Плазма физикасындағы бөлшектік ұялы әдісі

Mathematical technique used to solve a certain class of partial differential equations
In plasma physics, the particle in cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles (or fluid elements) in a Lagrangian frame are tracked in continuous phase space, whereas moments of the distribution such as densities and currents are computed simultaneously on Eulerian (stationary) mesh points. PIC methods were already in use as early as 1955,
even before the first Fortran compilers were available. The method gained popularity for plasma simulation in the late 1950s and early 1960s by Buneman, Dawson, Hockney, Birdsall, Morse and others. In plasma physics applications, the method amounts to following the trajectories of charged particles in self consistent electromagnetic (or electrostatic) fields computed on a fixed mesh.

For many types of problems, the classical PIC method invented by Buneman, Dawson, Hockney, Birdsall, Morse and others is relatively intuitive and straightforward to implement. This probably accounts for much of its success, particularly for plasma simulation, for which the method typically includes the following procedures:
Integration of the equations of motion. Interpolation of charge and current source terms to the field mesh. Computation of the fields on mesh points. Interpolation of the fields from the mesh to the particle locations. Models which include interactions of particles only through the average fields are called PM (particle mesh). Those which include direct binary interactions are PP (particle particle). Models with both types of interactions are called PP PM or P3M. Since the early days, it has been recognized that the PIC method is susceptible to error from so called discrete particle noise. This error is statistical in nature, and today it remains less well understood than for traditional fixed grid methods, such as Eulerian or semi Lagrangian schemes. Modern geometric PIC algorithms are based on a very different theoretical framework. These algorithms use tools of discrete manifold, interpolating differential forms, and canonical or non canonical symplectic integrators to guarantee gauge invariant and conservation of charge, energy momentum, and more importantly the infinitely dimensional symplectic structure of the particle field system. These desired features are attributed to the fact that geometric PIC algorithms are built on the more fundamental field theoretical framework and are directly linked to the perfect form, i. e., the variational principle of physics.

Inside the plasma research community, systems of different species (electrons, ions, neutrals, molecules, dust particles, etc.) are investigated. The set of equations associated with PIC codes are therefore the Lorentz force as the equation of motion, solved in the so called pusher or particle mover of the code, and Maxwell's equations determining the electric and magnetic fields, calculated in the (field) solver.

The real systems studied are often extremely large in terms of the number of particles they contain. In order to make simulations efficient or at all possible, so called super particles are used. A super particle (or macroparticle) is a computational particle that represents many real particles; it may be millions of electrons or ions in the case of a plasma simulation, or, for instance, a vortex element in a fluid simulation. It is allowed to rescale the number of particles, because the acceleration from the Lorentz force depends only on the charge to mass ratio, so a super particle will follow the same trajectory as a real particle would. The number of real particles corresponding to a super particle must be chosen such that sufficient statistics can be collected on the particle motion. If there is a significant difference between the density of different species in the system (between ions and neutrals, for instance), separate real to super particle ratios can be used for them.

Within plasma physics, PIC simulation has been used successfully to study laser plasma interactions, electron acceleration and ion heating in the auroral ionosphere, magnetohydrodynamics, magnetic reconnection, as well as ion temperature gradient and other microinstabilities in tokamaks, furthermore vacuum discharges, and dusty plasmas. Hybrid models may use the PIC method for the kinetic treatment of some species, while other species (that are Maxwellian) are simulated with a fluid model. PIC simulations have also been applied outside of plasma physics to problems in solid and fluid mechanics.

Computational application Web site License Availability Canonical Reference SHARP Proprietary ALaDyn GPLv3+ Open Repo: EPOCH GPLv3 Open Repo: FBPIC 3 Clause BSD LBNL Open Repo: LSP Proprietary Available from ATK MAGIC Proprietary Available from ATK OSIRIS GNU AGPL Open Repo PICCANTE GPLv3+ Open Repo: PICLas GPLv3+ Open Repo: PIConGPU GPLv3+ Open Repo: SMILEI CeCILL B Open Repo: iPIC3D Apache License 2.0 Open Repo: The Virtual Laser Plasma Lab (VLPL) Proprietary Unknown Tristan v23 Clause BSDOpen source, but also has a private version with QED/radiative modules VizGrain Proprietary Commercially available from Esgee Technologies Inc. VPIC 3 Clause BSD Open Repo: VSim (Vorpal) Proprietary Available from Tech X Corporation Warp 3 Clause BSD LBNL Open Repo: WarpX 3 Clause BSD LBNL Open Repo: ZPIC AGPLv3+ Open Repo:ultraPICAProprietaryCommercially available from Plasma Taiwan Innovation Corporation.