A new insight to the problem of creating an inverse electron distribution function and practical recommendations for experimental searches for such media in glow discharges

After the creation of the first gas lasers, it was shown that a medium with an inverse free electron distribution function (EDF) in gases with a Ramsauer minimum of elastic scattering will amplify electromagnetic waves. However, unlike the laser technology, this practically important problem has not yet been solved. One of the main reasons is a significant simplification of the Boltzmann kinetic equation for a spatially homogeneous medium, when it depends only on one variable - the electron velocity. Since real laboratory plasma objects are always localized in a limited volume, the EDF depends on both energy and coordinates. Taking this into account, a new insight on solving the problem of inverse EDF is formulated and substantiated. Based on the results of numerical modeling and theoretical analysis, criteria and scaling are presented for assessing the possible inversion of the EDF under specific conditions. The objects of study are spatially inhomogeneous media with a non-local EDF which corresponds to the parameter pL < 5 cmTorr. According to the analysis, first of all, attention should be paid to the near-anode plasma of glow discharges with a flat and hollow cathode, to the non-uniform positive column of the discharge (created, for example, by introducing a diaphragm), as well as to the two-chamber designs of the plasma of the ICP and CCP discharges, when the power from an external source is introduced into the working chamber, and the resulting plasma diffuses into the second, ballast chamber.