Plasma evolution after electrical breakdown in Earth and Martian atmospheres

The classical breakdown theory predicts the conditions required for electrical breakdown but does not generally determine whether a discharge subsequently remains spatially localized or evolves into a transport-dominated state. This distinction is particularly important in low-pressure environments such as the Martian atmosphere, where successful electrical breakdown may be followed by strong spatial spreading and weak post-breakdown confinement. In this work, we develop a reduced reaction–drift–diffusion framework to characterize the competition between ionization amplification, diffusion, field-driven transport, and nonlinear plasma-density evolution during near-threshold discharge evolution. Two dimensionless transport parameters are introduced to organize post-breakdown plasma behavior into transport-dominated, transitional, and amplification-dominated regimes. The reduced analysis yields an approximate marginal condition, Γ≈1+Ξ, separating transport-loss-dominated and amplification-dominated evolution within the assumptions of the near-threshold model. Numerical simulations incorporating pressure-dependent transport, Townsend-type ionization, nonlinear density-dependent loss, and a prescribed non-uniform electric field predict substantially enhanced spreading under the Martian parameterization, including an approximately 3.8-fold larger RMS transport width, reduced peak plasma density, and weaker post-breakdown confinement. In contrast, the Earth-like case remains comparatively localized under the same external field geometry. These results demonstrate that electrical breakdown and subsequent plasma confinement constitute distinct stages of discharge evolution governed by different reaction–transport balances. The proposed framework provides a reduced-order interpretation linking breakdown accessibility with subsequent transport behavior and offers a computationally inexpensive diagnostic for assessing transport-regime transitions in weakly ionized near-threshold plasmas.