  We consider the radiation properties and processes of a gas with a population
inversion using the formalism based on the Maxwell-Bloch equations. We focus on
the maser action and Dicke's superradiance to establish their relationship in
the overall radiation process during the temporal evolution of the system as a
function of position. We show that the maser action and superradiance are not
competing phenomena but are rather complementary, and define two distinct
limits for the intensity of radiation. Masers characterise the quasi-steady
state limit, when the population inversion density and the polarisation
amplitude vary on time-scales longer than those of non-coherent processes
affecting their evolution (e.g., collisions), while superradiance defines the
fast transient regime taking place when these conditions are reversed. We show
how a transition from a maser regime to superradiance will take place whenever
a critical threshold for the column density of the population inversion is
reached, at which point a strong level of coherence is established in the
system and a powerful burst of radiation can ensue during the transient regime.
This critical level also determines the spatial region where a transition from
the unsaturated to the saturated maser regimes will take place; superradiance
can thus be seen as the intermediary between the two. We also quantify the gain
in radiation intensity attained during the superradiance phase relative to the
two maser regimes, and show how the strong coherence level during superradiance
is well suited to explain observations that reveal intense and fast radiation
flares in maser-hosting regions.
