An implicit, conservative, asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrary magnetic fields*

We propose a new electrostatic particle-in-cell algorithm able to use large timesteps compared to particle gyro-period in non-uniform external magnetic fields [1,2]. The algorithm extends earlier electrostatic fully implicit PIC implementations [3] with a new asymptotic- preserving (AP) particle-push scheme [4] that allows timesteps much larger than particle gyroperiods. In the large-timestep limit, the AP integrator preserves all the averaged particle drifts, while recovering particle full orbits with small timesteps. The scheme allows for a seamless, efficient treatment of particles in coexisting magnetized and unmagnetized regions, conserves energy and charge exactly, and does not spoil implicit solver performance. Non-uniform magnetic fields require modifications to the standard Crank-Nicolson orbit integrator [4,5] to capture all first-order drifts for timesteps much larger than the gyrofrequency. We demonstrate by numerical experiment that significant speedups are possible vs. the standard fully implicit electrostatic PIC algorithm without sacrificing solution quality and while preserving strict charge and energy conservation. 

[1] G. Chen and L. Chacón, J. Comput. Phys., 487 (2023)

[2] O. Koshkarov, L. Chacón, G. Chen, L. Ricketson, in preparation

[3] G. Chen, L. Chacón, and D. C. Barnes, J. Comput. Phys., 230 (2011)

[4] L. Ricketson and L. Chacón. J. Comput. Phys., 418 (2020)

[5] O. Koshkarov, L. Chacón, G. Chen, L. Ricketson, J. Comput. Phys., 459, 111146 (2022)