  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.
