Experimental study of secondary electron emission and its role in atmospheric electricity

Paschen's law underlies our understand of scaling properties of electric discharges. It describes non-thermal, self-sustained discharges occurring in high voltage, low current, and low-pressure conditions between two parallel plate electrodes (e.g., Raizer et al., 1991, ISBN:978-3540194620). It was originally established experimentally for various gas mixtures. J.S.E. Townsend (1915, ISBN: 978-5878309981) developed a formal theory that relies on an exponential fit of the primary ionization coefficient ($\alpha \approx Ap\exp{-Bp/E}$) and the poorly understood secondary electron emission ($\gamma$). In their reference book on gas discharge, Raizer, et al. (1991 p.75) state that ``The data on $\gamma$ are incomplete and often contradictory.'' The commonly used (A, B, $\gamma$) constants do not traditionally consider electrodes' geometries and materials. Riousset et al (2022, under review) proposed a new formalism suitable for non-planar geometries using the reduced effective ionization coefficient $\flatfrac{\alpha_{\rm eff}}{p}$ and mobility ($\rm \mu p$). The new model accounts for volume and drift velocity changes along the avalanche path via a power law approximation of $\rm \mu p$. Here we propose to use this new formalism and explicitly characterize the constants A, B in the effective ionization ($\alpha_{\rm eff}$) and C, D in the mobility ($\mu$). In addition, we develop an experimental setup for their validation. The discharges are produced in Embry-Riddle Aeronautical University's Dusty Plasma Chamber (DPC). The critical (initiation) voltage ($V_{\rm cr}$) is measured at specific pressures ($p$) and distances ($d$) in air and $\rm CO_2$ mixtures comparable to Earth and Mars atmospheres. Distances and pressure can be adjusted using a linear feedthrough (LFT) and mass flow controller (MFC), respectively. The added flexibility of the setup lets us control $p$ and $d$ independently and confirm Paschen's law. In addition, we seek to establish how $\gamma$ depends on the nature of the electrode, its geometry, as well as the gas of the environment. We show that the v.Engel-Steenbeck equation (Fridman \& Kennedy, 2004, doi:10.1201/9781482293630) and the assumed value of $\gamma$ do not adequately characterize the critical voltage under non-planar geometries. We propose a $\chi^2$-analysis to assess the dependencies of $\gamma$ on the environmental parameters and obtain accurate values for $A, B, C, D$. These variations may prove especially important for the initiation of Transient Luminous Events occurring near the ionosphere at low pressures.