Magneto-Fluid Dynamics Seminar

An energy-conserving and asymptotic-preserving time integrator for implicit PIC simulation of magnetized plasmas

Speaker: Lee Ricketson, Lawrence Livermore National Laboratory

Location: Warren Weaver Hall 905

Date: Tuesday, March 5, 2019, 11 a.m.


Tremendous progress has been made on implicit particle-in-cell (PIC) schemes in recent years.  They feature exact energy conservation and have been shown to be more robust to the finite grid instability than their explicit counterparts, making them quite powerful for long-time simulation.  Simultaneously, there has been increasing interest in implicit, full-orbit kinetic simulation that steps over the gyration time-scale as an alternative to gyrokinetics.  Such an approach would have the noteworthy advantage of being able to handle widely varying levels of magnetization within the computational domain.  We present a new full-orbit time integrator at the intersection of these two ideas.  The integrator is built on Crank-Nicolson and preserves the crucial exact energy conservation property of implicit PIC, but it also reproduces all first-order guiding center drifts and the correct gyroradius when stepping over the gyration time-scale, all while converging to the full orbit dynamics for small time-steps.  The key innovations are (1) the ability to capture the grad-B drift and mirror force without breaking energy conservation and (2) a detailed understanding of the time-step restrictions on the scheme along with an adaptive time-stepping strategy that ensures these restrictions are respected.  Results from several test problems are presented that demonstrate the scheme’s effectiveness.  Notably, we are able to predict trapped/passing boundaries, adiabatic invariance of magnetic moment, and behavior when passing through unmagnetized regions much more accurately than previous efforts. 


Work performed under the auspices of the U.S. Department of Energy by LLNL and LANL under contracts DE-AC52-07NA27344, DE-AC52-06NA25396, and supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.