Energy loss and charge transfer of argon in a laser-generated carbon plasma

Deceleration of fast ion rarefied beam due to Cherenkov interaction with ion-acoustic waves

The deceleration of a low-density beam of ions in plasma with developed ion-acoustic turbulence arising in strong electric field is described. The time and length of beam deceleration along and across the anisotropy axis of the wave number distribution of ion-acoustic waves are found. It is shown to what extent an increase in the strength of the electric field that generates turbulence is accompanied by a decrease in the time and length of braking. As the beam propagates along the anisotropy axis, its velocity decreases to approximately the velocity of ion sound, and the direction of propagation does not change. When the beam is decelerated with an initial velocity across the anisotropy axis, a velocity component appears along the anisotropy axis during deceleration, which results in the beam deflection from the initial direction. In this case, the modulus of the beam velocity at the end of deceleration is close to the ion sound velocity.

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.

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.

Charged particle interaction and energy dissipation in plasma is fundamentally interesting. Here the authors study proton stopping in laser-produced plasma for the moderate to strong coupling with electrons.

Correct calculation of nitrogen charge state passing through highly ionized carbon plasmas

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.

Molecular dynamics investigation of the stopping power of warm dense hydrogen for electrons

A variety of theoretical models have been proposed to calculate the stopping power of charged particles in matter, which is a fundamental issue in many fields. However, the approximation adopted in these theories will be challenged under warm dense matter conditions. Molecular dynamics (MD) simulation is a good way to validate the effectiveness of these models. We investigate the stopping power of warm dense hydrogen for electrons with projectile energies ranging from 400-10000 eV by means of an electron force field (eFF) method, which can effectively avoid the Coulomb catastrophe in conventional MD calculations. It is found that the stopping power of warm dense hydrogen decreases with increasing temperature of the sample at those high projectile velocities. This phenomenon could be explained by the effect of electronic structure dominated by bound electrons, which is further explicated by a modified random phase approximation (RPA) model based on local density approximation proper to inhomogeneous media. Most of the models extensively accepted by the plasma community, e.g., Landau-Spitzer model, Brown-Preston-Singleton model and RPA model, cannot well address the effect caused by bound electrons so that their predictions of stopping power contradict our result. Therefore, the eFF simulations of this paper reveals the important role played by the bound electrons on stopping power in warm dense plasmas.

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.

Experimental evidence for the enhanced and reduced stopping regimes for protons propagating through hot plasmas

Our understanding of the dynamics of ion collisional energy loss in a plasma is still not complete, in part due to the difficulty and lack of high-quality experimental measurements. These measurements are crucial to benchmark existing models. Here, we show that such a measurement is possible using high-flux proton beams accelerated by high intensity short pulse lasers, where there is a high number of particles in a picosecond pulse, which is ideal for measurements in quickly expanding plasmas. By reducing the energy bandwidth of the protons using a passive selector, we have made proton stopping measurements in partially ionized Argon and fully ionized Hydrogen plasmas with electron temperatures of hundreds of eV and densities in the range 1020-1021 cm-3. In the first case, we have observed, consistently with previous reports, enhanced stopping of protons when compared to stopping power in non-ionized gas. In the second case, we have observed for the first time the regime of reduced stopping, which is theoretically predicted in such hot and fully ionized plasma. The versatility of these tunable short-pulse laser based ion sources, where the ion type and energy can be changed at will, could open up the possibility for a variety of ion stopping power measurements in plasmas so long as they are well characterized in terms of temperature and density. In turn, these measurements will allow tests of the validity of existing theoretical models.

Energy transfer dynamics in strongly inhomogeneous hot-dense-matter systems

Direct measurements of energy transfer across steep density and temperature gradients in a hot-dense-matter system are presented. Hot-dense-plasma conditions were generated by high-intensity laser irradiation of a thin-foil target containing a buried metal layer. Energy transfer to the layer was measured using picosecond time-resolved x-ray emission spectroscopy. The data show two x-ray flashes in time. Fully explicit, coupled particle-in-cell and collisional-radiative atomic kinetics model predictions reproduce these observations, connecting the two x-ray flashes with staged radial energy transfer within the target.

CVD diamond detector with interdigitated electrode pattern for time-of-flight energy-loss measurements of low-energy ion bunches

Ion stopping experiments in plasma for beam energies of few hundred keV per nucleon are of great interest to benchmark the stopping-power models in the context of inertial confinement fusion and high-energy-density physics research. For this purpose, a specific ion detector on chemical-vapor-deposition diamond basis has been developed for precise time-of-flight measurements of the ion energy loss. The electrode structure is interdigitated for maximizing its sensitivity to low-energy ions, and it has a finger width of 100 μm and a spacing of 500 μm. A short single α-particle response is obtained, with signals as narrow as 700 ps at full width at half maximum. The detector has been tested with α-particle bunches at a 500 keV per nucleon energy, showing an excellent time-of-flight resolution down to 20 ps. In this way, beam energy resolutions from 0.4 keV to a few keV have been obtained in an experimental configuration using a 100 μg/cm² thick carbon foil as an energy-loss target and a 2 m time-of-flight distance. This allows a highly precise beam energy measurement of δE/E ≈ 0.04%-0.2% and a resolution on the energy loss of 0.6%-2.5% for a fine testing of stopping-power models.

Temperature measurement of hohlraum radiation for energy loss experiments in indirectly laser heated carbon plasma

For ion energy loss measurements in plasmas with near solid densities, an indirect laser heating scheme for carbon foils has been developed at GSI Helmholtzzentrum für Schwerionenforschung GmbH (Darmstadt, Germany). To achieve an electron density of 10^{22}cm^{3} and an electron temperature of 10-30eV, two carbon foils with an areal density of 100μg/cm^{2} heated in a double-hohlraum configuration have been chosen. In this paper we present the results of temperature measurements of both primary and secondary hohlraums for two different hohlraum designs. They were heated by the PHELIX laser with a wavelength of 527nm and an energy of 150J in 1.5ns. For this purpose the temperature has been investigated by an x-ray streak camera with a transmission grating as the dispersive element.

Experimental discrimination of ion stopping models near the Bragg peak in highly ionized matter

The energy deposition of ions in dense plasmas is a key process in inertial confinement fusion that determines the α-particle heating expected to trigger a burn wave in the hydrogen pellet and resulting in high thermonuclear gain. However, measurements of ion stopping in plasmas are scarce and mostly restricted to high ion velocities where theory agrees with the data. Here, we report experimental data at low projectile velocities near the Bragg peak, where the stopping force reaches its maximum. This parameter range features the largest theoretical uncertainties and conclusive data are missing until today. The precision of our measurements, combined with a reliable knowledge of the plasma parameters, allows to disprove several standard models for the stopping power for beam velocities typically encountered in inertial fusion. On the other hand, our data support theories that include a detailed treatment of strong ion-electron collisions.

The energy loss of ions in plasma is a challenging issue in inertial confinement fusion and many theoretical models exist on ion-stopping power. Here, the authors use laser-generated plasma probed by accelerator-produced ions in experiments to discriminate various ion stopping models near the Bragg peak.

Dynamic properties of the energy loss of multi-MeV charged particles traveling in two-component warm dense plasmas

The energy loss of multi-MeV charged particles moving in two-component warm dense plasmas (WDPs) is studied theoretically beyond the random-phase approximation. The short-range correlations between particles are taken into account via dynamic local field corrections (DLFC) in a Mermin dielectric function for two-component plasmas. The mean ionization states are obtained by employing the detailed configuration accounting model. The Yukawa-type effective potential is used to derive the DLFC. Numerically, the DLFC are obtained via self-consistent iterative operations. We find that the DLFC are significant around the maximum of the stopping power. Furthermore, by using the two-component extended Mermin dielectric function model including the DLFC, the energy loss of a proton with an initial energy of ∼15 MeV passing through a WDP of beryllium with an electronic density around the solid value n_{e}≈3×10^{23}cm^{-3} and with temperature around ∼40 eV is estimated numerically. The numerical result is reasonably consistent with the experimental observations [A. B. Zylsta et al., Phys. Rev. Lett. 111, 215002 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.215002]. Our results show that the partial ionization and the dynamic properties should be of importance for the stopping of charged particles moving in the WDP.

Nuclear-plus-interference-scattering effect on the energy deposition of multi-MeV protons in a dense Be plasma

The nuclear plus interference scattering (NIS) effect on the stopping power of hot dense beryllium (Be) plasma for multi-MeV protons is theoretically investigated by using the generalized Brown-Preston-Singleton (BPS) model, in which a NIS term is taken into account. The analytical formula of the NIS term is detailedly derived. By using this formula, the density and temperature dependence of the NIS effect is numerically studied, and the results show that the NIS effect becomes more and more important with increasing the plasma temperature or density. Different from the cases of protons traveling through the deuterium-tritium plasmas, for a Be plasma, a prominent oscillation valley structure is observed in the NIS term when the proton's energy is close to E_{p}=7MeV. Furthermore, the penetration distance is remarkably reduced when the NIS term is considered.

Thermal Density Functional Theory: Time-Dependent Linear Response and Approximate Functionals from the Fluctuation-Dissipation Theorem

The van Leeuwen proof of linear-response time-dependent density functional theory (TDDFT) is generalized to thermal ensembles. This allows generalization to finite temperatures of the Gross-Kohn relation, the exchange-correlation kernel of TDDFT, and fluctuation dissipation theorem for DFT. This produces a natural method for generating new thermal exchange-correlation approximations.

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.

Measurement of charged-particle stopping in warm dense plasma

We measured the stopping of energetic protons in an isochorically heated solid-density Be plasma with an electron temperature of ∼32  eV, corresponding to moderately coupled [(e^{2}/a)/(k_{B}T_{e}+E_{F})∼0.3] and moderately degenerate [k_{B}T_{e}/E_{F}∼2] "warm-dense matter" (WDM) conditions. We present the first high-accuracy measurements of charged-particle energy loss through dense plasma, which shows an increased loss relative to cold matter, consistent with a reduced mean ionization potential. The data agree with stopping models based on an ad hoc treatment of free and bound electrons, as well as the average-atom local-density approximation; this work is the first test of these theories in WDM plasma.

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.

A spectrometer on chemical vapour deposition-diamond basis for the measurement of the charge-state distribution of heavy ions in a laser-generated plasma

This article reports on the development and the first applications of a new spectrometer which enables the precise and time-resolved measurement of both the energy loss and the charge-state distribution of ion beams with 10 < Z < 30 at energies of 4-8 MeV/u after their interaction with a laser-generated plasma. The spectrometer is based on five 20 × 7 mm(2) large and 20 μm thick polycrystalline diamond samples produced via the Chemical Vapour Deposition (CVD) process and was designed with the help of ion-optical simulations. First experiments with the spectrometer were successfully carried out at GSI using (48)Ca ions at an energy of 4.8 MeV/u interacting with a carbon plasma generated by the laser irradiation of a thin foil target. Owing to the high rate capability and the short response time of the spectrometer, pulsed ion beams with 10(3)-10(4) ions per bunch at a bunch frequency of 108 MHz could be detected. The temporal evolution of the five main charge states of the calcium ion beams as well as the corresponding energy loss values could be measured simultaneously. Due to the outstanding properties of diamond as a particle detector, a beam energy resolution ΔEE ≈ 0.1% could be reached using the presented experimental method, while a precision of 10% in the energy loss and charge-state distribution data was obtained.