Electron-impact ionization rates for neutral He, Li, and Be in the Tsallis framework

The single-ionization rate coefficient of a plasma neutral depends both on the microscopic electron-impact cross section and on the macroscopic shape of the electron energy distribution function (EEDF). We present a reproducible benchmark and sensitivity study -- not a new theory -- of these two effects for the three lightest neutrals He, Li, and Be, combining the recommended Bell~\textit{et~al.}\ (1983) cross sections with a properly normalized two-temperature Tsallis $q$-generalized EEDF and varying $q$ on both sides of the Maxwellian limit and the hot-electron fraction $f_{\mathrm{hot}}$ at $T_{\mathrm{hot}}=10\,T_{\mathrm{bulk}}$. The calculation cleanly separates two independent uncertainty axes -- cross-section model (Bell vs.\ Lotz) and EEDF shape (Maxwellian vs.\ Tsallis). The Bell--Lotz spread on $\tau_M$ is small for He (within about $7\%$), moderate for Be ($\lesssim 17\%$), and largest for Li (up to $+95\%$ at $T=1$~keV); sub-extensive distributions ($q<1$) suppress ionization through a hard tail cut-off, while super-extensive distributions ($q>1$) enhance low-temperature ionization through a $\kappa$-like power-law tail with $\kappa=1/(q-1)$. The quantitatively safest non-Maxwellian cases are $q=1$ and $q=1.2$ ($\kappa=5$), which lie inside the finite-mean-energy regime; the cases $q=1.4$ and $q=1.6$ are retained as heavy-tail stress tests and should be read as qualitative trends rather than as quantitatively reliable predictions. Both EEDF effects scale with $I_p/k_BT$, so He responds most strongly and Li least. The full numerical pipeline is released as a persistent reproducibility package, intended as a drop-in non-Maxwellian ionization module for collisional-radiative and ionization-balance modelling of light-neutral plasmas.