Influence of kinetic effects in large-scale magnetic reconnection with multi-hierarchy simulation code KAMMUY

TL;DR

The paper addresses multiscale magnetic reconnection by coupling large-scale ideal MHD with localized PIC regions in a multi-hierarchy framework named KAMMUY. It develops and validates a robust MHD–PIC coupling scheme, including interlocking quantity exchanges, PIC-to-MHD and MHD-to-PIC conversions, time integration, grid/time-step rules, and filtering, implemented on GPUs. Through energy-conservation tests, wave-propagation studies, and a shock-tube case, it demonstrates that small-scale kinetic activity remains confined to the PIC region while MHD structures propagate without distortion, and that the global reconnection rate is largely insensitive to the PIC-domain size—even when Hall fields extend over $O(10-100)\lambda_i$. The results imply that large-scale solar-flare–relevant systems can be efficiently simulated with embedded PIC regions, enabling first-principles investigation of kinetic effects in expansive plasmas. The work provides a practical pathway for applying kinetic-fluid coupling to other shock and reconnection problems and outlines key considerations for grid-ratio choices, particle loading, and interface treatment.

Abstract

Magnetic reconnection is a multiscale phenomenon where fluid- and particle-scale processes interact. The particle-in-cell (PIC) method, capable of resolving kinetic (particle-scale) physics, is extensively used to study the kinetic effects in magnetic reconnection. Meanwhile, because of the high computational cost, PIC simulations cannot capture the interaction between kinetic and fluid dynamics, which poses a major obstacle to understanding magnetic reconnection in large-scale phenomena such as solar flares. A multi-hierarchy simulation that combines Magnetohydrodynamics (MHD) and PIC provides a promising means to overcome these spatial and temporal scale gaps. We developed a multi-hierarchy simulation code KAMMUY (Kinetic And Magnetohydrodynamic MUlti-hierarchY simulation code), in which an ideal MHD simulation for a large domain and a PIC simulation for a smaller domain are solved in parallel with mutual information exchange. To validate the code, we conducted test simulations of MHD wave propagation and the shock tube problem. The results demonstrate that short-wavelength, high-frequency waves generated in the PIC region do not propagate into the MHD region, whereas MHD-scale structures propagate smoothly into the PIC region, highlighting the capability of our code for numerical studies of magnetic reconnection. By applying the KAMMUY code to magnetic reconnection while varying the PIC domain size, we find that the reconnection rate remains unchanged, regardless of the extent of the PIC region where the Hall magnetic field is present. It suggests that the spatial extension of the Hall magnetic field on the scale of $10 \sim 100 λ_i$ does not influence the reconnection rate.

Figures (20)

• Figure 1: Schematic pictures of MHD and PIC grids. The upper panel shows the physical quantities of $\rho, \bm{v}, \bm{B}, p$ in MHD grid (solid line). The lower panel shows the physical quantities of $\bm{B}, \bm{E}, \bm{j}$ and particles (orange and light-blue circles) in PIC grid (dotted line). Dotted lines are drawn in MHD grid to emphasize that PIC grid is embedded in MHD region and is smaller than MHD grid. Alt text: The $\rho, \bm{v}, \bm{B}$ and $p$ of MHD are at the cell center. The $E_z$ and $j_z$ of PIC are at the cell center. $B_y, E_x$ and $j_x$ of PIC are at the face center in $x$ direction. $B_x, E_y$ and $j_y$ of PIC are at the face center in $y$ direction. The $B_z$ of PIC is at the edge of cell.
• Figure 2: Schematic picture of multi-hierarchy simulation in space. Solid and dotted line show MHD and PIC grids and orange and light-blue circles show particles in PIC. Blue area corresponds to the purely MHD region, yellow area corresponds to the purely PIC region, and green area is the interface region. PIC has the green and yellow region and MHD has the whole region. Alt text: Schematic picture of multi-hierarchy simulation in space.
• Figure 3: Schematic picture of multi-hierarchy simulation scheme of exchanging physical quantities between MHD and PIC. The upper panel shows MHD domain; blue region corresponds to purely MHD region, green region corresponds to interface region where physical quantities of MHD and PIC are mixed, and yellow region corresponds to PIC embedded region. The lower two panels show PIC domain; boundary thick line represents MHD grid and thin line inside represents PIC grid. In this figure $8 \times 8$ PIC grids correspond to 1 MHD grid. Physical quantities of PIC are averaged and sent to MHD, and those of MHD are interpolated and sent to PIC. Alt text: Three figures are shown; one MHD domain and two PIC domains which represent the exchanges of the physical quantities between MHD and PIC.
• Figure 4: Schematic picture of multi-hierarchy simulation scheme in time. MHD and PIC are integrated with exchanging physical quantities with each other. Alt text: Schematic picture of multi-hierarchy simulation in time.
• Figure 5: Time evolution of the total energy in multi-hierarchy simulations and PIC simulation. The dotted line shows the result of multi-hierarchy simulation with 20 ppc, and the solid line shows the result with 100 ppc. Black line shows the result of PIC simulation with 100 ppc. Alt text: The horizontal axis shows the time $\omega_{pe} t$. The range in horizontal axis is from 0 to 3500. The axis shows the total energy divided by the initial total energy. The range in axis is from 0.95 to 1.05.