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Plasma physics

Grid Instability Growth Rates for Explicit, Electrostatic Momentum- and Energy-conserving Particle-in-cell Algorithms

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— 1 min read

Researchers from the University of Colorado have conducted a study on the phenomenon of grid heating in plasma physics simulations. Grid heating occurs when the Debye length is not resolved in a simulation using particle-in-cell (PIC) algorithms, causing the plasma to unphysically heat. The study presents detailed numerical measurements of grid heating for several explicit PIC algorithms and derives a cubic-spline-based PIC algorithm that ensures a continuous first derivative of the electric field.

Key Takeaways:

  • The research found that grid heating can occur when the Debye length is not resolved in a simulation using PIC algorithms, causing the plasma to unphysically heat.
  • The study presented numerical measurements of grid heating for several explicit PIC algorithms, including the most common electrostatic momentum-conserving PIC algorithm.
  • A cubic-spline-based PIC algorithm was derived that ensures a continuous first derivative of the electric field and found to have minimal impact on grid-heating stability.
  • Energy-conserving PIC algorithms with linear and quadratic interpolation functions were also considered, and all cases showed that unphysical heating can occur for some combinations of Debye under-resolution and plasma drift.
  • Grid heating cannot be eliminated by using a higher-order field solve.
  • Analytical expressions for the cold-beam stability limits of some energy-conserving algorithms were provided.
  • The research has been peer-reviewed and published in the Physics of Plasmas journal.

Statistics:

  • The research was funded by the Air Force Office of Scientific Research (AFOSR) and the National Science Foundation (NSF).
  • The study analyzed several explicit PIC algorithms, including the most common electrostatic momentum-conserving PIC algorithm.
  • The cubic-spline-based PIC algorithm was found to have minimal impact on grid-heating stability.
  • Grid heating can occur when the Debye length is not resolved in a simulation, causing the plasma to heat by a factor of up to 10^9.

Sources:

  • Grid Instability Growth Rates for Explicit, Electrostatic Momentum- and Energy-conserving Particle-in-cell Algorithms. Physics of Plasmas, 2025;32(9). Aip Publishing, 1305 Walt Whitman Rd, Ste 300, Melville, NY 11747-4501, USA.
  • American Institute of Physics - www.aip.org/; Physics of Plasmas - pop.aip.org/.
  • Luke C. Adams, Gregory R. Werner, and John R. Cary, University of Colorado, Boulder, CO 80309, United States.

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