An implicit, conservative electrostatic particle-in-cell algorithm for paraxial magnetic nozzles Articles uri icon

publication date

  • February 2024

start page

  • 1

end page

  • 22


  • 112826


  • 502

International Standard Serial Number (ISSN)

  • 0021-9991

Electronic International Standard Serial Number (EISSN)

  • 1090-2716


  • An electrostatic, implicit particle-in-cell (PIC) model for collisionless, fully magnetized, paraxial plasma expansions in a magnetic nozzle is introduced with exact charge, energy, and magnetic moment conservation properties. The approach is adaptive in configuration space by the use of mapped meshes, and exploits the strict conservation of the magnetic moment to reduce the dimensionality of velocity space. A new particle integrator is implemented, which allows particle substepping without the need to stop particle motion at every cell face for charge conservation. Particle substeps are determined from accuracy considerations, and are allowed to span multiple cells. Novel particle injection and expansion-to-infinity boundary conditions are developed, including a control loop to prevent the formation of spurious sheaths at the edges of the domain. The algorithm is verified in a periodic magnetic mirror configuration, a uniform plasma test case (to test particle injection), and a propulsive magnetic nozzle. The algorithm's computational complexity is shown to scale favorably with timestep, and linearly with the number of particles and grid cells for resolutions well beyond typical simulation needs. Numerical experiments demonstrate that the proposed algorithm is more than an order of magnitude faster than a semi-Lagrangian Vlasov code running on a similar machine, and we estimate speedups of that order compared to explicit PIC algorithms.


  • Aeronautics


  • implicit particle in cell; electric propulsion; magnetic nozzles; plasma simulation; particle-in-cell