MD versus PIC-FEM

Both Molecular Dynamics (MD) with a Lennard-Jones (LJ) potential and the Particle-in-Cell (PIC) method with a Finite Element Method (FEM) mesh are computational approaches for modeling plasma, but they operate on vastly different scales and principles, making them suitable for distinct aspects of an H-mode fusion plasma in a stellarator-tokamak hybrid. MD, an atomistic, first-principles technique using the LJ potential (designed for neutral, non-bonded atoms, and a crude approximation for plasma), models the true, individual motion and short-range interactions of plasma ions and electrons. This method inherently captures kinetic and collisional effects with high fidelity, though the LJ potential is a significant simplification for the long-range Coulomb and magnetic forces present in a fusion plasma. Due to its need to resolve the Debye length and plasma frequency for millions of particles, MD is computationally intractable for the macroscopic scales of the entire H-mode core plasma, which spans meters and lasts for seconds. Instead, MD is typically restricted to studying nanoscale, short-time phenomena, such as plasma-material interactions at the divertor boundary or detailed studies of turbulent energy dissipation at very small scales, where the magnetic shaping is only an indirect boundary condition.

In contrast, the PIC-FEM method is a hybrid, macro-kinetic approach designed specifically for the physics of magnetized, large-scale plasmas. PIC represents the plasma as a collection of "macro-particles" (super-particles), each representing thousands of actual plasma ions or electrons. These particles move according to the Lorentz force and the self-consistent E and B fields. The genius of the method lies in decoupling the particle motion from the field computation; the charge and current densities from the macro-particles are interpolated onto a spatial grid (the FEM mesh), where Maxwell's equations are solved using the FEM to find the electromagnetic fields. FEM is particularly advantageous here for its ability to handle the complex, arbitrary geometries and boundary conditions—including the H-mode pedestal and the active, non-axisymmetric magnetic shaping of the stellarator-tokamak hybrid walls—with high accuracy and flexibility, which is crucial for modeling equilibrium and stability.

The comparison, therefore, highlights a fundamental trade-off between physical detail and computational scale. The PIC-FEM method is the workhorse for modeling the global stability of the H-mode, the transport of energy and particles across the shaped magnetic surfaces, and the large-scale turbulence (like ELMs and ITGs), effectively capturing the essential macroscopic dynamics of the fusion device. It can handle the multi-meter domain and the multi-second timescales necessary for a fusion experiment. MD with LJ, though conceptually more fundamental by treating every particle, is severely limited in scope for a practical fusion device simulation. It simply cannot scale to the size required to model the global effects of the arbitrary controlling magnetic fields in a stellarator-tokamak hybrid. While specialized, fully-kinetic MD could provide benchmark data for small volumes, the PIC-FEM approach is the necessary compromise to realistically simulate the kinetic processes, field dynamics, and complicated magnetic shaping that defines the operational regime of this advanced fusion concept.

General Physics would like to create both MD and PIC simulations to develop complete models for a new stellarator tokamak hybrid with pixelated magnetics. We hope for a combined DEMO design utilizing W7X concepts, THEA's pixelated magnetics, and ITER's scale.