When does the Schwinger preheating occur?

When the inflaton couples to photons and amplifies electric fields, charged particles produced via the Schwinger effect can dominate the universe after inflation, which is dubbed as the Schwinger preheating. Using the hydrodynamic approach for the Boltzmann equation, we numerically study two cases, the Starobinsky inflation model with the kinetic coupling and the Watanabe-Kanno-Soda inflation model. The Schwinger preheating is not observed in the latter model but occurs for a sufficiently large inflaton-photon coupling in the first model. We analytically address its condition and derive a general attractor solution of the electric fields. The occurrence of the Schwinger preheating in the first model is determined by whether the electric fields enter the attractor solution during inflation or not.