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We propose and analyze a class of particle methods for the Vlasov equation
with a strong external magnetic field in a torus configuration. In this regime,
the time step can be subject to stability constraints related to the smallness
of Larmor radius. To avoid this limitation, our approach is based on
higher-order semi-implicit numerical schemes already validated on dissipative
systems [3] and for magnetic fields pointing in a fixed direction [9, 10, 12].
It hinges on asymptotic insights gained in [11] at the continuous level. Thus,
when the magnitude of the external magnetic field is large, this scheme
provides a consistent approximation of the guiding-center system taking into
account curvature and variation of the magnetic field. Finally, we carry out a
theoretical proof of consistency and perform several numerical experiments that
establish a solid validation of the method and its underlying concepts.
