Time-dependence of the electron energy distribution function in the nitrogen afterglow

Abstract

In this paper, we present an investigation of the time-relaxation of the electron energy distribution function (EEDF) in the nitrogen afterglow of an /spl omega//2/spl pi/=433 MHz flowing discharge at p=3.3 torr, in a tube with inner radius R=1.9 cm. We solve the time-dependent Boltzmann equation, including the term for creation of new electrons in associative/Penning reactions, coupled to a system of rate balance equations for the heavy-particles. The EEDFs are also obtained experimentally, from second derivatives of digitized probe characteristics measured using a triple probe technique, and compared with the calculations. It is shown that an equilibrium between the vibrational distribution function of ground-state molecules N/sub 2/(X/sup 1//spl Sigma//sub g//sup +/,v) and low-energy electrons is rapidly established, in times /spl sim/10/sup -7/ s. In these early instants of the postdischarge, a dip is formed in the EEDF around 4 eV. The EEDF finally reaches a quasi-stationary state for t/spl gsim/10/sup -6/ s, although the electron density still continues to decrease beyond this instant. Collisions of highly excited N/sub 2/(X/sup 1//spl Sigma//sub g//sup +/,v/spl gsim/35) molecules with N(/sup 4/S) atoms are in the origin of a maximum in the electron density occurring downstream from the discharge at /spl sime/2/spl times/10/sup -2/ s. These reactions create locally the metastable states N/sub 2/(A/sup 3//spl Sigma//sub u//sup +/) and N/sub 2/(a'/sup 1//spl Sigma//sub u//sup -/), which in turn ionize the gas in associative/Penning processes. Slow electrons remain for very long times in the postdischarge and can be involved in electron stepwise processes with energy thresholds smaller than /spl sim/2-3 eV.