A four-field model for collisionless reconnection: Hamiltonian structure and numerical simulations

A 4-field model for magnetic reconnection in collisionless plasmas is investigated both analytically and numerically. The model equations are shown to admit a non-canonical Hamiltonian formulation with four infinite families of Casimir invariants [1]. Numerical simulations show that, consistently with previously investigated models [2,3], in the absence of significant fluctuations along the toroidal direction, reconnection can lead to a macroscopic saturated state exhibiting filamentation on microsocopic scales, or to a secondary Kelvin-Helmholtz-like instability, depending on the value of a parameter measuring the compressibility of the electron fluid. The novel feature exhibited by the four-field model is the coexistence of significant filamentation with a secondary instability when magnetic and velocity perturbations along the toroidal direction are no longer negligible. An interpretation of this phenomenon in terms of Casimir invariants is given.\\[0pt] [1] E. Tassi et al., Plasma Phys. Contr. Fus., 50, 085014 (2008)\\[0pt] [2] D. Grasso et al., Phys. Rev. Lett. 86, 5051 (2001)\\[0pt] [3] D. Del Sarto, F. Califano and F. Pegoraro, Phys. Plasmas 12, 012317 (2005)