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Helium (He) nanodroplets irradiated by intense near-infrared laser pulses form a nanoplasma by avalanche-like electron impact ionizations (EIIs) even at lower laser intensities where He is not directly field ionized, provided that the droplets contain a few dopant atoms which provide seed electrons for the EII avalanche. In this theoretical paper on calcium and xenon doped He droplets we elucidate the mechanism which induces ionization avalanches, termed ignition. We find that the partial loss of seed electrons from the activated droplets starkly assists ignition, as the Coulomb barrier for ionization of helium is lowered by the electric field of the dopant cations, and this deshielding of the cation charges enhances their electric field. In addition, the dopant ions assist the acceleration of the seed electrons (slingshot effect) by the laser field, supporting EIIs of He and also causing electron loss by catapulting electrons away. The dopants’ ability to lower the Coulomb barriers at He as well as the slingshot effect decrease with the spatial expansion of the dopant, causing a dependence of the dopants’ ignition capability on the dopant mass. Here, we develop criteria (impact count functions) to assess the ignition capability of dopants, based on (i) the spatial overlap of the seed electron cloud with the He atoms and (ii) the overlap of their kinetic energy distribution with the distribution of Coulomb barrier heights at He. The relatively long time delays between the instants of dopant ionization and ignition (incubation times) for calcium doped droplets are determined to a large extent by the time it takes to deshield the dopant ions. [ABSTRACT FROM AUTHOR]