Energy loss of heavy ions in dense plasma. II. Nonequilibrium charge states and stopping powers

Target Density Effects on Charge Transfer of Laser-Accelerated Carbon Ions in Dense Plasma

We report on charge state measurements of laser-accelerated carbon ions in the energy range of several MeV penetrating a dense partially ionized plasma. The plasma was generated by irradiation of a foam target with laser-induced hohlraum radiation in the soft x-ray regime. We use the tricellulose acetate (C_{9}H_{16}O_{8}) foam of 2  mg/cm^{3} density and 1 mm interaction length as target material. This kind of plasma is advantageous for high-precision measurements, due to good uniformity and long lifetime compared to the ion pulse length and the interaction duration. We diagnose the plasma parameters to be T_{e}=17  eV and n_{e}=4×10^{20}  cm^{-3}. We observe the average charge states passing through the plasma to be higher than those predicted by the commonly used semiempirical formula. Through solving the rate equations, we attribute the enhancement to the target density effects, which will increase the ionization rates on one hand and reduce the electron capture rates on the other hand. The underlying physics is actually the balancing of the lifetime of excited states versus the collisional frequency. In previous measurement with partially ionized plasma from gas discharge and z pinch to laser direct irradiation, no target density effects were ever demonstrated. For the first time, we are able to experimentally prove that target density effects start to play a significant role in plasma near the critical density of Nd-glass laser radiation. The finding is important for heavy ion beam driven high-energy-density physics and fast ignitions. The method provides a new approach to precisely address the beam-plasma interaction issues with high-intensity short-pulse lasers in dense plasma regimes.

The role of collisional ionization in heavy ion acceleration by high intensity laser pulses

We present here simulation results of the laser-driven acceleration of gold ions using the EPOCH code. Recently, an experiment reported the acceleration of gold ions up to 7 MeV/nucleon with a strong dependency of the charge-state distribution on target thickness and the detection of the highest charge states [Formula: see text]. Our simulations using a developmental branch of EPOCH (4.18-Ionization) show that collisional ionization is the most important cause of charge states beyond Z = 51 up to He-like Au.

Benchmark Experiment to Prove the Role of Projectile Excited States Upon the Ion Stopping in Plasmas

We report on a precision energy loss measurement and theoretical investigation of 100  keV/u helium ions in a hydrogen-discharge plasma. Collision processes of helium ions with protons, free electrons, and hydrogen atoms are ideally suited for benchmarking plasma stopping-power models. Energy loss results of our experiments are significantly higher than the predictions of traditional effective charge models. We obtained good agreement with our data by solving rate equations, where in addition to the ground state, also excited electronic configurations were considered for the projectile ions. Hence, we demonstrate that excited projectile states, resulting from collisions, leading to capture-, ionization-, and radiative-decay processes, play an important role in the stopping process in plasma.

Charge-Transfer Processes in Warm Dense Matter: Selective Spectral Filtering for Laser-Accelerated Ion Beams

We investigate, both experimentally and theoretically, how the spectral distribution of laser accelerated carbon ions can be filtered by charge exchange processes in a double foil target setup. Carbon ions at multiple charge states with an initially wide kinetic energy spectrum, from 0.1 to 18 MeV, were detected with a remarkably narrow spectral bandwidth after they had passed through an ultrathin and partially ionized foil. With our theoretical calculations, we demonstrate that this process is a consequence of the evolution of the carbon ion charge states in the second foil. We calculated the resulting spectral distribution separately for each ion species by solving the rate equations for electron loss and capture processes within a collisional radiative model. We determine how the efficiency of charge transfer processes can be manipulated by controlling the ionization degree of the transfer matter.

Calculations on charge state and energy loss of argon ions in partially and fully ionized carbon plasmas

The energy loss of argon ions in a target depends on their velocity and charge density. At the energies studied in this work, it depends mostly on the free and bound electrons in the target. Here the random-phase approximation is used for analyzing free electrons at any degeneracy. For the plasma-bound electrons, an interpolation between approximations for low and high energies is applied. The Brandt-Kitagawa (BK) model is employed to depict the projectile charge space distribution, and the stripping criterion of Kreussler et al. is used to determine its equilibrium charge state Q(eq). This latter criterion implies that the equilibrium charge state depends slightly on the electron density and temperature of the plasma. On the other hand, the effective charge Q(eff) is obtained as the ratio between the energy loss of the argon ion and that of the proton for the same plasma conditions. This effective charge Q(eff) is larger than the equilibrium charge state Q(eq) due to the incorporation of the BK charge distribution. Though our charge-state estimations are not exactly the same as the experimental values, our energy loss agrees quite well with the experiments. It is noticed that the energy loss in plasmas is higher than that in the same cold target of about, ∼42-62.5% and increases with carbon plasma ionization. This confirms the well-known enhanced plasma stopping. It is also observed that only a small part of this energy loss enhancement is due to an increase of the argon charge state, namely only ∼2.2 and 5.1%, for the partially and the fully ionized plasma, respectively. The other contribution is connected with a better energy transfer to the free electrons at plasma state than to the bound electrons at solid state of about, ∼38.8-57.4%, where higher values correspond to a fully ionized carbon plasma.

Predictions for the energy loss of light ions in laser-generated plasmas at low and medium velocities

The energy loss of light ions in dense plasmas is investigated with special focus on low to medium projectile energies, i.e., at velocities where the maximum of the stopping power occurs. In this region, exceptionally large theoretical uncertainties remain and no conclusive experimental data are available. We perform simulations of beam-plasma configurations well suited for an experimental test of ion energy loss in highly ionized, laser-generated carbon plasmas. The plasma parameters are extracted from two-dimensional hydrodynamic simulations, and a Monte Carlo calculation of the charge-state distribution of the projectile ion beam determines the dynamics of the ion charge state over the whole plasma profile. We show that the discrepancies in the energy loss predicted by different theoretical models are as high as 20-30%, making these theories well distinguishable in suitable experiments.

Role of charge transfer in heavy-ion-beam-plasma interactions at intermediate energies

In this paper we investigate the influence of the plasma properties on the charge state distribution of a swift heavy ion beam interacting with a plasma. The main finding is that the charge state in plasma can be lower than in cold matter. The charge state distribution is determined by the ionization and recombination rates which are balancing each other out. Both, ionization and recombination rates, as well as atomic excitation and decay rates, depend on the plasma parameters in different ways. These effects have been theoretically studied by Monte Carlo simulations on the example of an argon ion beam at an energy of 4MeV/u in a carbon plasma. This study covers a plasma parameter space ranging from ion densities from 10(18) to 10(23) cm(-3) and electron temperatures from 10 to 200 eV.

Heavy ion charge-state distribution effects on energy loss in plasmas

According to dielectric formalism, the energy loss of the heavy ion depends on its velocity and its charge density. Also, it depends on the target through its dielectric function; here the random phase approximation is used because it correctly describes fully ionized plasmas at any degeneracy. On the other hand, the Brandt-Kitagawa (BK) model is employed to depict the projectile charge space distribution, and the stripping criterion of Kreussler et al. is used to determine its mean charge state [Q]. This latter criterion implies that the mean charge state depends on the electron density and temperature of the plasma. Also, the initial charge state of the heavy ion is crucial for calculating [Q] inside the plasma. Comparing our models and estimations with experimental data, a very good agreement is found. It is noticed that the energy loss in plasmas is higher than that in the same cold gas cases, confirming the well-known enhanced plasma stopping (EPS). In this case, EPS is only due to the increase in projectile effective charge Q(eff), which is obtained as the ratio between the energy loss of each heavy ion and that of the proton in the same plasma conditions. The ratio between the effective charges in plasmas and in cold gases is higher than 1, but it is not as high as thought in the past. Finally, another significant issue is that the calculated effective charge in plasmas Q(eff) is greater than the mean charge state [Q], which is due to the incorporation of the BK charge distribution. When estimations are performed without this distribution, they do not fit well with experimental data.

Stopping power of nonideal, partially ionized plasmas

The stopping power of strongly coupled, partially ionized plasmas is investigated for charged beam particles with arbitrary velocities. Our approach is based on kinetic equations of the Boltzmann type that are suitably generalized to describe three-particle collisions. In this way, we consider elastic collisions between the beam and free plasma particles as well as the ionization and excitation of composite plasma particles by beam particle impact. Explicit expressions for both contributions are given in terms of the momentum transfer cross section that has been generalized for three-particle collisions. For fast beam particles, we obtain a generalized Bethe formula that includes correction terms due to the nonideality of the target plasma. Results are shown for hydrogen, carbon, and argon plasmas. Considerable modifications compared to the ideal behavior arise for strongly coupled plasmas. In particular, we are able to describe the Mott transition in the stopping power of dense, partially ionized plasmas.

Laser-assisted stopping power of a hot plasma for a system of correlated ions

The laser-assisted stopping power of a fully ionized plasma for the system of two correlated test charges is investigated. The general expressions for the stopping power are applied to a low-density and a low-temperature plasma in a low-energy beam-plasma experiment [J. Jacoby et al., Phys. Rev. Lett. 74, 1550 (1995)]. The effect of the interaction between the beam test charges, described by a correlation term, is to increase the stopping power of the laser-assisted plasma compared to the case where the charges are infinitely separated. However, the laser field affects the correlation between the test charges and contributes to decrease the plasma stopping power, as compared to the laser-free dicluster case.

Beam-plasma coupling effects on the stopping power of dense plasmas

The stopping power for ion beams in dense plasmas is investigated on the basis of quantum kinetic equations. Strong correlations between the beam ions and the plasma particles which occur for high ion charge numbers and strongly coupled plasmas are treated on the level of the statically screened T-matrix (binary collision) approximation. Dynamic screening effects are included using a combined scheme which considers both close collisions and collective effects. Applying this approach, the ion charge number dependence of the stopping power is determined. The result is a modification of the Z(2)(b) scaling law. In particular, the stopping power is reduced for strong beam-plasma coupling. Good agreement is found between T-matrix results and simulation data (particle-in-cell and molecular dynamics) for low beam velocities.