@Article{TreumannBaumGonz:2012:MaFiLi,
               author = "Treumann, R. A. and Baumjohann, W. and Gonzalez, W. D.",
          affiliation = "{} and {} and {Instituto Nacional de Pesquisas Espaciais (INPE)}",
                title = "Collisionless reconnection: Magnetic field line interaction",
              journal = "Annales Geophysicae",
                 year = "2012",
               volume = "30",
                pages = "1515--1528",
             abstract = "Magnetic field lines are quantum objects carrying one quantum Fi0 
                         = 2 Pi h/e of magnetic flux and have finite radius m. Here we 
                         argue that they possess a very specific dynamical interaction. 
                         Parallel field lines reject each other. When confined to a certain 
                         area they form two-dimensional lattices of hexagonal structure. We 
                         estimate the filling factor of such an area. Anti-parallel field 
                         lines, on the other hand, attract each other.We identify the 
                         physical mechanism as being due to the action of the gauge 
                         potential field, which we determine quantum mechanically for two 
                         parallel and two antiparallel field lines. The distortion of the 
                         quantum electrodynamic vacuum causes a cloud of virtual pairs. We 
                         calculate the virtual pair production rate from quantum 
                         electrodynamics and estimate the virtual pair cloud density, pair 
                         current and Lorentz force density acting on the field lines via 
                         the pair cloud. These properties of field line dynamics become 
                         important in collisionless reconnection, consistently explaining 
                         why and how reconnection can spontaneously set on in the 
                         field-free centre of a current sheet below the electron-inertial 
                         scale.",
                  doi = "10.5194/angeo-30-1515-2012",
                  url = "http://dx.doi.org/10.5194/angeo-30-1515-2012",
                 issn = "0992-7689",
                  url = "www.ann-geophys.net/30/1515/2012/",
        urlaccessdate = "09 maio 2024"
}