, this increasing trend will not continue permanently. After reaching a certain level of gas number density and interaction thickness (ngas.x), an equilibrium is established among all the carbon species (negative, neutral and positive). At this point, further changes in gas number density or interaction path length will have poor effect on the composition of the carbon species, as the rate of conversion between different ions reaches a dynamic equilibrium. This specific thickness is referred to as the equilibrium thickness85,86. Determining the exact value of this point is one of the key objectives in charge exchange calculations because optimal design of the charge exchange cell requires achieving conditions that maximize the conversion efficiency of negative carbon ions to positive ones, without causing unnecessary increases in gas injection rate that could lead to issues such as gas leakage into the accelerating tube.

The natural abundances of carbon isotopes are highly unequal; 12C and 13C account for approximately 98.93% and 1.07% of stable carbon, respectively, while 14C is present at about 1.2 × 10⁻12 relative to 12C in the atmosphere87. When using a tandem accelerator for radiocarbon dating, the negative carbon ion beam (C⁻) undergoes charge exchange in the stripper section, resulting in the formation of positively charged carbon ions. In the specific case of the NSTRI tandem accelerator, the beam is accelerated to an energy of 1.7 MeV before entering the stripper section.

These isotopes are being accelerated under the same voltage, arrive at the stripper section with different velocities due to their mass differences. This velocity variation directly influences the charge exchange cross-sections for each isotope, affecting their probabilities of undergoing electron detachment or electron capture interactions.

The velocity of each isotope after acceleration (v) can be determined using the non-relativistic kinetic energy by Eq. (2):

graphic file with name d33e1231.gif 2

Where E is the kinetic energy, and m is the mass of the isotope. In Fig. 5, the difference in cross-section values for different carbon isotopes at a kinetic energy of 1.7 MeV is shown. For example, at 1.7 MeV, 12C has an energy of about 141.7 keV/amu, whereas 13C and 14C have about 130.8 keV/amu and about 121.4 keV/amu, respectively. As a result, under the same kinetic energy, the lighter isotopes will have higher velocities than the heavier ones. On the other hand, the electron detachment and electron capture cross sections for carbon ions interacting with nitrogen gas is proportional to Inline graphic, where Inline graphic is the atomic unit of velocity and Inline graphicis ion velocity75. These differences are substantial and were carefully considered in the calculations.

Fig. 5.

Fig. 5

Open in a new tab

Cross section differences for different carbon isotopes: (a) σ(q, q+1), (b) σ(q, q-1).

Geometry and design assumption

The stripper section in a tandem accelerator is positioned between the low-energy and high-energy sections of the accelerating tube, with its primary function being the conversion of negative ions to positive ions. In the gaseous stripper system, a suitable gas is injected into this section to achieve the required atomic density for the charge exchange process. As the gas number density increases, the probability of interaction between negative ions and gas molecules rises, leading to a higher conversion rate of these ions into positive ones. This process continues until the equilibrium thickness is reached. After reaching this equilibrium thickness, further increases in gas number density will not affect the amount of charge exchange.

However, since ion acceleration requires maintaining a high vacuum level of around 10−6 mbar in the accelerating tube36, controlling gas leakage from the charge exchange cell to these regions becomes an important challenge. One possible solution to prevent gas leakage is the use of a physical window to separate the stripper section from the accelerating tube. However, this approach presents serious challenges, as the presence of the window in the beam path results in a significant loss of beam intensity and emittance growth.

Therefore, the design of the stripper section must ensure that the maximum gas number density in the beam path is achieved with the minimum gas injection rate, while also minimizing gas leakage into the accelerating tube. To achieve this, the appropriate geometric design of the Charge Exchange cell (Ch. Ex.) and the distribution of gas inside it play a critical role. A schematic of a tandem accelerating tube is shown in Fig. 6.

Fig. 6.

Fig. 6

Open in a new tab

Schematic of a tandem accelerating tube.

The amount of gas leakage from the stripper section to the sides of the accelerating tube can be calculated using the Eq. (3)88:

graphic file with name d33e1320.gif 3

Where Q is the amount of gas leaking from point 1 to point 2 in Pa·m3·s−1, P1​ and P2​ are the pressures at points 1 and 2 in Pa and C is the vacuum conductance in m3.s−188]. As indicated by the Eq. (3), the amount of gas leakage from the stripper section to the sides of the accelerating tube is directly related to the vacuum conductance (C). Since vacuum conductance is a quantity dependent on the system’s geometry, an appropriate design of the dimensions and structure of the stripper section can have an important effect on reducing gas leakage.

Therefore, to optimize the accelerator’s performance and maintain the suitable vacuum in the accelerating tube, it is essential to design the stripper section geometry with a proper vacuum conductance. The optimized geometry for the stripper section is shown in Fig. 7, and the parameters affecting vacuum conductance are indicated.

Fig. 7.

Fig. 7

Open in a new tab

optimized geometry for the stripper section.

The authors reported the optimization of the charge exchange section dimensions aimed at minimizing gas leakage into the accelerator tube in Reference89. The calculations related to this optimization were performed using the Free Molecular Flow interface in COMSOL Multiphysics software90. This software uses the Angular Coefficient Method for vacuum-related calculations, which enables precise examination of pressure distribution and gas leakage.

In the Angular Coefficient Method91, the gas flow is calculated by integrating the flux from all surfaces that fall within the line-of-sight of a specific surface. In other words, each surface can receive gas from other surfaces within its line-of-sight, and the gas transfer between different surfaces depends on their angle and distance from each other. This method is highly accurate and efficient for flow calculations in the free molecular regime, where collisions between gas molecules are negligible.

As a result, for vacuum simulations, such as the stripper section in a tandem accelerator, which operates in the molecular flow regime, this method can be used to model gas leakage and pressure distribution accurately within the accelerating tube.

As shown in Fig. 6, the stripper section has its own dedicated vacuum pump, while each of the high energy and low energy sections of the accelerating tube have a separate ones. In this simulation, the nitrogen gas throughput considered 10 SCCM (Standard Cubic Centimeter per Minute). The vacuum pump speeds for both the accelerating tube sections and the stripper section are set to 300 L/s, with the gas temperature maintained at 20 °C. As a result, the optimized dimensions for the charge exchange section are presented in Table 4, in accordance with reference89. The nitrogen gas pressure profile along the accelerator beam path (including the stripper section and accelerating tube sections) for these optimized dimensions and the specified boundary conditions is shown in Fig. 8.

Table 4.

Optimum dimensions for stripper section.

L1 L2 L3 L4 L5 L6 L7 L8
40 cm 20 cm 20 cm 5 cm 9 cm 1.2 cm 20 cm 1.2 cm
Open in a new tab

Fig. 8.

Fig. 8

Open in a new tab

The pressure profile along the accelerator beam path with a gas throughput of 10 SCCM.

According to Eq. (1), by having the cross-section values for the possible interactions in the stripper section and determining the appropriate geometric dimensions, the efficiency of the charge exchange process can be calculated for each gas throughput. This calculation is carried out using simulations in COMSOL Multiphysics, coupling two interfaces: Free Molecular Flow and Charged Particle Tracing. In this process, first, using the Free Molecular Flow interface and considering the geometry of the cell and vacuum pumps, the required amount of gas for the charge exchange process is injected into the stripper section. Then, under steady-state conditions, the gas number density distribution along the accelerator beam path is determined. This step is particularly important for controlling the amount of injected gas and preventing its adverse effects on low- and high-energy sections of the accelerating tube. Once the steady-state gas distribution is obtained, the Charged Particle Tracing interface is employed to simulate the motion of carbon ions through the stripper section. This interface uses the Monte Carlo method to account the interactions such as Coulomb collisions and charge exchange processes. The collision cross-section is a key parameter in these simulations, as it directly influences the mean free path and determines the probability of each interaction occurring.

By integrating these two interfaces, the interaction cross-sections and the gas number density distribution along the beam path are used to compute the occurrence rate of each charge exchange processes listed in Table 3. This enables a realistic estimation of trajectories and charge state of carbon ions within the stripper section.

Experimental setup

In order to experimentally investigate the pressure behavior and validate the simulation results, the stripper section of the NSTRI tandem accelerator was constructed and assembled. After the construction of the stripper section and its associated connections, the section was mounted onto two 100-mm vacuum T-joints, serving as a representative of the low and high energy sections of the accelerating tube. This configuration enabled pressure readings at different positions, thereby providing a criterion for evaluating the amount of gas leakage into the low- and high-energy sections of the accelerating tube. In this experiment, the pressure was measured at three main regions: the stripper section, the charge-exchange cell, and the accelerating tube. Due to the geometric symmetry of the setup, pressure was measured on only one side of the accelerating tubes (low-energy and high-energy sections) and taken as representative of the opposite side; this serves as a diagnostic for gas leakage from the stripper region into the accelerating tubes. The general view of the experimental setup illustrated in Fig. 9.

Fig. 9.

Fig. 9

Open in a new tab

General view of the experimental setup.

For maintaining appropriate vacuum conditions during the experiments, three independent pumping systems were employed for the stripper cell, the stripper section, and the accelerating tube ensuring separate vacuum control in each part. To ensure the proper functioning of the vacuum gauges and to estimate their measurement error, two ports were incorporated into the stripper section, enabling the chamber pressure to be monitored from two independent locations. The gauges were pre-labeled and tested under both low- and high-vacuum conditions. In the first stage, only the rotary pump was operated, and after one hour the pressure values were recorded at low vacuum condition. Subsequently, with the turbomolecular pumps activated and the system reaching high vacuum after two hours, the pressure was measured again. Once stable vacuum conditions were achieved, the pressure readings at different stages of operation and the final assignment of each gauge were recorded and are summarized in Table 5. The small variations observed among the readings confirmed the accuracy of the gauges and their reliability for further measurements.

Table 5.

Vacuum gauges accuracy verification and their installation locations.

Gauge No. Pressure at low vacuum (mbar) Pressure at high vacuum (mbar) Final position in the setup
1 1.7 × 10− 2 7.3 × 10− 7 Ch. Ex. Cell
2 1.5 × 10− 2 9.4 × 10− 7 Stripper Section
3 1.7 × 10− 2 9.6 × 10− 7 Accelerating Tubes
Open in a new tab

Since the pressure inside the charge exchange cell could not be measured directly, a T-junction in the gas injection line was utilized to provide access for a pressure reading. The geometry of this configuration was simulated in Free Molecular Flow of COMSOL Multiphysics, and the ratio between the gauge reading and the actual pressure inside the cell was determined. This ratio was then used as a correction factor to estimate the true cell pressure from the measured values.

The gas injection system consisted of a nitrogen cylinder at 100 psi connected to a mass flow meter with a precision of 0.001 SCCM, enabling highly accurate gas flow control. In this experiment, nitrogen gas was injected into the system within a range of 0.5–10 SCCM in steps of 0.5 SCCM, while the pressure in the four regions of the setup was recorded simultaneously. The gas injection system is shown in Fig. 10.

Fig. 10.

Fig. 10

Open in a new tab

Gas injection system.

Results

Using the optimized dimensions of the stripper section and the available cross-section values for the interactions listed in Table 3, calculations were performed to determine the final distribution of different charge states for each carbon isotope (12C, 13C, and 14C) after passing through this section. These calculations were conducted to evaluate the impact of different gas throughput on the charge exchange process, with the goal of identifying the equilibrium gas thickness at which the distribution of charge states reaches a steady state.

For each gas throughput, the charge state distribution of carbon ions after exiting the stripper section was calculated, and the behavior of each isotope under different gas conditions was analyzed. Due to the variations in the isotope’s velocities and consequently in the interaction cross-sections, it was observed that the efficiency of producing each charge state differs among the isotopes. As expected, due to the low cross-section values of the interactions leading to the formation of carbon ions with charge states higher than 4+, such charge states were not produced during the charge exchange process. This confirms that the probability of generating such highly charged carbon ions using a gas stripper system is extremely low, and therefore, gas strippers are not practical for achieving these charge states. Figure 11 shows the simulation of carbon ion beam’s trajectory through the stripper section, demonstrating the charge exchange process.

Fig. 11.

Fig. 11

Open in a new tab

Simulation of carbon ion beam’s trajectory through the stripper section.

Figure 12 shows the gas-target thickness along the beam path for various gas throughputs and Fig. 13 provides a comparative analysis of the resulting charge-state distributions for the carbon isotopes across the same throughput range, which is used to identify optimal operating conditions in the accelerator.

Fig. 12.

Fig. 12

Open in a new tab

Gas target thickness along the beam path in the stripper section.

Fig. 13.

Fig. 13

Open in a new tab

Fraction of all charge states for different carbon isotopes at various gas throughputs.

In Monte Carlo simulations, the number of m successful outcomes in N independent trials follows a binomial distribution. Therefore, the estimated fraction Inline graphichas a standard deviation of Inline graphic92. Across all Monte Carlo calculations performed, the maximum relative statistical error was found to be 1.58%, which is sufficiently small for the objectives of this study.

To determine the equilibrium thickness in the stripper section, a dimensionless parameter, Alpha (α), was defined. This parameter is the ratio of the charge exchange efficiency at a given gas throughput to that at the next higher rate, and it was calculated for each charge state of carbon isotopes across various gas throughputs. The concept of equilibrium thickness is based on the assumption that, at a certain point, further increases in gas number density no longer affect the charge exchange efficiency and the α value gradually approaches to 1. Therefore, when the α value for all charge states of a particular isotope reaches 1, the corresponding gas thickness can be considered the equilibrium thickness for that isotope.

The variation of the α value as a function of gas throughput for different carbon isotopes is presented in Fig. 14. Ultimately, the equilibrium thickness of nitrogen gas for the entire system was defined as the highest value among the equilibrium thicknesses of all isotopes. This approach ensures optimal and complete charge exchange performance across all carbon isotopes.

Fig. 14.

Fig. 14

Open in a new tab

α value vs. gas throughput for different carbon isotopes: (a)12C, (b) 13C, (c) 14C.

As the NSTRI tandem accelerator is currently in the design phase and a 1.7 MeV carbon beam is not available for validation, we validated our stripper calculations with experimental data from Reference86. Specifically, we compared the result of charge-state fractions calculations with the 1.7 MeV measurements in nitrogen gas at equilibrium thickness, where the charge-state distributions are well described by a Gaussian profile due to the central-limit behavior of numerous independent electron-loss/capture events. In Fig. 15, blue points denote the calculated fractions from this study, red points denote the experimental data from Ref.86, and the red curve is the Gaussian fit applied to the measurements. Figure 15 shows close agreement between calculated fractions in this study and the measurements, supporting the adequacy of the model and the credibility of the results.

Fig. 15.

Fig. 15

Open in a new tab

carbon charge state fractions; blue points: calculated in this study, red points: experimental data from Ref86.

Due to the specific geometry of the gas injection line, where a T-junction was employed to access the pressure reading, the measured pressure at the gauge location differed from the actual pressure inside the charge exchange cell. To quantify this difference, the geometry of the gas injection line and the stripper section was simulated in COMSOL Multiphysics, and the pressure distribution in this region was calculated. The simulation result for a gas throughput of 10 SCCM, shown alongside the experimental setup, is presented in Fig. 16. Based on this analysis, the pressure at the gauge location was found to be approximately 2.7 times higher than the actual pressure inside the charge exchange cell.

Fig. 16.

Fig. 16

Open in a new tab

(a) Simulated pressure distribution in the T-junction region for gas throughput of 10 SCCM, (b) Experimental setup.

To validate the simulation results, pressure values at different sections of the system were experimentally measured and compared with those obtained from the simulations. For this purpose, the pressure was measured in the accelerating tubes, the stripper section, the charge exchange cell, and the high-energy section of accelerating tube at gas injection rates ranging from 0.5 to 10 SCCM with increments of 0.5. The results of this comparison between the simulation and the measurements are presented in Fig. 17.

Fig. 17.

Fig. 17

Open in a new tab

Comparison of measured and calculated pressure values. (a) Ch. Ex. cell, (b) stripper section, (c) accelerating tubes.

Conclusion

The main advantages of AMS based radiocarbon dating over other methods include the need for only a very small amount of sample, high sensitivity for detecting very old samples, and the ability to separate and remove interferences caused by other isotopes. A tandem accelerator is required to apply this method. The power supply for NSTRI tandem accelerator has already been developed and is capable of generating a voltage of 1.7 MV.

In this paper, following the steps of derivation of cross section of interactions and simulating the charge exchange process has resulted in an increased charge exchange efficiency and the determination of the equilibrium thickness.

The initial step in designing the stripper system is to accurately derive the cross-sections of the relevant interactions within the stripper region. To achieve this, various data sources providing cross-section values were reviewed and compared at the desired energy. Considering the relationship between ion energy and velocity, as well as the mass differences among carbon isotopes, it was found that the cross-sections for each interaction differ among isotopes during the charge exchange process. Therefore, these differences should be carefully considered in the calculations.

The charge exchange interactions for all three carbon isotopes (12C, 13C, and 14C) were calculated using a coupled approach that combines the Free Molecular Flow and Charged Particle Tracing interfaces in COMSOL Multiphysics software. The purpose of these calculations was to determine the equilibrium gas thickness required for efficient stripping of the carbon beam. After designing the optimal geometry of the stripper section, the equilibrium thickness was carried out at a gas throughput of 9 SCCM, resulting in a value of 2.3 × 1016 cm−2.

Accurately determining the ratio of stable carbon isotopes (12C and 13C) to 14C is fundamental for radiocarbon dating by AMS. Since ion velocity depends on both energy and mass, carbon isotopes with different masses exhibit slightly different velocities at the same energy, which in turn leads to differences in their charge-exchange cross-sections. This research indicates that, after reaching the equilibrium gas thickness in the stripper section, the 14C/12C stripping ratios for charge states 1+, 2+, and 3 + are 1.22, 1.01, and 0.89, respectively, while the corresponding 14C/13C ratios are 1.52, 1.09, and 0.76. These results demonstrate the inherent isotopic fractionation occurring during the stripping process. In practical AMS radiocarbon dating, such differences are corrected through calibration against standards; nevertheless, the present findings highlight the intrinsic nature of these effects and emphasize the necessity of careful calibration to ensure accurate 14C quantification.

Additionally, the calculated results were validated with measurements from reference86, showing excellent agreement between the model and the experimental data. This further confirms the reliability of the calculation approach used in this study.

Finally, the optimized geometry of the stripper section was constructed and experimentally tested. The pressure was measured in the low-energy section, stripper section, charge-exchange cell, and high-energy section. The obtained values were compared with the simulation results, and this comparison confirmed the validity of the simulation, as the measured pressure values showed good agreement with the simulated results.

The results demonstrate that this optimized geometry and structure are capable of achieving the required atomic density for reaching the equilibrium thickness of the carbon beam, with a length approximately one-third that of common stripper sections used in tandem accelerators.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary Material 1 (535.8KB, jpg)

Acknowledgements

The authors would like to express their gratitude to M. Nazari, R. Roozehdar Mogaddam, M. Aghayan, H. Mirzae, M. Shirshekan and M. Sadafi for their valuable guidance and insightful discussions throughout this work. We also gratefully acknowledge the High-Performance Computing Center at the Nuclear Science and Technology Research Institute (NSTRI) for providing essential computational resources and technical support that contributed to the success of this research.

Author contributions

M. Mohseni Kejani: Writing – original draft, Visualization, Validation, Software. F. Ghasemi: Writing – review & editing, Supervision, Resources, Methodology.F. Abbasi Davani: Writing – review & editing, Supervision, Resources. Sh. Sanaye Hajari: Writing – review & editing, Validation, Methodology. M. Lamehi Rachti: Writing – review & editing, Methodology.

Data availability

All processed data supporting the findings of this study are included within the article and its supplementary information files. Due to the large volume (~3 TB) of the full raw simulation data, these datasets have not been publicly uploaded but are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

8- References

  • 1.Murray, A. et al. Optically stimulated luminescence dating using quartz. Nat. Reviews Methods Primers. 1(1), 72 (2021). [Google Scholar]
  • 2.Williams, M. et al. Late Quaternary floods and droughts in the Nile valley, Sudan: new evidence from optically stimulated luminescence and AMS radiocarbon dating. Q. Sci. Rev.29, 9–10 (2010). [Google Scholar]
  • 3.Zhang, J. F., Liu, C. L., Wu, X. H., Liu, K. X. & Zhou, L. P. Optically stimulated luminescence and radiocarbon dating of sediments from Lop Nur (Lop Nor), China. Quat. Geochronol.10, 150–155 (2012). [Google Scholar]
  • 4.Mischke, S. et al. Radiocarbon and optically stimulated luminescence dating of sediments from Lake Karakul. Tajikistan Quaternary Geochronology. 41, 51–61 (2017). [Google Scholar]
  • 5.Shewan, L. et al. Dating the megalithic culture of laos: Radiocarbon, optically stimulated luminescence and U/Pb zircon results. PloS one. 16(3), e0247167 (2021). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 6.Bíl, M. et al. A chronology of landsliding based on archaeological and documentary data: Pavlovské vrchy Hills, Western Carpathian Flysch Belt, Sci. Rep.10(1), 976 (2020). [DOI] [PMC free article] [PubMed]
  • 7.Sellwood, E. et al. Optical bleaching front in bedrock revealed by spatially-resolved infrared photoluminescence. Sci. Rep.9(1), 2611 (2019). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 8.Prasad, A. K., Poolton, N. R., Kook, M. & Jain, M. Optical dating in a new light: A direct, non-destructive probe of trapped electrons. Sci. Rep.7(1), 12097 (2017). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 9.Richard, M. et al. Multi-method dating reveals 200 ka of Middle Palaeolithic occupation at Maras rock shelter, Rhône Valley, France. Sci. Rep.14(1), 20474 (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 10.Li, Y., Song, Y., Lai, Z., Han, L. & An, Z. Rapid and cyclic dust accumulation during MIS 2 in Central Asia inferred from loess OSL dating and grain-size analysis. Sci. Rep.6(1), 32365 (2016). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 11.Bossema, F. G. et al. A novel method for dendrochronology of large historical wooden objects using line trajectory X-ray tomography. Sci. Rep.11(1), 11024 (2021). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 12.Tintner, J. et al. MD dating: molecular decay (MD) in pinewood as a dating method. Sci. Rep.10(1), 11255 (2020). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 13.Douglass, A. Climate and trees. Nat. Magazine. 12, 51–53 (1928). [Google Scholar]
  • 14.Muigg, B. et al. Tree rings reveal signs of Europe’s sustainable forest management long before the first historical evidence. Sci. Rep.10(1), 21832 (2020). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 15.Faraji, M. et al. Accurate dating of stalagmites from low seasonal contrast tropical Pacific climate using Sr 2D maps, fabrics and annual hydrological cycles. Sci. Rep.11(1), 2178 (2021). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 16.Hajdas, I. et al. Radiocarbon dating. Nat. Rev. Methods Primers. 1(1), 62 (2021). [Google Scholar]
  • 17.McFadgen, B. G., Knox, F. & Cole, T. Radiocarbon calibration curve variations and their implications for the interpretation of New Zealand prehistory. Radiocarbon36(2), 221–236 (1994).
  • 18.Fairbanks, R. G. et al. Radiocarbon calibration curve spanning 0 to 50,000 years BP based on paired 230Th/234U/238U and 14 C dates on pristine corals. Q. Sci. Rev.24, 16–17 (2005). [Google Scholar]
  • 19.Ramsey, C. B., Buck, C. E., Manning, S. W., Reimer, P. & Van der Plicht, H. Developments in radiocarbon calibration for archaeology. Antiquity80(310), 783–798 (2006).
  • 20.Wigley, T. & Muller, A. Fractionation corrections in radiocarbon dating. Radiocarbon23(2), 173–190 (1981).
  • 21.Olsson, I. U. & Osadebe, F. A. Carbon isotope variations and fractionation corrections in 14 C dating. Boreas3(4), 139–146 (1974).
  • 22.Gulliksen, S. Isotopic fractionation of Norwegian materials for radiocarbon dating. Radiocarbon22(3), 980–986 (1980).
  • 23.Bonani, G. et al. Fractionation, precision and accuracy in 14 C and 13 C measurements. Nucl. Instrum. Methods Phys. Res., Sect. B. 29(1–2), 87–90 (1987). [Google Scholar]
  • 24.Johnson, R. et al. Archaeologic sherd dating: Comparison of thermoluminescence dates with radiocarbon dates by beta counting and accelerator techniques. Radiocarbon28(2A), 719–725 (1986).
  • 25.Stuiver, M. Carbon-14 dating: a comparison of beta and ion counting. Science202(4370), 881–883 (1978). [DOI] [PubMed] [Google Scholar]
  • 26.Jones, G., Jull, A. T., Linick, T. & Donahue, D. J. Radiocarbon dating of deep-sea sediments: A comparison of accelerator mass spectrometer and beta-decay methods. Radiocarbon31(2), 105–116 (1989).
  • 27.Grootes, P., Stuiver, M., Farwell, G., Schaad, T. & Schmidt, F. Enrichment of 14 C and sample preparation for beta and ion counting. Radiocarbon22(2), 487–500 (1980).
  • 28.Brannon, H., Taggart, M. & Williams, M. Proportional counting of carbon dioxide for radiocarbon dating. Rev. Sci. Instrum.26(3), 269–273 (1955). [Google Scholar]
  • 29.Nydal, R. Proportional counting technique for radiocarbon measurements. Rev. Sci. Instrum.33(12), 1313–1320 (1962). [Google Scholar]
  • 30.Kaizer, J. et al. Methods of radiocarbon determination in wine and bone samples by gas proportional counting technique. Radiocarbon60(4), 1139–1149 (2018).
  • 31.Brown, T. A., Nelson, D. E., Mathewes, R. W., Vogel, J. S. & Southon, J. R. Radiocarbon dating of pollen by accelerator mass spectrometry. Quatern. Res.32(2), 205–212 (1989). [Google Scholar]
  • 32.Linick, T. W., Damon, P. E., Donahue, D. J. & Jull, A. J. Accelerator mass spectrometry: the new revolution in radiocarbon dating. Quatern. Int.1, 1–6 (1989). [Google Scholar]
  • 33.Harris, D. The impact on archaeology of radiocarbon dating by accelerator mass spectrometry. Philosophical Trans. Royal Soc. Lond. Ser. Math. Phys. Sci.323(1569), 23–43 (1987). [Google Scholar]
  • 34.Hedges, R. Radiocarbon dating by accelerator mass spectrometry: some recent results and applications. Philosophical Trans. Royal Soc. Lond. Ser. A. 323(1569), 57–73 (1987). Mathematical and Physical Sciences. [Google Scholar]
  • 35.Donahue, D. J. Radiocarbon analysis by accelerator mass spectrometry. Int. J. Mass Spectrom. Ion Process.143, 235–245 (1995). [Google Scholar]
  • 36.Hellborg, R. Electrostatic Accelerators (Springer, 2005).
  • 37.Hinterberger, F. Electrostatic Accelerators (2006).
  • 38.Uchiyama, T. et al. Electrostatic accelerators with high energy resolution. Nucl. Instrum. Methods Phys. Res., Sect. B. 56, 1036–1038 (1991). [Google Scholar]
  • 39.Van de Graaff, R. Tandem electrostatic accelerators. Nucl. Instrum. Methods. 8(2), 195–202 (1960). [Google Scholar]
  • 40.Shima, K., Ishii, S., Takahashi, T. & Sugai, I. Optimum thickness of carbon stripper foils in tandem accelerator in view of transmission and lifetime. Nucl. Instrum. Methods Phys. Rese. Sect. A460(2–3), 233–238 (2001).
  • 41.von Reden, K. et al. Carbon nanotube foils for electron stripping in tandem accelerators. Nucl. Instrum. Methods Phys. Res., Sect. B. 261(1–2), 44–48 (2007). [Google Scholar]
  • 42.Liechtenstein, V. K. et al. Preparation and comparative testing of advanced diamond-like carbon foils for tandem accelerators and time-of-flight spectrometers. Nucl. Instrum. Methods Phys. Rese. Sect. A438(1), 79–85 (1999).
  • 43.Shima, K. et al. Lifetime of charge stripping foils and transmission of heavy ions in 12UD-pelletron tandem accelerator. Nucl. Instrum. Methods Phys. Res. Sect. B. 139, 1–4 (1998). [Google Scholar]
  • 44.Davydenko, V. et al. Stripping target of 2.5 MeV 10 mA tandem accelerator. in AIP Conference Proceedings Vol. 763 332–336 (American Institute of Physics, 2005).
  • 45.Hotchkis, M. et al. Sulphur hexafluoride as a stripper gas for tandem accelerators. Nucl. Instrum. Methods Phys. Res., Sect. B. 302, 14–18 (2013). [Google Scholar]
  • 46.Makarov, A., Ostreinov, Y., Taskaev, S. & Vobly, P. Modification of the argon stripping target of the tandem accelerator. Appl. Radiat. Isot.106, 53–56 (2015). [DOI] [PubMed] [Google Scholar]
  • 47.Kolesnikov, Y. A., Koshkarev, A., Taskaev, S. Y. & Shchudlo, I. Diagnostics of the Efficiency of a Gas Stripping Target of a Tandem Accelerator with Vacuum Insulation. Instruments Experimental Techniques. 63, 310–314 (2020). [Google Scholar]
  • 48.Saitoh, Y., Chiba, A. & Narumi, K. Transmission of cluster ions through a tandem accelerator of several stripper gases. Rev. Sci. Instrum.80, 10 (2009). [DOI] [PubMed]
  • 49.Aghayan, M., Masoudi, S. F., Ghasemi, F., Wuensch, W. & Shaker, H. Development of a novel approach for construction of high gradient braze-free S-band cavities. Sci. Rep.11(1), 18840 (2021). [DOI] [PMC free article] [PubMed] [Google Scholar]
  • 50.Zarei, S., Davani, F. A., Rachti, M. L. & Ghasemi, F. Design of a side coupled standing wave accelerating tube for NSTRI e-Linac. J. Instrum.12(09), P09026 (2017). [Google Scholar]
  • 51.Zarei, S. et al. Construction and measurement of the prototype side-coupled standing-wave tube for electron Linac. J. Instrum.18(10), T10006 (2023). [Google Scholar]
  • 52.Kejani, M. M., Ghasemi, F., Davani, F. A., Ahmadiannamin, S. & Zarei, S. Multiphysics analysis of side-coupled RF cavity. J. Instrum.14(07), P07001 (2019). [Google Scholar]
  • 53.Ghasemi, F., Nazari, M., Abbasi, F. & HasanPour, O. Design and simulation of a 1 MeV, 100 mA parallel-fed capacitive coupled cascade industrial accelerator. J. Instrum.15(01), T01001 (2020). [Google Scholar]
  • 54.Mirzaei, H. et al. Development and performance analysis of the 200 keV Cockcroft-Walton ion accelerator. Results Phys.68, 108089 (2025). [Google Scholar]
  • 55.Agha-Aligol, D. et al. Analysis of 18th–19th century’s historical samples of Iranian ink and paper belonging to the Qajar dynasty. Appl. Phys. A. 89, 799–805 (2007). [Google Scholar]
  • 56.Agha-Aligol, D., Oliaiy, P., Mohsenian, M., Lamehi-Rachti, M. & Shokouhi, F. Provenance study of ancient Iranian luster pottery using PIXE multivariate statistical analysis. J. Cult. Herit.10(4), 487–492 (2009). [Google Scholar]
  • 57.Hassanzadeh, A., Lamehi-Rachti, M., Oliaiy, P., Rahighi, J. & Shokouhi, F. External PIXE analysis of old inks and papers. Int. J. PIXE. 9(03–04), 481–485 (1999). [Google Scholar]
  • 58.Agha-Aligol, D., Jafarizadeh, M. & Moradi, M. Micro-PIXE: a powerful technique in measurement and determination of raw materials of glass artifacts of Parthian period From Shaur (Susa). J. Res. Archaeometry. 4(1), 47–65 (2018). [Google Scholar]
  • 59.Sodaei, B., Gol, D. A. A. & Khosravi, L. Typology, Morphology, and elemental analysis of Early Islamic period glass bracelets from Jahangir dome and Goriye tape in Ilam province. J. Res. Archaeometry. 9(2), 1–20 (2023). [Google Scholar]
  • 60.Kakuee, O. et al. External PIXE analysis of an Iranian 15th century poetry book. Nucl. Instrum. Methods Phys. Res., Sect. B. 273, 178–181 (2012). [Google Scholar]
  • 61.Kakuee, O., Fathollahi, V., Oliaiy, P. & Mesbahi, S. Investigation of mordants for dyeing of yarns in ancient Persian carpets (15th–17th century) by IBA methods. Nucl. Instrum. Methods Phys. Res., Sect. B. 450, 294–298 (2019). [Google Scholar]
  • 62.Kameshki, N., Amirhajloo, S., Agha-Aligol, D., Shahsavari, M. & Fazel, L. Lustre Production in Kerman; Typology and Elemental analysis of Lustrewares of Exhibition and Pottery Bank of Arg-e Bam. J. Res. Archaeometry. 7(1), 81–101 (2021). [Google Scholar]
  • 63.Sodaei, B., Aligol, D. A. & Khosravi, L. Manufacturing Technology and Usage of Glass Fragments in Jahangir Dome and Goriye, Sasanid Sites in Western Iran. Near East. Archaeol.86(2), 132–148 (2023). [Google Scholar]
  • 64.Shokouhi, F. et al. Elemental Analysis of Ancient Iranian Luster Decorated Pottery. Int. J. PIXE. 12, 03n04 (2002). [Google Scholar]
  • 65.Borgia, I. et al. Characterisation of decorations on Iranian (10th–13th century) lustreware. Appl. Phys. A. 79, 257–261 (2004). [Google Scholar]
  • 66.Oliaiy, P., Agha-Aligol, D., Shokouhi, F. & Lamehi‐Rachti, M. Analysis of Iranian postage stamps belonging to the Qajar dynasty (18th–20th century’s) by micro‐PIXE. X-Ray Spectrometry: Int. J.38(6), 479–486 (2009). [Google Scholar]
  • 67.Ahmadi, S., Shokouhi, F., Oliaiy, P., Lamehi-Rachti, M. & Rahighi, J. Characterisation of the Wall Painting Pigments of Baghcheh Joogh Castle by PIXE. Int. J. PIXE. 15, 03n04 (2005). [Google Scholar]
  • 68.Dmitriev, I., Nikolaev, V., Teplova, Y. A., Popov, B. & Vinogradova, L. Experimental investigation of the effective cross sections for the annihilation and formation of fast negative ions in atomic collisions. SOVIET Phys. JETP23, 5 (1966).
  • 69.Ormrod, J. & Michel, W. Charge equilibrium fractions and charge-exchange cross sections for fast ions in nitrogen and argon. Can. J. Phys.49(5), 606–620 (1971). [Google Scholar]
  • 70.Matic, M. & Cobic, B. Electron loss by C-and O-ions in gaseous targets. J. Phys. B: At. Mol. Phys.4(1), 111 (1971). [Google Scholar]
  • 71.Belkova, Y. A., Novikov, N. & Teplova, Y. A. Analysis of the relationship between the electron-capture and electron-loss cross sections for carbon ions. J. Surf. Investig.3, 188–191 (2009).
  • 72.Fogel, I. M., Ankudinov, V. & Pilipenko, D. Electron capture and loss in collisions of fast carbon and oxygen atoms with gas molecules. SOVIET Phys. JETP35, 8 (1959).
  • 73.Dmitriev, I., Teplova, Y. A., Belkova, Y. A. & Novikov, N. Charge exchange cross sections of carbon ions. J. Surf. Investig.2, 270–273 (2008).
  • 74.Dmitriev, I., Nikolaev, V., Fateeva, L. & Teplova, Y. A. Experimental study of electron loss by multiply charged ions in gases. J. Exp. Theory Phys.15, 11 (1962).
  • 75.Tonuma, T., Miyazawa, Y., Karasawa, T. & Kohno, I. Charge Exchange of Carbon and Nitrogen Ions in Nitrogen Gas. Jpn. J. Appl. Phys.9(11), 1306 (1970). [Google Scholar]
  • 76.Tonuma, T. et al. Charge changing of energetic heavy ions in gases. J. Phys. Soc. Jpn.34(1), 148–155 (1973). [Google Scholar]
  • 77.Anholt, R. et al. Intermediate-velocity atomic collisions: Electron capture and loss in 10–42-MeV C ions. Phys. Rev. A. 37(4), 1105 (1988). [DOI] [PubMed] [Google Scholar]
  • 78.Knudsen, H., Andersen, L., Haugen, H. & Hvelplund, P. Electron loss from fast one-electron ions colliding with He, N2, and Ar. Phys. Scr.26(3), 132 (1982). [Google Scholar]
  • 79.Nikolaev, V., Dmitriev, I., Fateeva, L. & Teplova, Y. A. Experimental investigation of electron capture by multiply charged ions. SOVIET Phys. JETP-USSR. 13(4), 695–702 (1961). [Google Scholar]
  • 80.Dmitriev, I., Nikolaev, V., Tashaev, Y. A. & Teplova, V. A. Experimental study of the loss and capture of electrons by fast unexcited and metastable heliumlike ions in ion-atomic collisions. Zh Eksp. Teor Fiz.67, 2047–2063 (1974). [Google Scholar]
  • 81.Hoffman, J., Miller, G. & Lockwood, G. Charge transfer of ground-state C+, N+, and O+ in N2 and H2. Phys. Rev. A25(4), 1982 (1930).
  • 82.Lockwood, G. J., Miller, G. H. & Hoffman, J. M. Charge transfer of C+, N+, and O + in N 2 and H 2. Phys. Rev. A. 18(3), 935 (1978). [Google Scholar]
  • 83.Moran, T. & Mathur, B. Charge transfer reactions of C+, N+, and O+ ions with H 2 and N 2. Phys. Rev. A. 21(3), 1051 (1980). [Google Scholar]
  • 84.Rottmann, L. et al. Single-electron capture by 100–1500-keV C+ ions in several atomic and molecular targets. Phys. Rev. A. 46(7), 3883 (1992). [DOI] [PubMed] [Google Scholar]
  • 85.Kiisk, M. et al. The charge state distribution of a carbon beam measured at the lund pelletron accelerator with the newly installed terminal pumping system in use. Nucl. Instrum. Methods Phys. Res. Sect. A481(1–3), 1–8 (2002).
  • 86.Sarkar, M., Shukla, N., Banerji, N. & Mohapatra, Y. Transmission and charge state distribution of carbon ions emerging from nitrogen gas target format? in a tandem accelerator: Impact of stripper gas pressure. Phys. Rev. Special Topics—Accelerators Beams. 15(10), 100101 (2012). [Google Scholar]
  • 87.Taylor, R. E. & Bar-Yosef, O. Radiocarbon dating: an archaeological perspective (Routledge, 2016).
  • 88.O’Hanlon, J. F. A user’s guide to vacuum technology (Wiley, 2003).
  • 89.Kejani, M. M., Ghasemi, F., Davani, F. A., Hajari, S. S. & Rachti, M. L. Design and optimization of charge exchange cell for high energy H – to H+ conversion. Int. J. Hydrog. Energy. 102, 1367–1376 (2025). [Google Scholar]
  • 90.Kejani, M. M., Ghasemi, F., Davani, F. A., Hajari, S. S. & Rachti, M. L. https://www.comsol.com/. [DOI] [PMC free article] [PubMed]
  • 91.Calafà, M. Characterization of the angular coefficient method on 2D and 3D piecewise smooth boundaries. Comput. Appl. Math.43(8), 450 (2024). [Google Scholar]
  • 92.Fishman, G. Monte Carlo: Concepts, Algorithms, and Applications (Springer Science & Business Media, 2013).

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplementary Material 1 (535.8KB, jpg)

Data Availability Statement

All processed data supporting the findings of this study are included within the article and its supplementary information files. Due to the large volume (~3 TB) of the full raw simulation data, these datasets have not been publicly uploaded but are available from the corresponding author upon reasonable request.

Articles from Scientific Reports are provided here courtesy of Nature Publishing Group

RESOURCES