Investigation on the temporal evolution of the Druyvesteyn distribution function between sheath and presheath region in material processing plasmas

Abstract The energy distribution of particles in a gaseous system is primarily understood by the Maxwell–Boltzmann distribution function. However, in the case of partially ionized discharge plasmas which provide a unique attribute in the event of material processing, a Druyvesteyn distribution function rather than a Maxwellian function becomes a key contributor in understanding the electron energy distribution functions. Alteration in the distribution function from Maxwellian to Druyvesteyn is evident in the presence of external forces on the plasma particles, especially when electrons are heated by the electric field. In the present work, we study the time evolution of the Druyvesteyn distribution function in the presence of the external electric field. We found a rapid departure in nature from its equilibrium form and observed that the effusion process of electrons in the sheath regions can be controlled by applying the external electric field. The longitudinal current density increases with time, which is contrary to the case of the transverse current density. It indicates that the unidirectional flow reaching saturation with time is a collimated yield of the electrons. Also, electron energy reaches saturation and the distribution function shrinks with time, which indicates a monochromatic (monoenergetic) yield of electrons. Moreover, collimation and monochromatism can be controlled by the external electric field. Such control is quite desirable in material processing. On the application side, the methodology can be harnessed to generate plasma plume which has a potential application in the creation of biomedical plasma apparatuses.