Analytical solution of steady reconnection outflows in a time-varying three-dimensional reconnection model with generalized spatiotemporal distributions

Magnetic reconnection is a fundamental mechanism for energy conversion in the realms of space physics, astrophysics, and plasma physics. Over the past few decades, obtaining analytical solutions for three-dimensional (3D) magnetic reconnection has remained a challenging endeavor. Due to the complexity and nonlinearity of the equations, analytical solutions can only be obtained when specific spatiotemporal distributions of magnetic fields or plasma flows are provided. Particularly, the evolution of reconnection flows in time-dependent 3D reconnection has not been analytically discussed. Additionally, quasi-steady magnetic reconnection persisting for several hours can be observed in the turbulent solar wind, which raises an important question: can steady reconnection flows theoretically exist in a time-dependent 3D magnetic reconnection model? In this study, a generalized analytical model for time-dependent kinematic 3D magnetic reconnection has been constructed. In the framework of pure analytical approach, it is firstly demonstrated that steady reconnection outflows can theoretically exist within a time-varying magnetic field. We have also analytically discussed the possibility of the existence of quasi-steady reconnection flows in 3D magnetic reconnection for turbulent magnetic fields in the solar wind. These findings broaden our understanding of the stability and necessary conditions for time-dependent 3D magnetic reconnection, offering new insights into quasi-steady reconnection phenomena in real cosmic environments.