PIC Algorithm Research Articles

Particle-in-cell plasma simulation codes on the Connection Machine

Methods for implementing three-dimensional, electromagnetic, relativistic PIC plasma simulation codes on the Connection Machine (CM-2) are discussed. The gather and scatter phases of the PIC algorithm involve indirect indexing of data, which results in a large amount of communication on the CM-2. Different data decompositions are described that seek to reduce the amount of communication while maintaining good load balance. These methods require the particles to be spatially sorted at the start of each time step, which introduces another form of overhead. The different methods are implemented in CM Fortran on the CM-2 and compared. It was found that the general router is slow in performing the communication in the gather and scatter steps, which precludes an efficient CM Fortran implementation. An alternative method that uses PARIS calls and the NEWS communication network to pipeline data along the axes of the VP set is suggested as a more efficient algorithm.

Computational Plasma Physics: With Applications of Fusion and Astrophysics

"Computational Plasma Physics: With Applications of Fusion and Astrophysics." Fusion Technology, 17(2), pp. 362–363 Additional informationNotes on contributorsDennis W. HewettDennis W. Hewett has worked in computational plasma physics starting with his PhD research at the University of Kansas in 1973 under Thomas P. Armstrong. While at Los Alamos from 1974 to 1982, he worked on a variety of problems in magnetic fusion research, including writing and using finite- and zero-electron mass hybrid models as well as other PIC procedures. He was also involved in developing new techniques for finding Vlasov equilibria and for solving systems of linearized equations that arise in resistive magnetohydrodynamics. His move to inertia I confinement fusion (ICF) at Lawrence Livermore National Laboratory resulted in a shift in emphasis for applications while still maintaining a strong interest in computational methods. He implemented a two-dimensional direct-implicit electromagnetic PIC algorithm that has lead to new developments in magnetic reconnection. His recent interests include considering new ways to use the radiationless or Darwin approximation of Maxwell’s equations and applications in particle sources and acceleration, particularly as they apply to heavy-ion-driven ICF.

Electromagnetic direct implicit plasma simulation

A 2D electromagnetic version of the direct implicit PIC algorithm has been developed and implemented in the new code AVANTI. The code has been tested on electron beam filamentation and magnetic reconnection problems and has fulfilled most of the promise of implicit PIC. It runs stably with an arbitrarily large time step and is quite robust with respect to large particle fluctuations that result when plasmas are represented with small numbers of particles per cell N c. Several numerical obstacles were overcome during the development of the AVANTI. A method of determining the implicit susceptibility ζ is described which allows the code to avoid a nonlinear instability associated with small N c We find a form of “Simplified differencing” that provides a very robust algorithm without need for explicit smoothing. Another hurdle is the solution of the EM field equations. If the collisionless skin depth is not well resolved in high density regions, the terms containing the tensor ζ dominate the E field equation and strongly couple the components. This strong coupling is handled by simultaneous solution of these equations-generalizing to simultaneous splitting in 2D. In regions where the skin depth is well resolved, terms associated with purely electromagnetic waves dominate but do not fit symmetrically into the simultaneous splitting scheme. Introducing the electrostatic potential, the troublesome asymmetric electrostatic part of E cancels but requires a fourth equation for φ to be solved simultaneously along with the three E components. Finally, extension and generalization of the conventional explicit PIC divergence correction step, necessary to maintain Gauss' law, is needed. By using a more complex form for the correction factor, one that incorporates some implicit shielding, the correction step provides an opportunity to control or prevent spuriously large implicit currents from moving across strong magnetic fields and across steep density gradients from vacuum regions.