Modeling of Thermodynamic Effects at Micro-nano Scale of Cathode Spots

Cathode spots are fundamental to discharge phenomena, driving material erosion and surface functionalization. However, conventional simulations rely on simplified time-averaged heat sources, failing to resolve the discrete, transient extinction and re-ignition dynamics of micro-spots. In this work, we establish a high-fidelity numerical framework based on the Transiently Random Jump (TRJ) model, which captures dual-scale stochastic spot kinetics by coupling microscopic spatial jittering with macroscopic jump intervals. By integrating these stochastic trajectories into a transient thermo-fluid dynamics framework, the model accurately captures highly localized, pulsed heat fluxes and predicts dynamic peak temperatures exceeding 7000 K. Mechanistic analysis reveals that the pulsed evaporative recoil force inside cathode craters acts as the principal hydrodynamic driver for liquid metal ejection, generating plasma jet velocities above 120 m/s. Experimental validation indicates that the TRJ framework quantitatively predicts complex, overlapping micro-crater morphologies. Furthermore, multi-spot interaction analysis demonstrates that spot clustering induces significant non-linear energy superposition and heightened thermodynamic perturbations compared to dispersed distributions. This work provides an essential theoretical foundation for predicting micro-scale surface morphology evolution and optimizing advanced discharge processes.