A $\delta f$ PIC method with Forward-Backward Lagrangian reconstructions

In this work we describe a $\delta f$ particle simulation method where the bulk density is periodically remapped on a coarse spline grid using a Forward-Backward Lagrangian (FBL) approach. This method is designed to handle plasma regimes where the densities strongly deviate from their initial state and may evolve into general profiles. We describe the method in the case of an electrostatic particle-in-cell scheme and validate its qualitative properties using a classical two-stream instability subject to a uniform oscillating drive.