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In the present work, we reanalyze the energy loss experimental data from Cayzac et al. [Nat. Commun. 8, 15693 (2017)10.1038/ncomms15693] using our successful ion charge state theoretical model. We predict lower nitrogen charge values, from 3.5+ to 5.0+, than the ones calculated by Cayzac et al., fitting better to their data. For energy loss estimations, we use the same stopping model, so our predictions agree better with the experimental data only due to our charge state model. Different projectile electron loss and capture processes are taken into account to estimate the projectile charge state. The projectile electron loss, or ionization, with plasma ions and free electrons are considered. On the other hand, the projectile electron capture, or recombination, with plasma free or bound electrons are also considered. The projectile ionization with plasma ions is shown as the main factor that modifies the mean charge of the projectile. Here, the new Kaganovich fitting formula for this projectile ionization is used because it seems to be more accurate than Gryzinsky's fitting in the low energy range. Our charge state model fits better with experimental data than any other model in the bibliography. Thus, it should be considered in any charge state and any energy loss estimation to obtain reliable results in future work.

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.

A novel method to determine the total hydrogen density and, accordingly, a precise plasma temperature in a lowly ionized hydrogen plasma is described. The key to the method is to analyze the energy loss of swift heavy ions interacting with the respective bound and free electrons of the plasma. A slowly developing and lowly ionized hydrogen theta-pinch plasma is prepared. A Boltzmann plot of the hydrogen Balmer series and the Stark broadening of the H_{β} line preliminarily defines the plasma with a free electron density of (1.9±0.1)×10^{16}  cm^{-3} and a free electron temperature of 0.8-1.3 eV. The temperature uncertainty results in a wide hydrogen density, ranging from 2.3×10^{16} to 7.8×10^{18}  cm^{-3}. A 108 MHz pulsed beam of ^{48}Ca^{10+} with a velocity of 3.652  MeV/u is used as a probe to measure the total energy loss of the beam ions. Subtracting the calculated energy loss due to free electrons, the energy loss due to bound electrons is obtained, which linearly depends on the bound electron density. The total hydrogen density is thus determined as (1.9±0.7)×10^{17}  cm^{-3}, and the free electron temperature can be precisely derived as 1.01±0.04  eV. This method should prove useful in many studies, e.g., inertial confinement fusion or warm dense matter.

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.

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.

In this work, proton and deuteron stopping due to free and bound electrons in partially ionized plasma targets is evaluated. The stopping of target free electrons is calculated using the dielectric formalism, well described in our previous works. In the case of target bound electrons, a short expression to calculate their contribution to the stopping is used, where mean excitation energies are obtained by means of the Hartree-Fock method. Experiments with different kinds of plasmas are analyzed. For LiH plasma, estimated plasma stopping fits experimental data very well, within the error bars, recognizing the well-known enhanced plasma stopping. In the case of CH_{2} plasma, we obtain, from estimated ionization, that total stopping power increases when target electron density does. Our estimations are very similar to experimental data which show the same behavior with target free and bound electron density. Finally, in Al plasma, we compare directly our calculations with experimental data finding a very close agreement, where both stoppings have the same dependence on target ionicity. All these comparisons verify our theoretical model which estimates the proton or deuteron energy loss in partially ionized plasmas.

In this work, we present a dielectric function including the three conservation laws (density, momentum and energy) when we take into account electron-electron collisions in a plasma at any degeneracy. This full conserving dielectric function (FCDF) reproduces the random phase approximation (RPA) and Mermin ones, which confirms this outcome. The FCDF is applied to the determination of the proton stopping power. Differences among diverse dielectric functions in the proton stopping calculation are minimal if the plasma electron collision frequency is not high enough. These discrepancies can rise up to 2% between RPA values and the FCDF ones, and to 8% between the Mermin ones and FCDF ones. The similarity between RPA and FCDF results is not surprising, as all conservation laws are also considered in RPA dielectric function. Even for plasmas with low collision frequencies, those discrepancies follow the same behavior as for plasmas with higher frequencies. Then, discrepancies do not depend on the plasma degeneracy but essentially do on the value of the plasma collision frequency.

Random phase approximation (RPA) has become one of the most used methods to describe the energy loss of charged particles in plasmas. The RPA is usually valid for high-velocity projectiles and in the weak coupling limit of the electron gas. However, for partially coupled plasmas RPA is not sufficient and the electronic coupling must be taken into account. This coupling can be considered through local field corrections. In this work, we have constructed a dynamical local field correction (DLFC) function from Mermin dielectric function. This DLFC function has the advantage to describe plasmas at any degeneracy. Mermin DLFC function is compared with other DLFC functions from the literature in the energy loss calculation. We see important differences between them; they are significant at low velocities and very relevant around the maximum, almost 30%.

The purpose of the present paper is to describe the effects of electron-electron collisions on the stopping power of plasmas of any degeneracy. Plasma targets are considered fully ionized so electronic stopping is only due to the free electrons. We focus our analysis on plasmas which electronic density is around solid values n(e) approximately = 10(23) cm(-3) and which temperature is around T approximately = 10 eV ; these plasmas are in the limit of weakly coupled plasmas. This type of plasma has not been studied extensively though it is very important for inertial confinement fusion. The electronic stopping is obtained from an exact quantum mechanical evaluation, which takes into account the degeneracy of the target plasma, and later it is compared with common classical and degenerate approximations. Differences are around 30% in some cases which can produce bigger mistakes in further energy deposition and projectile range studies. Then we consider electron-electron collisions in the exact quantum mechanical electronic stopping calculation. Now the maximum stopping occurs at velocities smaller than for the calculations without considering collisions for all kinds of plasmas analyzed. The energy loss enhances for velocities smaller than the velocity at maximum while decreases for higher velocities. Latter effects are magnified with increasing collision frequency. Differences with the same results for the case of not taking into account collisions are around 20% in the analyzed cases.

The objective of the present work is to examined the effects of plasma target electron-electron collisions on H2 + protons traversing it. Specifically, the target is deuterium in a plasma state with temperature Te=10 eV and density n=10(23) cm(-3), and proton velocities are vp=vth, vp=2vth, and vp=3vth, where vth is the electron thermal velocity of the target plasma. Proton interactions with plasma electrons are treated by means of the dielectric formalism. The interactions among close protons through plasma electronic medium are called vicinage forces. It is checked that these forces always screen the Coulomb explosions of the two fragmented protons from the same H2 + ion decreasing their relative distance. They also align the interproton vector along the motion direction, and increase the energy loss of the two protons at early dwell times while for longer times the energy loss tends to the value of two isolated protons. Nevertheless, vicinage forces and effects are modified by the target electron collisions. These collisions enhance the calculated self-stopping and vicinage forces over the collisionless results. Regarding proton correlated motion, when these collisions are included, the interproton vector along the motion direction overaligns at slower proton velocities (vp=vth) and misaligns for faster ones (vp=2vth, vp=3vth). They also contribute to a great extend to increase the energy loss of the fragmented H2 + ion. This later effect is more significant in reducing projectile velocity.

Fast ignition of an inertial confinement fusion target by an energetic proton beam is here re-examined. We put special emphasis on the role of the transverse dispersion of the beam induced during its travel between the proton source and the compressed deuterium-tritium (DT) fuel. The theoretical model and the computer code used in our calculations are presented. Different beam initial energy distributions are analyzed. We found that the beam exhibits small collective effects while multiple scattering collisions provide a substantial transverse dispersion of the beam. Therefore, the nuclear dispersion imposes severe restrictions on the schemes for fast ignitor even considering an ideal monoenergetic and noncorrelated proton beam.