partikelincell

Partikelincell, commonly referred to as the particle-in-cell (PIC) method, is a computational approach used to simulate systems of charged particles interacting through self-consistent electromagnetic fields. It is widely used in plasma physics, laser–plasma interactions, space plasmas, and accelerator science because it can capture kinetic effects beyond fluid models.

In a PIC simulation, a large ensemble of computational particles represents many physical particles and moves in continuous space under forces from electric and magnetic fields. The electromagnetic fields are defined on a fixed spatial grid. At each time step, the charges and currents of the particles are deposited onto the grid, producing source terms for Maxwell’s equations. The fields are then updated on the grid, typically by explicit time integration. The updated fields are interpolated back to particle positions to advance their velocities and positions.

Implementation details include interpolation schemes that couple particles and grid, such as cloud-in-cell (CIC) or higher-order shapes, and stable velocity updates using methods like the Boris pusher. Boundary conditions, grid resolution, and the number of particles per cell affect accuracy and statistical noise. PIC can be extended to three spatial dimensions with three velocity components (3D3V) or used in reduced-dimensional variants; it is also combined with Monte Carlo collision models (PIC-MCC) to include particle collisions.

Strengths of partikelincell include a kinetic, self-consistent description of particle distributions and field dynamics, suitable for non-equilibrium and nonlinear phenomena. Limitations include statistical noise from finite particle numbers, high computational cost, and restrictive time steps governed by the Courant condition.

Historically developed in the mid-20th century, the PIC framework remains foundational in computational plasma physics and continues to be deployed in research and software tools.