Proton stopping measurements at low velocity in warm dense carbon

Abstract

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 around the Bragg peak, that features the largest modeling uncertainties, remains virtually unexplored. Here, we report proton energy-loss measurements in warm dense plasma at unprecedented low projectile velocities, approaching significantly the Bragg-peak region. 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 consistent with recent first-principles simulations based on time-dependent density functional theory.

Mixed Stochastic-Deterministic Time-Dependent Density Functional Theory: Application to Stopping Power of Warm Dense Carbon

“…The low density, high proton velocity cases (0.5 g/cc v p = 4-5) was recently compared to experimental measurements and demonstrated superior agreement to standard models. [27] Here, we compare to the BRPA result with 4EPC, and the TD-OF-DFT result. We have added the 1s core electron contribution, estimated by the CBC method (also plotted), to the BRPA and TD-mDFT results.…”

“…Combining this ion-beam measurement with laser generation of WDM allows one to measure the ESP of WDM directly. [25][26][27] For velocities near the electron velocity, v e the ESP becomes sensitive to the density and temperature (ρ & T) of the system, allowing for a powerful diagnostic [26]. However, inference of ρ and/or T directly from energy loss measurements requires a predictive ESP model [28].…”

“…Often, the plasma conditions of WDM target can only be estimated from hydrody-namic calculations. [27,32] One needs an accurate atomistic and i.e. ab initio, model such as time-dependent density functional theory (TD-DFT), in order to validate these more approximate methods, or to provide an alternative method for comparison to experimental measured stopping.…”

“…A subset of these simulations were recently validated by experiment energyloss measurements. [27] In this article we will 1) briefly discuss the traditional models for ESP, 2) discuss the use of TD-DFT to calculate ESP at an atomistic level, 3) briefly review stochastic TD-DFT, 4) describe our mixed stochastic-deterministic TD-DFT method, and 5) present results for the stopping power of carbon at 0.5, 3.5, and 10 g/cc and a temperature of 10 eV, with comparison to dielectric models with bound-electron corrections and orbital-free TD-OF-DFT. Finally, we will attempt to combine atomistic calculation of electron relaxation times and Z * , from electrical conductivity calculations or electronic density of states to improve agreement between the model and atomistic TD-DFT.…”

Mixed stochastic-deterministic time-dependent density functional theory: application to stopping power of warm dense carbon

“…Measuring the loss of energy of the ion beam as it passes through a finite thickness target allows for the calculation of the target's electronic stopping power (ESP), the dominant contribution to the total stopping power for these ions. Combining this ion-beam measurement with laser generation of WDM allows one to measure the ESP of WDM directly [25][26][27]. For velocities near the electron velocity, v e the ESP becomes sensitive to the density and temperature (ρ & T) of the system, allowing for a powerful diagnostic [26].…”