g4chargeit: Geant4-based kinetic Monte Carlo simulations of charging in dielectric materials

Abstract

We present g4chargeit, a kinetic Monte Carlo framework built on Geant4 for self-consistent simulation of time-dependent electrostatic charging in dielectric materials. The model explicitly incorporates stochastic particle transport and scattering processes using validated Geant4 cross-sections, while self-consistently evolving the electric potential and field. As a representative application, we simulate the charging of regolith grains under average dayside conditions on the Moon. The surface of the Moon, in addition to other airless planetary bodies, are regularly exposed to solar ultraviolet photons and solar-wind plasma, creating a radiation environment in which electrostatic interactions among regolith grains become significant. Until now, simulations of regolith charging have often relied on analytical approximations that oversimplify grain geometry and interaction mechanisms. Our Geant4-based simulations reveal charge accumulation within intergrain micro-cavities, leading to repulsive electrostatic forces consistent with experimental observations. The framework establishes a multiscale approach that links microscopic scattering events to the continuity equation of surface charge density and to the formation of macroscopic surface charge patches in complex grain geometries. Although demonstrated here for planetary regolith, the method is general and applicable to a broad range of dielectric charging problems. The code is openly available at https://github.com/kgandhi63/g4chargeit.git.

Figures (6)

• Figure 1: Self-consistent simulation framework of g4chargeit. $N$ particles are sampled and transported through the geometry for the $n$-th iteration. The particle trajectories are saved in the ROOT file (denoted as $R_i$), and deposited charges are aggregated into a master charge list (denoted as Charges), which is used to compute the electric field. The custom AdaptiveSumRadialFieldMap.cc class (dashed box) is structured as follows: a charge octree, $O_{\mathrm{charge}}$, is constructed, followed by a field octree, $O_{\mathrm{field}}$, generated using a Barnes–Hut approximation to efficiently evaluate the electric field (resulting in a scalar potential $\varphi_A$ with a corresponding field $\vec{E}_A$ for a specific octree voxel $A$). The field octree is adaptively binned if the field gradient between neighboring cells exceeds the threshold $\Delta E_{th}$. An example of the refined $O_{\mathrm{field}}$ is shown as an inset, where the density of the pre-computed electric-field vectors (arrows) scales as the field approaches the deposited charge (center of the image). The dynamical process is repeated for $n$ iterations by self-consistently updating the charge distributions and field maps.
• Figure 2: Cross-section of hexagonally packed grains (with radius of $100\mu m$) overlaid with the electric-field map (gray arrows, scaled by field magnitude) in the $xz$-plane. Representative particle trajectories are shown for (a) photons undergoing a PE event, (b) $1keV$ protons, and (c) low-energy electrons (isotropic in angle). The electric-field maps for photons (a) and SW (b,c) are shown at iterations $n=39$ and $n=17$, respectively, with a dielectric constant of $\varepsilon_r=3.9$.
• Figure 3: Face illumination of (a) regularly packed grains, (b) irregularly packed grains, and (c) a realistic grain configuration. Particle trajectories of photons incident at 45$^\circ$ are shown in green. The horizontal green lines are due to PBC in the $x$-direction, where particles re-enter the box after exiting through the sides. (d) Photon energies are sampled from the differential flux at solar minimum (Ref. farrell_dust_2023). (e) Particles from the SW plasma are sampled from the differential flux of electrons (blue) and protons (red) (Ref. liFormationLunarSurface2023). SW electrons are isotropic with an average energy of $\sim$$12.7eV$, and SW protons are incident at 45$^\circ$ angle with an average energy of $\sim$$1.2keV$.
• Figure 4: (a) $|E_x|$ plotted against the equivalent lunar time $t_{\text{M}}$ for the photon (orange) and SW (purple) cases at the point $37\mu m$ above the midpoint between the sphere centers; red point in (b) and (c). The photon results are extrapolated using the expected extension (dashed orange line, least-squares fit to Eq. \ref{['eq:charge_diff']}). Results from Ref. Zimmerman_2016 are overlaid for comparison (gray lines). (b,c) Interpolated electric-field vectors in the $xz$-plane at (b) $t_{\text{M}}\sim0.06s$ and (c) $t_{\text{M}}\sim0.61s$. The background color shows the $x$-component of the electric field $E_x$. (d,e) Electric pressure ($x$-component) at $t_{\text{M}}\sim0.61s$ for (d) SW irradiation (equivalent fluence of $\Phi\sim10^{13}m^{-2}$) and (e) photons irradiation (equivalent fluence of $\Phi\sim10^{15}m^{-2}$). An attractive force between the spheres is observed for both SW and photon irradiation (adjacent regions with opposite colors, i.e., red–blue).
• Figure 5: Simulation results for irregularly packed grains under photon irradiation at (a) $t_{\text{M}}\sim0.52s$ (corresponding fluence $\Phi\sim2.0\times10^{15}m^{-2}$) and (b) $t_{\text{M}}\sim1.56s$ ($\Phi\sim5.6\times10^{15}m^{-2}$), followed by the SW case of (c) $t_{\text{M}}\sim0.55s$ ($\Phi\sim8.3\times10^{12}m^{-2}$) and (d) $t_{\text{M}}\sim1.54s$ ($\Phi\sim2.3\times10^{13}m^{-2}$). Each panel shows the $x$-component of the electric field ($E_x$, yellow–blue colormap), the $z$-component of the electric pressure ($f_z$, seismic colormap), and the electric-field vector (black arrows) in the $xz$-plane.