Equilibrium Mean Charge Research Articles

Change in the Non-Equilibrium and Equilibrium Mean Charge of Ions Depending on the Thickness of a Passed Matter Layer

Change in the Non-Equilibrium and Equilibrium Mean Charge of Ions Depending on the Thickness of a Passed Matter Layer

Charge-state dynamics of heavy-ion beams penetrating a hydrogen plasma

The dynamics of charge-state fractions of Au- and U-ion beams, penetrating hydrogen plasmas, is investigated for 1.4 and 3.6 MeV/u ion energies and plasma electron temperatures Te = (0.6 − 3.0) eV and densities Ne =(1016 − 1020) cm−3. Calculations of the fractions as a function of the plasma thickness are performed by solving the balance rate equations with calculated ionization and recombination rates including those for dielectronic recombination (DR). The DR rates are calculated by the recently created computer code DRIMP using the fully relativistic multi-configuration approach and the so-called shifted Maxwellian velocity distribution function. Calculated by this method DR rates of Au- and U-ion beams passing through a hydrogen plasma are presented for the first time. Using the results obtained, the temperatures Te and densities Ne are found at which the equilibrium mean charges q̄ of Au- and U-ion beams are maximal for hydrogen-plasma length L≤ 100 cm. Dependencies of the plasma equilibrium thicknesses Xeq on the initial charge q0 of incident ions are investigated, and it is found that Xeq values are minimal at q0≈q̄.

On ionization dynamics of metal targets irradiated by high-contrast relativistic-intense laser pulses

We perform simulation of irradiation of metal targets by high-contrast relativistic-intense laser pulses. The results of modeling show that the locally equilibrium mean charge of ions calculated with the aid of the Thomas–Fermi model is in good agreement with the model that considers time dependable collisional-radiative population kinetics of ground and excited states of ionized atoms. The main reason for this is a high density of plasma free electrons in the case of interaction of the high-contrast laser pulse with a step-like plasma density profile.

Charge-state dynamics of 1.4- and 11-MeV/u uranium ions penetrating H2 and He gas targets

Abstract Theoretical description and interpretation are presented of the recent experimental data on stripping of fast 238U ions, penetrating H2 and He gaseous targets: obtained in GSI, Darmstadt, Germany at 1.4 MeV/u with a H2 stripper, and in RIKEN, Saitama, Japan at 11 MeV/u with H2 and He strippers. Electron-loss and capture cross sections for uranium ions, interacting with H2 and He targets are calculated and used as input data in the BREIT code to obtain dynamic characteristics of uranium-ion beams: non-equilibrium and equilibrium charge-state fractions, mean and equilibrium charges, and equilibrium thicknesses. Special attention is paid for the calculation of the dynamic characteristics of 1.4-MeV/u uranium ions stripped by a H2 in a windowless gas target at GSI, using a newly designed pulsed gas cell with a pressure changing from ∼ 0.1 to ∼ 100 mbar along the ion beam. To explain the experimental data, a Gaussian pressure model for the H stripper is applied with account for the target-density effect. A possible deviation of the Bragg’s additivity rule for electron-capture cross sections for a H2 target is also considered and we predict that the equilibrium charge of a 1.4-MeV/u uranium beam in atomic hydrogen is larger than in molecular hydrogen, i.e., it is indicated that atomic hydrogen can be a more effective stripper than molecular hydrogen. Charge-changing cross sections and dynamic characteristics of 11-MeV/u uranium ions passing through He and H2 targets are calculated as well. Calculated equilibrium mean charge states q ¯ ( He ) = 67.8 and q ¯ ( H 2 ) = 75.7 are in agreement with RIKEN experimental data within 10%.

Gas-pressure dependence of charge-state fractions and mean charges of 1.4 MeV/u-uranium ions stripped in molecular hydrogen

Using a recently created BREIT computer code (Balance Rate Equations for Ion Transportation), evolutions of the charge-state fractions Fq(x) and equilibrium mean charge states q¯ are calculated for stripping of 1.4MeV/u-U4+ ions in H2 gas for target thicknesses x⩽100μg/cm2 (⩽3·1019molecule/cm2) and gas pressures 10-4⩽P⩽500mbar. Calculations of the non-equilibrium Fq(x) and equilibrium Fq0 distributions for ion charges 4⩽q⩽40 are performed by solving the balance (rate) equations with account for the multi-electron processes and the target-density effect. Calculated equilibrium mean charge state increases from q¯≈27.6 at P=10-4mbar to its saturated (maximum) value of q¯≈32.7 at pressures P≳250mbar while the equilibrium target thickness xeq increases from 20 to 50μg/cm2 (from 0.6 to 1.5 in units of 1019molecule/cm2) in the H2-pressure range considered. From the present calculations it is concluded that the maximum mean charge state q¯ which can be achieved in stripping of 1.4MeV/u-U4+ ions in H2 gas is about q¯≈33 at a gas pressure P≳250mbar.

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 mean charge states for low-Zions at≤1 MeV/uin carbon

Equilibrium mean charge states have been measured for 3--7 MeV lithium, boron, and carbon ions passing through thin carbon foils. The data are compared to the predictions of several semiempirical models of charge equilibrium in the $\ensuremath{\le}1\text{ }\text{MeV}/\text{u}$ regime. The current work underscores the general problem of extrapolating models developed for high-$Z$ projectiles to ions of low $Z$. A compilation of experimental data for low-$Z$ ions in the low-energy regime has been used to reparametrize a few of the charge equilibrium models. Experimental techniques, comments and suggestions on the nature of the equilibrium charge states of low-$Z$ ions are presented.

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+.

The influence of nonthermal particles and radiation on the charge state of heavy ions in solar cosmic rays

The influence of various types of nonthermal electron and proton distributions and photoionization on the charge state of energetic heavy elements moving in a plasma is investigated. The mean charges of Mg, Si, and Fe are calculated for a bi-Maxwellian distribution of the background electrons and for electron and neutral beams with power-law energy distributions. An anomalously high density of the nonthermal component is required to obtain substantial deviations of the equilibrium mean charges of these elements (a few charge units) from the case when they interact with a purely Maxwellian plasma. In this context, the mean charges for O, Ne, Mg, Si, and Fe ions are also calculated for a model with charge-consistent acceleration. The results indicate that photoionization does not significantly influence the charge state of solar cosmic rays if the parameters of the plasma are those characteristic of impulsive solar events.

Charge states of Mg and Si from stochastic acceleration in impulsive solar flares

We consider the acceleration of heavy ions in impulsive solar flares. In particular, we have performed Monte Carlo simulations of stochastic acceleration by Alfvén wave turbulence, and compare new results for magnesium and silicon ions with previous results for iron. The model takes into account stripping due to collisions with ambient electrons and heavy particles (protons and He +2) which becomes increasingly important for more energetic ions, as well as radiative and dielectronic recombination due to collisions with electrons. Spatial diffusion and Coulomb losses are also taken into account. For comparison, we also calculate equilibrium mean charges. We examine the effects of plasma parameters on the calculated energy-dependent charge state distributions of these elements, which can be compared with results from space-borne instruments in order to put constraints on the physical environment of the acceleration region.

Cross Sections of Charge Exchange for Fast He Ions Passing through Zn Vapor

Single and double electron loss and capture cross sections have been measured for He 0 , He 1+ and He 2+ ions passing through a Zn vapor target at energies ranging from 0.8 to 2.0 MeV. Uncertainties of the cross sections were improved by applying the Rutherford scattering method for the determination of the target thickness. When combined with other previous experimental data, obtained cross sections support the oscillatory dependence on target atomic number. In addition, the equilibrium mean charges of He ions were compared for solid and gas phases of the Zn element, but no density effect has been observed.

Z oscillation of mean charges of energetic ions emerging from a carbon foil: Correlation with the shell structure of ions.

Equilibrium mean charges q-bar of ions passing through a carbon foil were observed to oscillate vs projectile atomic number Z at ion energies 0.55, 1, and 2 MeV/u. The maxima of the oscillation take place for closed-shell ions having the electrons in mean number Z-q-bar = 10 and 28.

Target dependence of equilibrium mean charge of fast ions emerging from solids

Equilibrium mean charges of H and 4He ions emerging from solids were measured for many kinds of target materials, and were found to show an oscillatory dependence on target atomic number. This oscillation was found to be the reflection of electron shell structures of the target atoms. The electron capture cross sections of very fast 3He 2+ ions were also measured and interpreted on the same physical ground.

Equilibrium charge distributions for B, C, N ions passing through matter

Equilibrium charge state distributions for fast ( ν > ν 0, ν 0: Bohr velocity) B, C, and N ions penetrating through solid and gaseous targets are investigated by utilizing the atomic collision theory. For the electron capture process, the two-state atomic expansion method is used and the electron capture into the excited state of an ion from a target atom is taken into account. On the other hand, for the electron loss process, the Bon approximation is used. As the velocity of an ion increases, the equilibrium mean charge becomes saturated and the distribution width becomes narrower. Numerical calculations for charge state distributions show good agreement with the experimental results.

Ztdependence of equilibrium charge state distributions of MeV He ions emerging from solid

The equilibrium charge state distributions of He ions emerging from various solid targets were measured in the energy range 0.6-2.4 MeV. Atomically clean target surfaces were prepared by continuous evaporation for Ga, Ge, Se and In, and by heating for Sc, Fe, Ta, W and Pt. The measured charge fractions Fi (i=0, 1, 2) were tabulated at 0.2 MeV intervals. In this energy range, the ratio F1/F2 is represented fairly well by the empirical formula AE-B, where E is the energy and A and B are target-dependent constants. The present data, together with the previous data, show clearly oscillatory behaviour of the equilibrium mean charge of He ions with target atomic number Zt. This oscillation is found to be attributed to the shell structure of the target atom.

Equilibrium charge distributions for B, C, N ions passing through solid and gaseous media

Abstract The equilibrium charge state distributions (ECSD) for fast B, C, N ions penetrating through solid and gaseous targets are investigated with atomic collision theories. For the electron-capture and -loss processes, the two-state atomic expansion method and the Born approximation are used respectively. With the increase of the ion velocity, the equilibrium mean charge becomes saturated and the distribution width becomes narrower. The numerical calculations for the ECSD are in good agreement with the experimental results.

Calculation of the Equilibrium Mean Charge of Helium Ions

AbstractZ2‐oscillation of the equilibrium mean charge of 1 MeV He ions discovered by experiments is confirmed by calculating both the electron‐capture and ‐loss cross‐sections, employing two‐state atomic expansion method and Bron approximation, respectively. The calculations are in good agreement with the experimental results.

Charge Exchange of Fast Iodine Ions in a Dense Jet of Carbon Dioxide

Charge distribution measurements were made with 10-75 MeV iodine ions of various incident charge states traversing either a supersonic CO2-jet of variable density in the range 5 x 1014 to 1.5 x 1017 molecules/cm3 or a target of dilute CO2 with a maximum density of 5 x 1014 molecules/cm3. The equilibrium mean charge ts of the iodine ions in the jet is found to be higher than in the dilute gas. The maximum difference of about one charge unit is observed at 75 MeV. Ihere is no indication for a further increase of Lat gas densities above 5 x 1016 molecules/cm3. Cross sections for electron capture and loss were determined by means of a least-squares-evaluation of non-equilibrium charge distributions. Considerable decrease of the capture cross sections for some lower charge states has proved to be responsible for the increase ?, whereas the loss cross sections do not change measurably with increasing target density.