Towards 4th-order accurate 3D Magnetic Reconnection in Relativistic plasmas

Relativistic magnetic reconnection has been established as an efficient and universal mechanism that can accelerate particles. Reconnection promoted by the onset of the ideal tearing mode instability has resolved two major issues in the macroscopic resistive MHD framework: the paradox of super-tearing instability in Sweet-Parker current sheets, and the need for a mechanism to explain fast, spontaneous magnetic reconnection. Despite its significance, current three-dimensional (3D) models struggle to capture the ideal tearing mode instability on dynamical timescales due to computational limitations. In what follows, we present the preliminary results of one of the first sets of 4th-order accurate, GPU-accelerated, 3D simulations of ideal tearing dynamics within the resistive special relativistic MHD framework. The proposed simulations show a rapid conversion of magnetic energy into heat, with few regions where the electric field becomes strong enough to promote particle acceleration. Compared to the 2D counterparts where a saturation phase is eventually reached, 3D simulations see the onset of current-carrying modes and turbulence, which contribute to the final disruption of the initial current sheet and flux rope.