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[en] A generalized weight-based particle simulation scheme suitable for simulating magnetized plasmas, where the zeroth-order inhomogeneity is important, is presented. The scheme is an extension of the perturbative simulation schemes developed earlier for particle-in-cell (PIC) simulations. The new scheme is designed to simulate both the perturbed distribution ((delta)f) and the full distribution (full-F) within the same code. The development is based on the concept of multiscale expansion, which separates the scale lengths of the background inhomogeneity from those associated with the perturbed distributions. The potential advantage for such an arrangement is to minimize the particle noise by using (delta)f in the linear stage stage of the simulation, while retaining the flexibility of a full-F capability in the fully nonlinear stage of the development when signals associated with plasma turbulence are at a much higher level than those from the intrinsic particle noise.