  We propose a class of Particle-In-Cell (PIC) methods for the Vlasov-Poisson
system with a strong and inhomogeneous external magnetic field with fixed
direction, where we focus on the motion of particles in the plane orthogonal to
the magnetic field (so-called poloidal directions). In this regime, the time
step can be subject to stability constraints related to the smallness of Larmor
radius and plasma frequency. To avoid this limitation, our approach is based on
first and higher-order semi-implicit numerical schemes already validated on
dissipative systems [3] and for homogeneous magnetic fields [10]. Thus, when
the magnitude of the external magnetic field becomes large, this method
provides a consistent PIC discretization of the guiding-center system taking
into account variations of the magnetic field. We carry out some theoretical
proofs and perform several numerical experiments that establish a solid
validation of the method and its underlying concepts.
