Electron Acceleration in Time-dependent Kinematic Three-dimensional Magnetic Reconnection: The Role of Induced Electric Fields and Magnetic Topology

Particle acceleration during magnetic reconnection is a key process in space physics and astrophysics, yet the direct role of induced electric fields in fully time-dependent three-dimensional (3D) topologies remains poorly quantified. In true 3D reconnection, incorporating full temporal evolution into analytical theory is exceptionally challenging, and in existing 3D simulations, the role of the time-varying induced electric field is not easily isolated, since it is inherently entangled with other contributions. Moreover, no systematic study has compared particle acceleration across the primary 3D topologies, non-null, spine, and fan, including A-type, B-type, and X-type null geometries, within a unified, time-dependent framework. Here, we develop the first analytical, time-dependent models for these configurations, with the background magnetic field decaying as B(t) ∝ exp(−kt), allowing the decay rate k to serve as an independent control parameter for temporal dynamics. By systematically comparing electron energy spectra, representative trajectories, and field distributions, we establish a clear hierarchy of acceleration efficiency among topologies and identify the physical mechanisms that govern these differences. We further reveal a quadratic scaling of mean energy gain with k, ΔW ∝ k², a signature that emerges when the global induced electric field becomes the dominant driver of acceleration. Collectively, these findings reveal how magnetic geometry and the global field decay rate jointly control acceleration efficiency and its scaling, which might also provide a predictive physical basis for interpreting particle energization in extreme astrophysical events.