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We investigate transient radiation processes in the non-linear superradiance(SR) regime of the Doppler broadened Maxwell-Bloch equations when the velocitydistribution is of total bandwidth greatly exceeding that of the transientprocess itself. We demonstrate the formation of global polarisation phasecorrelation and the quenching of temporal structure if a smooth distribution isinverted above the critical threshold required to enter the non-linear SRregime. We propose candidate stochastic velocity distributions capable ofsustaining finite temporal structure in the non-linear emission process. Wedevelop a novel algorithm for simulating the Doppler broadened Maxwell-Blochequations which is $O(n)$ complex in the number of velocity channels $n$whenever the emerging polarisation correlation is of moderate bandwidth, and weapply it to a stochastic velocity distribution in order to demonstratesustained delay and duration of peak intensity in the widely Doppler broadenedlimit. We discuss the transverse inversion process and recognise anautoregulation mechanism on the number of molecules cooperatively participatingin SR emission. This mechanism has the effect of limiting the temporal durationof the intensity pulse to a lower bound proportional to the length of thesample, which we confirm through simulation.

Transient Structure in the Non-linear Superradiance Regime of Widely Doppler Broadened Media