This article was accepted into the corpus but its outbound wikilinks were never NER-processed — typical at the deepest BFS hop or when the run's entity cap was reached. No expansion funnel to show.
| Boris (algorithm) | |
|---|---|
| Name | Boris algorithm |
| Developers | J. P. Boris |
| Initial release | 1970s |
| Type | time-centered particle pusher |
| Field | Plasma physics; Computational physics; Astrophysics |
Boris (algorithm) is a numerical method widely used for integrating charged particle trajectories in electromagnetic fields within plasma physics, computational physics, and astrophysics contexts. It preserves phase-space volume and offers favorable energy and stability properties for long-time simulations of particles interacting with fields computed by solvers such as Particle-in-cell methods in codes developed at institutions like Los Alamos National Laboratory and Princeton University. The scheme is central to community codes and research projects across laboratories and universities including Lawrence Livermore National Laboratory, CEA and major observatories.
The algorithm is a second-order, time-centered, explicit integrator designed to advance particle positions and velocities under the Lorentz force from James Clerk Maxwell-derived electromagnetic fields and external forces used in simulations by groups at NASA and CERN. It is often combined with field solvers such as finite-difference schemes attributed to Kane Yee and charge-conserving current deposition techniques developed in the tradition of C. K. Birdsall and A. B. Langdon. Because of its wide use in codes like OSIRIS (code), VPIC, and EPOCH (code), it appears in studies spanning from laboratory plasma experiments at Princeton Plasma Physics Laboratory to space physics investigations at European Space Agency missions.
The core update splits acceleration by electric and magnetic contributions with a staggered "kick-rotate-kick" sequence that uses time-centered velocities akin to methods introduced by H. Yoshida and techniques used in symplectic integrators popularized by researchers at Stanford University. Starting from position and velocity arrays popular in implementations at Argonne National Laboratory, the velocity is first advanced half-step by the electric field (via Lorentz force components derived from Maxwell's equations), then rotated by the magnetic field through an exact rotation in the velocity plane using cross-product algebra familiar from works by Oliver Heaviside and Josiah Willard Gibbs, and finally kicked again by the electric field. The position update employs the midpoint velocity and maintains time-centered second-order accuracy analogous to leapfrog schemes used in Molecular dynamics by developers at Argonne and Oak Ridge National Laboratory.
The method is volume-preserving and exhibits long-term bounded energy error for charged-particle motion in static electromagnetic fields, properties analyzed in the tradition of backward error analysis by researchers at Courant Institute and ETH Zurich. It is non-symplectic in the strict Hamiltonian sense for systems with time-dependent fields but is closely related to symplectic splitting methods examined by authors at Caltech and Imperial College London. Stability against large magnetic fields and strong gyration is controlled by the timestep relative to the cyclotron frequency, a condition scrutinized in convergence studies at Max Planck Institute and MIT. Numerical dispersion and particle heating observed in coupled Particle-in-cell simulations have been compared across solvers in benchmarking efforts involving Oak Ridge, Los Alamos, and Lawrence Berkeley National Laboratory teams.
Implementations appear in languages and frameworks ranging from Fortran codes used at CERN to C++ and CUDA kernels developed at NVIDIA-partner laboratories; Python wrappers are provided by projects at NumPy-using research groups and by community tools at GitHub. Variants include implicit and semi-implicit extensions inspired by work at LLNL and Princeton that aim to relax timestep constraints, relativistic generalizations incorporating Lorentz factor updates used in Relativistic mechanics studies at SLAC National Accelerator Laboratory, and energy-conserving modifications proposed by researchers at University of Oxford and University of California, Berkeley. Multi-rate and adaptive timestep strategies used in hybrid fluid-kinetic codes at Dartmouth College and University of Chicago integrate the Boris core with substepping and Boris-corrected Boris push alternatives developed in community code bases.
The algorithm underpins simulations in magnetic confinement fusion research at Iter-related consortia and at Princeton Fusion Energy Institute, space weather modeling for missions by NOAA and ESA, laser-plasma interaction studies relevant to facilities such as National Ignition Facility, and particle acceleration research linked to observations from Hubble Space Telescope-era astrophysical investigations. It appears in studies of reconnection phenomena investigated by teams at Swedish Institute of Space Physics and Los Alamos, in beam dynamics simulations for accelerators at CERN and Fermilab, and in modeling of planetary magnetospheres studied by NASA and JAXA collaborations.
Performance assessments compare energy conservation, momentum preservation, and wall-clock efficiency across platforms including multi-core CPUs at Intel-based clusters and GPUs from NVIDIA. Benchmarks often use test problems like gyration in uniform magnetic fields, drift orbits influenced by electric fields, and two-stream instability scenarios ported across codes from EPCC and NERSC centers. Scalability studies conducted on large systems at Argonne and Oak Ridge measure runtime, memory footprint, and communication overhead when the Boris push is coupled to field solvers and current deposition algorithms, with GPU-accelerated variants showing order-of-magnitude throughput improvements in community reports.
The algorithm traces to the work of J. P. Boris and contemporaries in the 1970s within the milieu of Los Alamos National Laboratory and the evolving Particle-in-cell community influenced by pioneers such as C. K. Birdsall and A. B. Langdon. Subsequent theoretical clarifications and practical extensions were developed by researchers at Princeton University, Lawrence Livermore National Laboratory, and numerous university groups, forming a lineage of method improvements documented in conference venues like meetings of the American Physical Society, workshops at ICTP, and reports circulated through national laboratories. Contemporary citations and community adoption reflect contributions from international teams across Europe, North America, and Asia in adapting and optimizing the scheme for modern high-performance computing environments.
Category:Numerical algorithms