Radiation pattern and source size of particles in nanoplasmonic fusion

TL;DR

The paper addresses how to extract the size, duration, and space-time dynamics of nuclei emitted in laser-induced nanoplasmonic fusion by applying Hanbury Brown and Twiss (HBT) two-particle correlations to PIC-simulated emission from resonant nanorod antennas. It develops a formal emission framework using the non-thermal Cancelling Jüttner distribution and analyzes the correlation function $C(k,q)$ derived from the emission function $S(x,k)$, showing that under a sudden ignition limit the correlation reduces to $C(k,q) = 1 + \exp(-R^2 q^2)$, with finite duration contributing a $(\Delta\tau)^2$ term. A tractable single-fluid-cell model is presented to connect a Gaussian source profile to the observed correlations, and the work outlines a two-stage approach—from a single nano-rod to a macroscopic ignition region—to determine source size and anisotropy while preserving non-thermal dynamics to minimize energy loss. The results have potential practical impact for guiding non-thermal fusion strategies and experimental validation at facilities such as ELI-ALPS, by enabling extraction of spatial and temporal characteristics from proton emission patterns.

Abstract

For the angular radiation patterns of proton, deuteron or alpha emission we present a way using particle-in-cell simulation of laser induced nanoplasmonic fusion. The differential Hanbury-Brown and Twiss analysis is widely used in astrophysics and in relativistic heavy ion physics to determine the source size of emitted particles. Here, we show how this method could be adopted for inertial confinement fusion. This method aims to determine the parameters of emitted nuclei after the fusion target ignition. In addition to spatial volume, the method can detect specific space-time correlation patterns connected to the collective flow post-ignition. In the NAPLIFE project our aim is to avoid thermalization and fluidization as much as possible at each stage of the fusion process. As the original laser beam is non-thermal and not equilibrated in any way it is obvious that we can minimize energy loss if we exploit the initial available energy in a non-thermal way. The detailed dynamics of deuterium and alpha production is not aimed at and not addressed by this paper.

Figures (7)

• Figure 1: (color online) Schematic view of the calculation box (CB) and the transverse orientation of nanorod antenna (red, x-direction) relative to the two-sided laser irradiation (grey arrows, z-direction). The CB is divided into cubic cells in the PIC method. Lagrangian fluid cells of different particle species are represented by different types of marker particles. The length/thickness of nanorod antenna is resonant to the laser light frequency in the material of fusion fuel target. Conduction electrons are resonating within the nanorod antenna in orthogonal direction to the laser beam direction. The protons neighboring the nanorod antenna are attracted by the resonating electrons and moving parallel to the nanorod. I.e. in this mechanism the accelerated protons are orthogonal to the laser beam, in contrast to the usual TNSA configuration.
• Figure 2: The angular distribution calculated by an EPOCH PIC simulation, of accelerated protons along a nanorod antenna irradiated by a laser beam. The time profile of irradaition was a step function up to $t=$ 79.56 fs, from one side only. It was in the $z= 0^o$ direction with a 30mJ laser pulse, with constant intensity, $I=4\cdot 10^{17}$ W/cm$^2$, in the rest frame of the antenna. The antenna and the $\hbox{\boldmath$E$}$ field of the laser beam point in the orthogonal, $x = 90^o$ direction. The protons are emitted dominantly in the direction of the laser beam. The contour line shows the maximum energy of the emitted protons at the given angles, the scale indicates 100, 200, 300, 400 keV. The EPOCH code was run for one (85x25 nm) nanorod antenna in a calculational box (CB) having a box-size of 530 nm * 530 nm * 795 nm, with 5 nm cubic cells, with periodic boundary condition. Electrons in the rod were placed randomly with a number density of 5.9e28 electrons/m$^3$. The simulation was run for a period of 240 fs.
• Figure 3: The angular distribution, of emitted protons along a nanorod antenna irradiated from two sides in the LWFA configuration, in the $z= 0^o/180^o$ direction with a 30mJ laser pulse with constant intensity, $I=4\cdot 10^{17}$ W/cm$^2$, with a step function profile in the rest frame of the antenna. The distribution is shown one period $T_P$ after the initial transients, $t_o$, i.e. at $t_o + T_P = 11.94$ fs after the start if the irradiation. The antenna and the $\hbox{\boldmath$E$}$ field of the laser beam point int the $x = 90^o$ direction. The outermost contour (1.0 MeV/c) belongs to momentum of all protons emitted into a solid angle domain of 4$\pi$/300. The momentum of the most energetic protons is 13 keV/c. The number of proton marker particles in the EPOCH generated sample is 337058.
• Figure 4: The same as Fig. \ref{['a18']} for $t_o + 1.5 T_P = 13.26$ fs after the start if the irradiation, i.e. half period later. The direction of the motion of protons is reversed just as the electric field. The out most contour (50 MeV/c) belongs to momentum of all protons emitted into a solid angle domain of 4$\pi$/300. The momentum of the most energetic protons is 36 keV/c, more than earlier in Fig. \ref{['a18']}, but the increase of the total momentum in the domain is due to the increased number of the resonating protons.
• Figure 5: The same as Figs. \ref{['a18']} and \ref{['a20']} for $t_o + 2 T_P = 14.59$ fs after the start if the irradiation, i.e. another half period later. The direction of the motion of protons is reversed again. The out most contour (200 MeV/c) belongs to momentum of all protons emitted into the same a solid angle domain. The energy of the most energetic protons is 68 keV/c, more than before in Fig. \ref{['a20']}, but the increase of the total momentum in the domain is due to the increased number of the resonating protons. The angular spread of the distribution becomes narrower at the same time.