Low-velocity Stopping Research Articles

Proton stopping measurements at low velocity in warm dense carbon

Ion stopping in warm dense matter is a process of fundamental importance for the understanding of the properties of dense plasmas, the realization and the interpretation of experiments involving ion-beam-heated warm dense matter samples, and for inertial confinement fusion research. The theoretical description of the ion stopping power in warm dense matter is difficult notably due to electron coupling and degeneracy, and measurements are still largely missing. In particular, the low-velocity stopping range, that features the largest modelling uncertainties, remains virtually unexplored. Here, we report proton energy-loss measurements in warm dense plasma at unprecedented low projectile velocities. Our energy-loss data, combined with a precise target characterization based on plasma-emission measurements using two independent spectroscopy diagnostics, demonstrate a significant deviation of the stopping power from classical models in this regime. In particular, we show that our results are in closest agreement with recent first-principles simulations based on time-dependent density functional theory.

Anomalous Stopping and Charge Transfer in Proton-Irradiated Graphene.

We use first-principles calculations to uncover and explain a new type of anomalous low-velocity stopping effect in proton-irradiated graphene. We attribute a shoulder feature that occurs exclusively for channeling protons to enhanced electron capture from σ- and π-orbitals. Our analysis of electron emission indicates that backward emission is more sensitive to proton trajectory than forward emission and could thus produce higher contrast images in ion microscopy. For slow protons, we observe a steep drop in emission, consistent with predictions from analytical models.

Progress in understanding heavy-ion stopping

We report some highlights of our work with heavy-ion stopping in the energy range where Bethe stopping theory breaks down. Main tools are our binary stopping theory (PASS code), the reciprocity principle, and Paul’s data base. Comparisons are made between PASS and three alternative theoretical schemes (CasP, HISTOP and SLPA). In addition to equilibrium stopping we discuss frozen-charge stopping, deviations from linear velocity dependence below the Bragg peak, application of the reciprocity principle in low-velocity stopping, modeling of equilibrium charges, and the significance of the so-called effective charge.

Number-conserving linear response study of low-velocity ion stopping in a collisional magnetized classical plasma

The low-velocity stopping power of ions in a magnetized collisional plasma is studied through the linear response theory. The collisions are taken into account through a number-conserving relaxation time approximation. One of the major objectives of this study is to compare and contrast our theoretical results with those obtained through a diffusion coefficient formulation based on Dufty-Berkovsky relation.

Number-conserving linear-response study of low-velocity ion stopping in a collisional magnetized classical plasma

The results of a theoretical investigation of the low-velocity stopping power of ions in a magnetized collisional and classical plasma are reported. The stopping power for an ion is calculated through the linear-response (LR) theory. The collisions, which lead to a damping of the excitations in the plasma, are taken into account through a number-conserving relaxation time approximation in the LR function. In order to highlight the effects of collisions and magnetic field, we present a comparison of our analytical and numerical results obtained for nonzero damping or magnetic field with those for vanishing damping or magnetic field. It is shown that the collisions remove the anomalous friction obtained previously [Nersisyan et al., Phys. Rev. E 61, 7022 (2000)] for the collisionless magnetized plasmas at low ion velocities. One of the major objectives of this paper is to compare and to contrast our theoretical results with those obtained through a diffusion coefficient formulation based on the Dufty-Berkovsky relation evaluated for a magnetized one-component plasma modeled with target ions and electrons.

On plasma coupling and turbulence effects in low velocity stopping

The problem of stopping power (SP) for projectile ions is analysed in terms of the dielectric function and effective collision frequency for moderately dense and strongly coupled plasmas (SCP). We consider several issues regarding the calculation of stopping power for correlated ensembles of particles and oscillators. In particular, effects of group (few particle) modes, transition from positive to negative dispersion and excitation of collective modes up to suprathermal level at plasma targets are addressed. Linear SP of dense suprathermal (nonlinear) plasma targets at different levels of target plasma turbulence is estimated. The force of suprathermal plasma oscillations on the projectile ions is mostly in the nature of increased frictional drag. The results obtained show the possibility of increasing low velocity stopping (up to 'turbulent' values) in comparison with losses in equilibrium dense plasma targets. Experimental conditions to create specific turbulent targets as well as some connection between stopping phenomena and SCP transport properties are discussed briefly.

Nuclear stopping in transmission experiments

Energy-loss spectra, mean and peak energy loss, and straggling due to elastic nuclear scattering have been studied theoretically as a function of target thickness and deflection angle of an initially monochromatic and well-collimated ion beam. The goal of this work has been to provide a generally valid scheme for nuclear-stopping corrections, allowing to determine electronic-stopping forces from energy-loss spectra measured in transmission geometry. Calculations have been based on the generalized Bothe–Landau theory of energy loss and multiple scattering. Our peak energy losses at zero emergence angle show close (∼10%) agreement with predictions of Fastrup et al. on the basis of the Bohr–Williams theory. However, predicted mean and peak energy losses are found to more sensitively depend on the underlying interatomic potential than unrestricted, i.e. angle-integrated mean or peak energy losses. Both elastic energy loss and multiple scattering are known to obey scaling laws involving only two combinations of the pertinent variables and atomic parameters. The dependence on deflection angle and foil thickness of mean and peak energy loss obeys a simple combination of these scaling laws. Comments are made on potential errors due to uncertainties in the nuclear-stopping correction applied in the literature with specific reference to central papers in low-velocity stopping.

Stopping power of low-velocity ions in solids: inhomogeneous electron gas model

A self-consistent model for the calculation of electron scattering and stopping coefficients of slow ions in a non-homogeneous electron gas is developed. The model permits to account for realistic electron density profiles in the evaluation of the average energy loss of slow ions in solids. The screening parameter in the potential and the scattering phase shifts are calculated in a non-perturbative way, as a function of the local electron-gas density. We show that the inhomogeneity effect can modify the Z 1 dependence of the low-velocity stopping powers. The differences between previous calculations and experimental stopping-power data, for channeled and random incidence trajectories of ions in solids, are well explained by this approach.

Nonlinear hydrodynamic theory of electronic stopping power

We have formulated a fully nonlinear hydrodynamic theory of the electronic stopping power of charged particles in matter. In the zero velocity limit, our theory reduces to a Thomas-Fermi-Dirac-von Weiszäcker description of the electronic screening around an external point charge. With increasing velocity, the dynamic screening charge is obtained from a numerical solution of the hydrodynamic equations. We also introduce a fluid viscosity which allows one to simulate the single-particle excitations responsible for the low velocity stopping power. A comparison of our results for protons and antiprotons with linear response theory shows that nonlinearities in the screening are important for all velocities up to the stopping power maximum. In addition, comparison with earlier nonlinear quantum-mechanical calculations at low velocities shows that the hydrodynamic theory provides a realistic and accurate description of the stopping power phenomenon.

Z 1 oscillations in slow channeled ion stopping power

The oscillations of the stopping power as a function of the projectile ion nuclear charge Z t are studied in detail for the case of channeled ions at low velocities. A realistic density profile for the channel is used together with an electron gas model to calculate the stopping power within a local density approximation. Nonlinear calculations using density functional theory allow us to obtain the exact transport cross section to all orders in Z 1, using the phase shifts at the Fermi level for scattering of the valence electrons, that determines the low velocity stopping power. Comparison with some experiments is carried out.

On the slowing down of charged particles in an electron gas: an extension to the Fermi-Teller formula

An expression is obtained for the low-velocity stopping power of an electron plasma in thermal equilibrium, which applies for all degrees of plasma degeneracy. In the limit of high densities the result agrees with the Fermi-Teller approximation for a cold plasma, and with a previous approximation of Skupsky (1977) for all degeneracies. It gives better agreement with the Lindhard-Winther result (1964) at lower (metallic) densities for cold plasmas, and it also agrees with a previous result of Arista and Brandt (1981) in the opposite limit of dilute nondegenerate plasmas.

Modern problems of low-velocity stopping powers

Low velocity stopping powers pertain to regimes in electron plasmas of all degeneracies where the projectile velocities are less than the mean electron velocities in the medium. This field is now in a new phase of rapid development. Solutions to three basic problems are presented here. (1) The material dependence of stopping powers is traced to variations of the mean valence-electron densities in the periodic system. (2) The validity of effective charge theory is demonstrated in linear-response approximation. Effective charge is found to increase, for a given ionic charge, with the atomic number of the projectile. This theory permits distinct predictions that agree with experiment. (3) Extensions to hot plasmas of interest in fusion suggest the possibility of measuring the electron temperature of plasmas under the working conditions of controlled thermonuclear reactors by ion-beam analysis.

Material dependence of low-velocity stopping powers

Excitations of valence electrons determine the electronic stopping power of solids for atomic projectiles moving with velocities ${v}_{1}$ so that ${v}_{1}\ensuremath{\lesssim}{v}_{F}$, where ${v}_{F}$ is the Fermi velocity of the valence electron gas. Current data vary among elements according to their position in the periodic system in agreement with new theoretical developments. A comprehensive description emerges that permits predictions of the stopping power of solids and plasmas for low-velocity ions.

Low-velocity projectile- z3 effect on composite target - mean excitation energies derived from stopping power measurements

Previous Bethe-Bloch formula fits to several composite target stopping powers have indicated deviations from Bragg's additivity rule in derived mean excitation energies. Inclusion of low-velocity stopping power dependence on the projectile- z 3 alters these results in that the experiment-based mean excitation energies are considerably increased.