Time-dependent orbital-free density functional theory for electronic stopping power: Comparison to the Mermin-Kohn-Sham theory at high temperatures

Abstract

Electronic stopping power in warm dense matter can affect energy transport and heating in astrophysical processes and internal confinement fusion. For cold condensed matter systems, stopping power can be be modeled from first-principles using real time time-dependent density functional theory (DFT). However, high temperatures (10's to 100's of eV) may be computationally prohibitive for traditional Mermin-Kohn-Sham DFT. New experimental measurements in the warm dense regime motivates the development of first-principles approaches which can reach these temperatures. We have developed a time-dependent orbital free density functional theory, which includes a novel nonadiabatic and temperature-dependent kinetic energy density functional, for the simulation of stopping power at any temperature. The approach is nonlinear with respect to the projectile perturbation, includes all ions and electrons, and does not require a priori determination of screened interaction potentials. Our results compare favorably with Kohn-Sham for temperatures in the WDM regime, especially nearing 100 eV.PACS numbers: I. INTRODUCTIONStopping of high energy ions by materials is relevant to many applications, from biomedical imaging (proton computed tomography)[1], ion therapies[2, 3], radiation protection and damage [4,5]. Fusion reactions create high energy projectiles (e.g. α-particle, proton, deuterons) that deposit energy into the dense plasma as they are stopped. Accurate modeling of plasma stopping power is thus a key component for hydrodynamic modeling of internal confinement fusion (ICF) [6][7][8][9][10][11], astrophysical [12], and other fusion processes. These processes often occur inside or traverse the warm dense matter (WDM) range of densities and temperatures. In this regime, also known as the degenerate plasma, quantum mechanical processes dominate the electronic properties, while the nuclei can be treated as classical particles, and can make calculation of electronic stopping power, and other electronic response properties such as thermal and electrical conductivity a difficult task.For slow projectile velocities (v p ), much less than the Fermi velocity, v p v F , Born-Oppenheimer molecular dynamics, where the electrons are in their instantaneous thermal equilibrium state, can be utilized to calculate the ionic stopping [13]. For high velocitiy projectiles, with keV to MeV kinetic energy, nonadiabatic energy loss from the nuclei to the electrons dominates stopping. Analytical approaches, based on either homogeneous or local electron densities and linear response to the projectile, are often used to estimate electronic stopping power [6,[14][15][16][17]. For warm dense systems these methods can be inaccurate and often require ad-hoc cut-offs, interpolations, or additional approximate projectile-plasma pseudo-interaction potential [15,16].Recently, an increased effort to directly simulate stopping power from first-principles using time-dependent density functional theory (TD-DFT), both for low temperature materials and in warm de...

Proton stopping measurements at low velocity in warm dense carbon

“…It has been shown in Ref. 30,31 that the TD-OF-DFT theory agrees with the high-velocity data of Ref. 34 , but predicts deviations of up to 20 % from classical stopping-power predictions for WDM conditions at low projectile velocities.…”

“…Thirdly, we employ an ab initio approach based on a recently developed time-dependent density functional theory (TD-DFT), including an orbital-free (TD-OF-DFT) version 30,31 and a full Kohn-Sham approach (TD-KS-DFT) utilizing a mixed basis of deterministic and stochastic orbitals 67 . It has been shown in Ref.…”

“…This leads to even larger theoretical discrepancies than in classical plasmas, in particular for low projectile velocities approaching the Bragg peak. There, temperature and degeneracy effects on the stopping power are expected to be important and significant deviations from classical theories are predicted [27][28][29][30][31] .…”

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

“…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. [31,33] For ambient conditions, direct simulation of ESP through TD-DFT, using periodic boundary conditions, has arisen as a high accuracy method for calculation of ESP [34,35]. However, for WDM its application is limited due to a combination of finite simulation-box effects and increased computational cost due to high temperatures.…”

“…However, for WDM its application is limited due to a combination of finite simulation-box effects and increased computational cost due to high temperatures. This lead us to the development of orbital-free TD-DFT methods [31,33], which proved accurate at high velocities but are insufficient for velocities near the Bragg Peak [31]. Fortunately, the development of stochastic DFT / TD-DFT (sDFT / TD-sDFT) provide a feasible alternative to orbital-free TD-DFT or analytical models, while retaining the full accuracy of Kohn-Sham (KS) DFT [36,37].…”