Equilibrium Charge State Distributions Research Articles

Stripping features of 2-MeV/u sulfur-ion beams penetrating carbon foils

The dynamics of charge-state fractions of sulfur-ion beams stripped by carbon foils at 2.0 MeV/u is investigated as a function of the initial-ion charge state q0 of the incident beam using experimental data and theoretical calculations. Experimental dependencies of the ion fractions, mean charges and equilibrium foil thicknesses on q0 are explained using the BREIT code, based on the analytical solution of the balance rate equations, as well as the ETACHA code. Experimental equilibrium charge-state distribution is qualitatively reproduced by both codes, demonstrating the capability of their approaches to the density effect. It is shown experimentally and theoretically that the non-equilibrium charge-state fractions and equilibrium foil thicknesses strongly depend on the initial ion charge q0.

Accelerator mass spectrometry of 236U with He stripping at the Centro Nacional de Aceleradores

In January 2015, the 1 MV AMS facility at the Centro Nacional de Aceleradores (CNA, Seville, Spain) was upgraded with He stripping. In this work, we present a comprehensive study of the uranium transmission through the accelerator together with the background sources that limit the current sensitivity of our system to measure the 236U/238U atom ratio. In addition to the well-known background caused by scattered 235U3+ molecular fragments, we identify an additional component, not observed with Ar gas, that we relate to scattered 238U3+ molecular fragments. Stripper gas pressures below the one corresponding to the equilibrium charge state distribution are used to minimize the resulting overall background, which is in the (0.8–1.3) × 10−10 range. This is at least a factor of 3 higher than the background obtained with Ar gas. On the other hand, new information on the stripping process of U on He gas at the 400–1000 keV stripping energy range is presented. A maximum transmission of 45% for U3+ is achieved at about 650 keV, which correspond to a stripping yield of about 50%. This is the maximum yield that can be actually obtained working with He gas at low energies according to previous results.

Measurement of the equilibrium charge state distributions of Ni, Co, and Cu beams in Mo at 2 MeV/u: Review and evaluation of the relevant semi-empirical models

Equilibrium charge state distributions of stable 60Ni, 59Co, and 63Cu beams passing through a 1μm thick Mo foil were measured at beam energies of 1.84MeV/u, 2.09MeV/u, and 2.11MeV/u respectively. A 1-D position sensitive Parallel Grid Avalanche Counter detector (PGAC) was used at the exit of a spectrograph magnet, enabling us to measure the intensity of several charge states simultaneously. The number of charge states measured for each beam constituted more than 99% of the total equilibrium charge state distribution for that element. Currently, little experimental data exists for equilibrium charge state distributions for heavy ions with 19≲Zp,Zt≲54 (Zp and Zt, are the projectile’s and target’s atomic numbers respectively). Hence the success of the semi-empirical models in predicting typical characteristics of equilibrium CSDs (mean charge states and distribution widths), has not been thoroughly tested at the energy region of interest. A number of semi-empirical models from the literature were evaluated in this study, regarding their ability to reproduce the characteristics of the measured charge state distributions. The evaluated models were selected from the literature based on whether they are suitable for the given range of atomic numbers and on their frequent use by the nuclear physics community. Finally, an attempt was made to combine model predictions for the mean charge state, the distribution width and the distribution shape, to come up with a more reliable model. We discuss this new “combinatorial” prescription and compare its results with our experimental data and with calculations using the other semi-empirical models studied in this work.

The influence of the beam charge state on the analytical calculation of RBS and ERDA spectra

Analytical codes dedicated to the analysis of Ion Beam Analysis data rely on the accuracy of both the calculations and of basic data such as scattering cross sections and stopping powers. So far, the effect of the beam charge state of the incoming beam has been disregard by general purpose analytical codes such as NDF. In fact, the codes implicitly assume that the beam always has the equilibrium charge state distribution, by using tabulated stopping power values e.g. from SRIM, which are in principle valid for the effective charge state. The dependence of the stopping power with the changing charge state distribution is ignored. This assumption is reasonable in most cases, but for high resolution studies the actual change of the charge state distribution from the initial beam charge state towards equilibrium as it enters and traverses the sample must be taken into account, as it influences the shape of the observed data. In this work, we present an analytical calculation, implemented in NDF, that takes this effect into account. For elastic recoil detection analysis (ERDA), the changing charge state distribution of the recoils can also be taken into account. We apply the calculation to the analysis of experimental high depth resolution ERDA data for various oxide layers collected using a magnetic spectrometer.

A SIMPLE METHOD FOR MODELING COLLISION PROCESSES IN PLASMAS WITH A KAPPA ENERGY DISTRIBUTION

We demonstrate that a nonthermal distribution of particles described by a kappa distribution can be accurately approximated by a weighted sum of Maxwell-Boltzmann distributions. We apply this method to modeling collision processes in kappa-distribution plasmas, with a particular focus on atomic processes important for solar physics. The relevant collision process rate coefficients are generated by summing appropriately weighted Maxwellian rate coefficients. This method reproduces the rate coefficients for a kappa distribution to an estimated accuracy of better than 5%. This is equal to or better than the accuracy of rate coefficients generated using "reverse engineering" methods, which attempt to extract the needed cross sections from the published Maxwellian rate coefficient data and then reconvolve the extracted cross sections with the desired kappa distribution. Our approach of summing Maxwellian rate coefficients is easy to implement using existing spectral analysis software. Moreover, the weights in the sum of the Maxwell-Boltzmann distribution rate coefficients can be found for any value of the parameter kappa, thereby enabling one to model plasmas with a time-varying kappa. Tabulated Maxwellian fitting parameters are given for specific values of kappa from 1.7 to 100. We also provide polynomial fits to these parameters over this entire range. Several applications of our technique are presented, including the plasma equilibrium charge state distribution (CSD), predicting line ratios, modeling the influence of electron impact multiple ionization on the equilibrium CSD of kappa-distribution plasmas, and calculating the time-varying CSD of plasmas during a solar flare.

Equilibrium and non-equilibrium charge-state distributions of 2.0 MeV/u carbon ions passing through carbon foils

Both equilibrium and non-equilibrium charge-state distributions were studied experimentally for 2.0MeV/u carbon ions after passing through carbon foils. Measured charge-state distribution established the equilibrium at a target thickness of 10μg/cm2 and this remained unchanged until a maximum target thickness of 98μg/cm2. The equilibrium charge-state distribution, the equilibrium mean charge-state, and the width and skewness of the equilibrium distribution were compared with predictions using existing semi-empirical formulae as well as simulation results, including the ETACHA code. It was found that charge-state distributions, mean charge states, and distribution widths for C2+, C3+, and C4+ incident ions merged into quasi-equilibrium values at a target thickness of 5.7μg/cm2 in the pre-equilibrium region and evolved simultaneously to the ‘real equilibrium’ values for all of the initial charge states, including C5+ and C6+ ions, as previously demonstrated for sulfur projectile ions at the same velocity (Imai et al., 2009). Two kinds of simulation, ETACHA and solution of rate equations taking only single electron transfers into account, were used, and both of them reproduced the measured charge evolution qualitatively. The quasi-equilibrium behavior could be reproduced with the ETACHA code, but not with solution of elementary rate equations.

Numerical simulation of an experimental analogue of a planetary magnetosphere

Recent improvements to the Omega Laser Facility's magneto-inertial fusion electrical discharge system (MIFEDS) have made it possible to generate strong enough magnetic fields in the laboratory to begin to address the physics of magnetized astrophysical flows. Here, we adapt the MHD code AstroBEAR to create 2D numerical models of an experimental analogue of a planetary magnetosphere. We track the secular evolution of the magnetosphere analogue and we show that the magnetospheric components such as the magnetopause, magnetosheath, and bow shock, should all be observable in experimental optical band thermal bremsstrahlung emissivity maps, assuming equilibrium charge state distributions of the plasma. When the magnetosphere analogue nears the steady state, the mid-plane altitude of the magnetopause from the wire surface scales as the one-half power of the ratio of the magnetic pressure at the surface of the free wire to the ram pressure of an unobstructed wind; the mid-plane thickness of the magnetosheath is directly related to the radius of the magnetopause. This behavior conforms to Chapman and Ferraro's theory of planetary magnetospheres. Although the radial dependence of the magnetic field strength differs between the case of a current-carrying wire and a typical planetary object, the major morphological features that develop when a supersonic flow passes either system are identical. Hence, this experimental concept is an attractive one for studying the dynamics of planetary magnetospheres in a controlled environment.

Charge state distribution of 16O from the 4He(12C,16O)γ reaction of astrophysical interest studied both experimentally and theoretically

In astrophysics, 4He(12C,16O)γ reaction places an important role. At Kyushu University Tandem accelerator Laboratory (KUTL), the measurement of 4He(12C,16O)γ cross section is in progress in the energy range of astrophysical nuclear reaction. Since the charge state of product 16O ions after passing through the gas target is spread and only one charge state can be measured at terminal detector, it is necessary to know the charge state distribution of 16O ions passing through the He gas target precisely. Here, we report the charge state distribution of the 16O recoils both experimentally and theoretically. Experimentally, we measured the equilibrium charge state distribution of 16O ions in the windowless helium gas target with the beam energy of primary 16O ions at 7.2, 4.5, and 3.45MeV at KUTL. The measured results showed a Gaussian distribution for the charge state fraction. Theoretically, we proposed a framework for the charge state distribution study. Charge state distribution was computed by solving a set of differential equations including a series of charge exchange cross sections. For the ionization cross section, plane-wave Born approximation was applied and modified by taking target atomic screening as a function of momentum transfer into account. For the capture cross section, continuum distorted wave approximation was applied and the influence of the gas target density was taken into account in the process of electron capture. Using above charge exchange cross sections, the charge state evolution was simulated. According to the equilibrium distribution, we compared the theoretical calculation to the experimental data. After taking into account the density effects in the charge exchange process, the theoretical charge state distributions shows a good agreement with the experimental data. Both experimental and theoretical results are useful to understand the charge fraction of recoil oxygen created via 4He(12C,16O)γ reaction, especially in the energy range of astrophysical nuclear reaction.

High-resolution study of x-rays emitted from highly charged S ions using a bent-crystal spectrometer

We have measured the projectile x-rays from 56 MeV sulphur ions in collision with thin carbon foils using a high-resolution bent-crystal spectrometer. The resolution of the spectrometer is good enough to resolve lines arising from transitions in H-, He- and Li-like ions. The line energies are compared with values from the NIST x-ray database. The data have also been used to generate the approximate equilibrium charge state distribution, which is compared with semi-empirical model predictions.

Charge Equilibrium of a Laser-Generated Carbon-Ion Beam in Warm Dense Matter

Using ion carbon beams generated by high intensity short pulse lasers we perform measurements of single shot mean charge equilibration in cold or isochorically heated solid density aluminum matter. We demonstrate that plasma effects in such matter heated up to 1eV do not significantly impact the equilibration of carbon ions with energies 0.045-0.5 MeV/nucleon. Furthermore, these measurements allow for a first evaluation of semiempirical formulas or abinitio models that are being used to predict the mean of the equilibrium charge state distribution for light ions passing through warm dense matter.

Theoretical interpretation of equilibrium charge-state distributions of 4He ions backscattered from metallic foils using extended Bohr theory

Equilibrium charge-state distributions (ECSD’s) for He0, He+, and He++ backscattered by the foils made of silver have been measured using a post-acceleration system, and simulated by the extended Bohr theory. The kinematics behavior of the backscattered ions is understood from Rutherford backscattering spectrometry (RBS). The results from these measurements have been integrated with the data available in the literature to cover a wide energy range of the incident singly charged helium ion He+. The detected charge states increase from 0 to +Z with the incident ion energy. A formula for calculating He0 distribution, for the studied energy range, has been proposed. The ratio of singly to doubly ionized helium ions backscattered from thin Ag-foils, F(He\(^+)\)/F(He\(^{++})\), has been measured as a function of incident ion velocity. The use of a semi-classical approach, based on the theory of Bohr, allows a satisfactory theoretical description of F(He\(^+)\)/F(He\(^{++})\) ratios. It has been found that the measured and simulated ratios are strongly decreased with the incident velocity. The present study has demonstrated that the satisfactory fits of ECSD’s and the ratio of the fractions are mainly accounted to the contribution of both free valance electrons of the target and screened target nucleus in the calculation of total electron loss cross section.

Theoretical Interpretation of Atomic Charge Exchange between Singly Charged Helium Ions and Aluminum Foils

An experimental method for determining the equilibrium charge state of fast helium ions backscattered by solid Al-foils has been conducted using single Silicon Surface Barrier Detector (SBD) in a post acceleration system (PAS). The charge state measurements have been conducted to cover a wide energy range of the incident singly charged helium ion He+. The detected charge states increases from 0 to +Z with the incident ion's velocity. The method consists of measuring the charge states of ions after backscattering from the Al-foil as a function of projectile velocity and also finding the charge state distributions as a function of Al-foil thickness. The measurements are conducted for two types of Al-foil, one of which is thinner (2.5, 4.0, 5.4 ?g/cm2) and the other of which is of the order of an equilibrium foil thickness, where thicknesses of 6.8, 8.1, 9.5, and 10.8 were used. Ratios of equilibrium charge state yields for singly to doubly ionized He ions; He+1 and He+2, were also measured. The kinematics behavior of the measured He0, He+ and He+2 fractions is understood by the well-known Rutherford Backscattering Spectrometry technique (RBS). It has been shown that the dominant processes occurring to a fast He+ ions traversing Al-foil are the capture of the electron from the Al-atom to vacant state in the ion and the stripping of the bound electron from the He+ ion. The charge composition of the ion beams changes when it backscatters Al-foil, which thick enough for multiple atomic collisions, leading eventually to an equilibrium charge state distribution (ECSD). It was found that the theoretical calculations for electron-capture and loss ratios, based of semi-classical approach of Bianconi, are successful in describing the measured He ions. The satisfactory fits of the measured equilibrium charge state fractions (ECSF's) are mainly accounted to the contribution of both free valance electrons of the target and screened target nucleus in the calculation of total electron-loss cross sections. Bianconi approach is also applied to describe the measured mean equilibrium charges (MEC). The agreement between experiment and theory in this investigation is accounted to the reliability of the used post-acceleration system where all the backscattering charge-states, at certain incident ion's velocity, are separated and collected in one measurement.

Equilibrium charge state distributions for boron and carbon ions emerging from carbon and aluminum targets

Abstract Equilibrium charge state distributions of boron and carbon ions through carbon and aluminum targets were measured with an energy range of 3–6 MeV. Comparisons of the data with relevant semi-empirical models for the equilibrium mean charge states and for the charge state distribution widths could provide valuable insight on the underlying mechanisms for a fast ion to lose or capture electrons. In-depth examinations of the experimental results in combination with semi-empirical models suggest that equilibrium charge state distributions are well represented by Gaussian distributions.

Equilibrium and non-equilibrium charge-state distributions of 2 MeV/u sulfur ions passing through carbon foils

Both equilibrium and non-equilibrium charge-state distributions for 2.0 MeV/u sulfur ions after passing through carbon foils were studied experimentally. For the equilibrium charge-state distribution, incident ions of S 7+, S 12+, S 14+ and S 16+ were injected into carbon foils 54, 98, 150 and 200 μg/cm 2 in thickness, whereas for the non-equilibrium distributions, new measurements for S 15+ and S 16+ incidences were made through carbon foils of 0.9–10 μg/cm 2 to supplement our previous experiments regarding S 6+−S 14+ incidences [M. Imai, M. Sataka, K. Kawatsura, K. Takahiro, K. Komaki, H. Shibata, H. Sugai, K. Nishio, Nucl. Instr. and Meth. B 230 (2005) 63; M. Imai, M. Sataka, K. Kawatsura, K. Takahiro, K. Komaki, H. Shibata, H. Sugai, K. Nishio, Nucl. Instr. and Meth. B 256 (2007) 11]. Mean charge states for S 6+–S 14+ incidences as functions of the penetration thickness merged at 6.9 μg/cm 2 and changed together until reaching equilibrium at around 100 μg/cm 2, while those for S 15+ and S 16+ incidences took different paths to equilibrium, which was also the case for distribution widths for S 6+–S 14+, S 15+ and S 16+ incidences. An equilibrium mean charge state of 12.68 and distribution width of 1.11 were attained with equilibrium charge distributions between 6+ and 16+.

Rutherford Backscattering Spectrometry of Electrically Charged Targets: Elegant Technique for Measuring Charge-State Distribution of Backscattered Ions

We found that surface charging during Rutherford backscattering spectrometry (RBS) of sapphire enabled us to measure the charge-state distribution of ions backscattered at the surface. For a Cu/Au-deposited Al2O3 sample, two components, higher- and lower-energy ones, were resolved on both Cu and Au peaks in the RBS random spectrum. For a single-crystalline Al2O3 sample, a double-peak structure was clearly observed on both Al and O surface peaks in the RBS aligned spectrum. The charge-state distribution can be obtained from the intensity of each component. The results obtained here were compared with previous data for the equilibrium charge-state distribution.

Equilibrium charge-state distributions for S and Si ions emerging from iron and gadolinium targets with velocities near their K-shell electron velocity

Equilibrium charge-state distributions of Si and S ions with energies between 84 and 237 MeV were measured after passage through iron and gadolinium targets. Knowledge of these exit charge distributions is critical for interpreting g-factor measurements on exotic nuclei produced as radioactive beams. The data for both targets are in agreement with the empirical parameterization of the mean charge state proposed recently by Schiwietz and Grande. The distribution widths are in agreement with the formula of Baudinet-Robinet.

A study of the charge state approach to the stopping power of MeV B, N and O ions in carbon

The charge state approach has been applied to describe the electronic stopping powers of swift O, N and B ions in carbon. According to the charge state model, the contributions to the electronic stopping power of energetic projectiles passing through solid targets are due to collisional interactions and the charge-exchange process. The definition of fractional effective charge from Brandt and Kitagawa has been introduced into the model. This approach requires knowledge of the equilibrium charge state distributions and of the charge-exchange cross sections for both electronic capture and loss processes. Both measured data and empirical calculations of the equilibrium charge state fraction are used in the study, and the electronic capture cross sections are obtained with the Eikonal Brinkman–Kramers approximation (EBK). By comparing the numerical results with the latest experimental data as well as empirical values, it is shown that the present approach slightly overestimates the energy loss at the intermediate velocity region.

Highly excited states of sulphur projectiles inside a carbon target

The satellite and hypersatellite K X-ray lines emitted by sulphur projectiles (with energies 9.6, 16.0, 22.4, 32.0, 65, 79, 99 and 122 MeV) passing through carbon foils (with different thickness varying from 15 to 210 μg/cm2) have been measured using a Si(Li) detector. We use a theoretical model based on the single-configuration Dirac–Fock calculations and equilibrium charge state distribution to interpret the experimental K X-ray spectra parameters. For all projectile energies, we evaluate the probability of K-hole creation, the average population of L-shell, and the average population of the 3p and 4p subshells. In the case of 9.6–32.0 MeV beam energy we evaluate also the population of L and M shells of sulphur projectiles. For the energy range 65–122 MeV, we estimate the probability of appearance of the most important configurations. The lifetimes of the studied states is also deduced.

Charge fraction of 6.0 MeV/n heavy ions with a carbon foil: Dependence on the foil thickness and projectile atomic number

We measured the charge fraction of 6.0 MeV/n heavy ions (C, Ne, Si, Ar, Fe and Cu) with a carbon foil at the NIRS-HIMAC injector. At this energy they are stripped with a carbon foil before being injected into two synchrotron rings with a maximum energy of 800 MeV/n. In order to find the foil thickness ( D E) at which an equilibrium charge state distribution occurs, and to study the dependence of the D E-values on the projectile atomic number, we measured the exit charge fractions for foil thicknesses of between 10 and 350 μg/cm 2. The results showed that the D E-values are 21.5, 62.0, 162, 346, 121, 143 μg/cm 2 for C, Ne, Si, Ar, Fe, Cu, respectively. The fraction of Ar 18+ ions was actually improved to 33% at 320 μg/cm 2 from ∼15% at 100 μg/cm 2. For Fe and Cu ions, the D E-values were found to be only 121 and 143 μg/cm 2; there is a large gap between Ar and Fe, which is related to the differences in the ratio of the binding energy of the K-shell electrons to an electron energy (3.26 keV) corresponding to the velocity of a 6.0 MeV/n projectile. The well-known “two disjoint Gaussians (shell effect)” was also observed in the measured charge fractions of both Fe and Cu. The results of the charge fractions were also compared with other data and to calculations of Rozet et al. [2], in which there was a good agreement for light ions (C); however, a significant difference was observed for ion species heavier than Ne.

Charge state studies of low energy heavy ions passing through hydrogen and helium gas

Studies of the charge state distribution of low energy (<1.5 MeV/u), low Z (<13) heavy ions passing through hydrogen and helium gas of varying target pressure have been performed using separate windowless gas target systems at TRIUMF and the University of Naples. Semi-empirical relationships have been deduced to estimate the equilibrium charge state distributions as a function of beam energy. From these distributions, cross-sections for the relevant charge changing reactions have been deduced.