Particle acceleration in coalescent and squashed magnetic islands I. Test particle approach

Aims. Magnetic reconnection in large Harris-type reconnecting current sheets (RCSs) with a single X-nullpoint often leads to the occurrence of magnetic islands with multiple O- and X-nullpoints. Over time these magnetic islands become squashed, or coalescent with two islands merging, as has been observed indirectly during coronal mass ejection and by in-situ observations in the heliosphere and magnetotail. These points emphasise the importance of understanding the basic energising processes of ambient particles dragged into current sheets with magnetic islands of different configuration. Methods. Trajectories of protons and electrons accelerated by a reconnection electric field are investigated using a test particle approach in RCSs with different 3D magnetic field topologies defined analytically for multiple X- and O-nullpoints. Trajectories, densities, and energy distributions are explored for 10(6) thermal particles dragged into the current sheets from different sides and distances. Results. This study confirms that protons and electrons accelerated in magnetic islands in the presence of a strong guiding field are ejected from a current sheet into the opposite semiplanes with respect to the midplane. Particles are found to escape O-nullpoints only through the neighbouring X-nullpoints along (not across) the midplane following the separation law for electrons and protons in a given magnetic topology. Particles gain energy either inside O-nullpoints or in the vicinity of X-nullpoints that often leads to electron clouds formed about the X-nullpoint between the O-nullpoints. Electrons are shown to be able to gain sub-relativistic energies in a single magnetic island. Energy spectra of accelerated particles are close to power laws with spectral indices varying from 1.1 to 2.4. The more squashed the islands the larger the difference between the energy gains by transit and bounced particles, which leads to their energy spectra having double maxima that gives rise to fast-growing turbulence. Conclusions. Particles are shown to gain the most energy in multiple X-nullpoints between O-nullpoints (or magnetic islands). This leads to the formation of electron clouds between magnetic islands. Particle energy gains are much larger in squashed islands than in coalescent ones. In summary, particle acceleration by a reconnection electric field in magnetic islands is much more effective than in an RCS with a single X-nullpoint.