Particle in Cell

The term Particle -in- Cell (PIC to German as " particles in a cell") referred to in theoretical physics, a technique for solving certain classes of partial differential equations. The core element is that simulated particles ( or elements of a fluid ) in an Eulerian reference frame (so that it is possible to solve the equations of motion of the fluid elements in the form of Euler 's equations ) in a continuous phase space can be calculated, while fields of a distribution of eg Densities and currents are calculated on the Eulerian ( stationary ) grid points.

PIC methods have been used as early as 1955, even before the availability of the first Fortran compiler. The process won for plasma simulations in the course of the late 1950s and early 1960s popularity by Oscar Buneman, John M. Dawson, Hockney, Birdsall, Morse and others.

In plasma physics calculations allows this method of calculation, the trajectory of charged particles in self-consistent electromagnetic (and / or electrostatic ) fields to follow.

Technical aspects

For many problems, the PIC method can be very intuitive and straight forward to implement. This is probably one of the reasons for its success, especially for plasma simulations, in which typically the following tasks must be completed:

• Interpolation of the force effect of the fields of the grid points on the particles
• Integration of the equations of motion for the particle / fluid elements
• Interpolation of the charge and current densities at the grating
• Calculation of the fields on the grid points

Unlike in the physical reality of the forces on the particles will not change significantly when approaching particles at distances on the order of fractions of a lattice pitch. This may, but need not be considered as a problem of PIC simulation.

Depending on how the forces are calculated on the particles, a distinction is made different PIC models. If only the interaction of the particles are calculated with the grid in the simplest case, one speaks of a PM (Particle -Mesh particle- grid) model. Models that draw only the particle-particle interaction into account, called according to PP (Particle - Particle, Particle - particle) model. Models that take into account both types of interactions are called according to PP -PM or P3M.

Even in the early days of the simulation method, it was recognized that the PIC simulation sensitive to the so-called discrete Teilchenrauschen, Eng. discrete particle noise responding. This error is statistical in nature, and to date, this type of error remains rather less well understood than the sources of error in traditional approaches that do purely fixed-grid.

A good source for assessing the numerical accuracy of a PIC simulation remains the observation of conserved quantities, particularly in terms of energy.

Applications

Within plasma physics PIC simulations have been successfully used for laser-plasma interactions, electron acceleration and ion heating in the ionosphere under the influence of polar lights, magneto hydrodynamics, to study reconnection, as thus ion - temperature - gradient and other instabilities in tokamaks were examined.

PIC simulations have been applied to problems to outside of the plasma physics in solid mechanics and fluid mechanics.