In this article we investigate the validity of the lowest‐order diffusion or P1 approximation of the Boltzmann equation. This is done by considering a narrow band of electrons in energy space. The analysis shows that if the spatial derivative can be neglected, i.e., for a distributed source of electrons, the P1 approximation is valid all the cases considered (for e.g., N2). When the spatial derivative cannot be neglected, which is the case for a spatially localized source of electrons, then the region of validity of the P1 approximation is much more restrictive. High‐pressure discharges are examples of a distributed source. Electrons generated for swarm experiments are examples of a spatially localized source of electrons.

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