Three-dimensional fan magnetic reconnection and particle acceleration in the solar corona

Aims. Particle acceleration by the reconnection electric field in three-dimensional magnetic geometries in the solar corona is discussed. The acceleration times, defined by the particle escape from the vicinity of a magnetic null, and the corresponding energy gains are calculated. Methods. An exact global magnetohydrodynamic solution for fan magnetic reconnection is used to constrain the magnetic and electric fields in the vicinity of the null. Expressions for the particle acceleration times and energy gains are derived by applying the WKB approximation to the equation of motion in nonrelativistic and ultrarelativistic limits. Results. It is shown that the energies of the accelerated particles can be limited by the particle escape from the null rather than by the total electric potential at the reconnection site. For typical coronal parameters, the finite escape time limits proton energies if the Lundquist number is less than 10(12) and electron energies if the Lundquist number is less than 10(18). Conclusions. Particle acceleration by the electric field, associated with fan magnetic reconnection in solar flares, can explain proton energies of the order of a few MeV and electron energies of the order of a few hundred keV in the case of classical electric resistivity. Energies up to a few hundred MeV can be reached if the resistivity at the reconnection site is turbulent. These estimates agree with typical solar flare observations.