We investigate the possibility of the production of an ionized domain by the ionization of the atmosphere by cosmic rays amplified by relativistic runaway electron avalanches (RREAs), the polarization of which could lead to the localized boosting of thundercloud fields, triggering the sequence of processes leading to lightning development. For this goal, a 2D numerical model was developed of atmospheric discharges in a self‐consistent electric field allowing for the kinetics of high‐energy REs, low‐energy electrons, and positive and negative ions. The effects are tested for cosmic ray air showers and for the continuous background of low‐energy cosmic radiation. It is shown that lightning cannot be triggered by the joint action of the cosmic ray shower and RREAs. On the contrary, with realistic rates of the cloud charging, the RREAs seeded by low‐energy cosmic rays, produce a plasma domain, at the edges of which the electric field of the cloud is enhanced above the magnitude required for the selfsustained growth of the free electron population, potentially resulting in lightning initiation.
