Orbits of charged particles in the current sheet located in the fan of a magnetic null point are described analytically in both nonrelativistic and ultrarelativistic limits. An orbit instability effect is described, which limits the acceleration times and kinetic energy gains in the reconnection-related electric field. The use of an analytical self-consistent MHD solution to derive the magnetic field configuration near the null point leads to constraints on local parameters in the magnetic reconnection region. As a consequence, conditions can be identified for efficient particle acceleration in realistic reconnecting geometries. Applications to particle acceleration in solar flares are discussed.
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