High-order implicit particle-in-cell method for plasma simulations at solid densities.

Area of Science:

• Plasma Physics
• Computational Physics
• Numerical Methods

Background:

• Explicit particle-in-cell (PIC) methods face numerical instabilities with relaxed constraints.
• Standard implicit PIC methods suffer from numerical cooling.
• Simulating plasmas at solid densities requires robust and accurate computational techniques.

Purpose of the Study:

• To develop a high-order implicit multidimensional particle-in-cell (PIC) method for simulating plasmas at solid densities.
• To eliminate numerical instabilities and cooling inherent in existing PIC methods.
• To enhance the accuracy and efficiency of plasma simulations.

Main Methods:

• Utilized a Yee space-time arrangement with a leapfrog algorithm for electromagnetic fields and particle advancement.
• Implemented a novel field solver to eliminate numerical instabilities, allowing relaxed time step and grid resolution.
• Developed a particle pusher combining the Boris method with Newton-Krylov iteration to improve precision and reduce iteration time.

Main Results:

• The developed implicit PIC method successfully eliminated numerical instabilities and cooling.
• The particle pusher algorithm achieved several orders of magnitude increase in precision accuracy.
• The method demonstrated significantly decreased iteration times compared to pure Newton-Krylov methods.
• Successful benchmark tests included Weibel instability and relativistic laser-plasma interactions.

Conclusions:

• The high-order implicit multidimensional PIC method provides a stable, accurate, and efficient approach for simulating plasmas at solid densities.
• This method overcomes limitations of explicit and standard implicit PIC techniques.
• The validated code is suitable for complex problems like relativistic laser-plasma interactions.