A unified self-consistent model for calculating ion stopping power in ICF plasma

Abstract

A new unified self-consistent ion stopping power model for use in ion-driven inertial confinement fusion (ICF) target design has been developed. This model includes sophisticated treatments for electron density distribution of an atom in plasmas and a full random phase approximation stopping function that extrapolates the zero temperature Lindhard stopping function to arbitrary temperatures. It is shown that this model provides accurate ion stopping power for cold materials, including both low-Z and high-Z elements. For finite temperature plasmas, the model accounts for the stopping effects due to electrons in ground states, excited states, resonance states, and continuum states in a self-consistent manner. There is no separation treatment for “bound” and “free” electrons. Hence, the model enables the calculations of ion stopping power to be made within a single model for a wide range of beam and target conditions relevant to ICF studies.

Partial ionization in dense plasmas: Comparisons among average-atom density functional models

“…With regard to our MIS definition (22) for TF models, we see by the negative sign of u xc (n, T ) at all rvalues that it adds to the nuclear attraction; thus, the fraction of bound electrons is increased, leading to the result Z * T F xc < Z * T F , obtained by substituting (23) into (22). This conclusion is consistent with MIS calculations reported in Ref.…”

“…From then on, we need not deal with the bound electrons, and the electron density n e (r) now refers only to the free-electron density, with average densities satisfying n e = Zn i . Thus, the use of the MIS simplifies calculations of equilibrium properties as well as dynamical, non-equilibrium properties such as stopping of fast charges [5,22], temperature relaxation [23,24], or ion microfield fluctuations [25,26]. The reason that such constructions are needed is simply that "all-electron" calculations are extremely costly in the context of time-dependent DFT [27,28]) and other relevant methods.…”

Self-Consistent Simulation of Transport and Energy Deposition of Intense Laser-Accelerated Proton Beams in Solid-Density Matter

“…Calculations and measurements of proton energy deposition in specialized ICF targets (hot dense plasmas), where collisional drag dominates, have also been well documented [15][16][17][18][19]. However, due to the uniquely high intensity of a laser-accelerated proton beam, its interaction with soliddensity matter is still not well understood because the thermodynamic state (charge, density and temperature distributions) of the matter significantly changes, and collective beam behaviors become important.…”

“…For f bound , we use the high-velocity Bethe-Bloch formula [13] with mean ionization potential and shell corrections using the experimental fitting method [25]. For f free , both binary collisions and plasma oscillation excitations are considered using the homogeneous semiclassical Chandrasekhar approximation [15,19].…”

Heavy Ion Beam Illumination Uniformity in Heavy Ion Beam Inertial Confinement Fusion

“…In the middle beam energy region, we calculate the bound stopping power from the Bethe equation with the shell correction (11) . At low beam energies, the stopping power theory is mostly evaluated by the Thomas-Fermi model of the atom (11) (12) (20) . Therefore we use the LSS equation at the low beam energy domain to calculate the bound electron stopping power (11) .…”