Large-scale kinetic simulations of colliding plasmas within a hohlraum of indirect-drive inertial confinement fusion

The National Ignition Facility has recently achieved successful burning plasma and ignition using the inertial confinement fusion (ICF) approach. However, there are still many fundamental physics phenomena that are not well understood, including the kinetic processes in the hohlraum. Shan et al. [Phys. Rev. Lett. 120, 195001 (2018)] utilized the energy spectra of neutrons to investigate the kinetic colliding plasma in a hohlraum of indirect drive ICF. However, due to the typical large spatial-temporal scales, this experiment could not be well simulated by using available codes at that time. Utilizing our advanced high-order implicit PIC code, LAPINS, we were able to successfully reproduce the experiment on a large scale of both spatial and temporal dimensions, in which the original computational scale was increased by approximately seven to eight orders of magnitude. Not only is the validity of the explanation of the experiment confirmed by our simulations, i.e., the abnormally large width of neutron spectra comes from beam-target nuclear fusions, but also a different physical insight into the source of energetic deuterium ions is provided. The acceleration of deuterium ions can be categorized into two components: one is propelled by a sheath electric field created by the charge separation at the onset, while the other is a result of the reflection of the potential of the shock wave. The robustness of the acceleration mechanism is analyzed with varying initial conditions, e.g., temperatures, drifting velocity, and ion components. This paper might serve as a reference for benchmark simulations of upcoming simulation codes and may be relevant for future research on mixtures and entropy increments at plasma interfaces.

Figure 1

(a) Schematic diagram of the colliding plasmas within a hohlraum. It illustrates various phenomena such as collisional interaction, shock formation, collisionless ion reflection, and nuclear reactions. (b) The simulation setup. An absorbing layer with a high density and a low temperature is only used for measuring the neutron energy spectra and is removed when investigating the properties of the shock wave in other simulation cases.

Figure 2

(a)–(c) Temporal evolution of the density profiles of electrons, deuterium ions (${\mathrm{D}}^{+}$), and gold ions (${\mathrm{Au}}^{50+}$), respectively. The black dashed line depicts the trajectory of the shock front, with a velocity of $V_{\text{sh}}=662\mathrm{km}/\mathrm{s}$, while the dotted line represents the initial trajectory of reflected ions with double the velocity, $2V_{\text{sh}}$. (d)–(f) Phase-space distributions of gold ions and deuterium ions at different times. The white-black color map and colorful color map are used to represent the phase density of gold ions and deuterium ions, respectively.

Figure 3

The temporal evolution of the energy spectra of deuterium ions. The total spatial energy spectra are presented in (a), while the time-integrated energy spectra obtained at the location of $z=1200\mu \mathrm{m}$ are displayed in (b).

Figure 4

(a) Top-view schematic diagram of the setup of a neutron spectrometer in a hohlraum experiment. (b) Comparison of the neutron spectra obtained in the simulation with that of the experimental data. The solid lines of different colors are the simulated data over different electron temperatures $T_{e1}$, fitted with Gaussian profiles. The experimental data presented by Shan et al. [14] is depicted as light blue circles. (c) Numerical results obtained from Eq. (4) for various incident energies of deuterium ions, denoted as $E_{\text{D}}$.

Figure 5

(a)–(c) Phase-space distributions for gold ions and deuterium ions concerning electron temperature $T_{e1}$ of the gold plasma. The white-black color map and colorful color map represent the phase density of gold ions and deuterium ions, respectively. (d) Comparison of Mach numbers obtained from simulations (represented by blue crosses) and theoretical calculation results from Eqs. (5) and (6) (represented by blue and red solid lines).

Figure 6

(a)–(d) Phase-space distributions of gold ions and deuterium ions at different times with an initial velocity of $450\mathrm{km}/\mathrm{s}$ of the gold plasma. The white-black color map and colorful color map are used to represent the phase density of gold ions and deuterium ions, respectively.

Figure 7

(a)–(d) Phase-space distributions for carbon ions (${\mathrm{C}}^{6+}$) and deuterium ions (${\mathrm{D}}^{+}$) with different mixing ratios and the same electron density at the time of 333 ps. The mixing ratios are 1:1, 1:2, 1:3, and 1:4, respectively. The blue-orange color map and red-yellow color map are used to represent the phase density of deuterium ions and carbon ions, respectively.