Electron-filling kinetics of 2D states on a helium film

The details of charging a free liquid-helium surface with electrons are discussed. It is shown that the thickness of the helium film varies during this process and gradually decreases under the action of electron pressure on the helium surface. In turn, the pressure depends on the film thickness. Hence, the self-consistent kinetic problem arises with characteristic relaxation time $\tau$ mainly of hydrodynamic origin (viscous adjustment of the film thickness to the variable electron pressure). The value of $\tau$ is quite sensitive to the film thickness $d (\tau \propto d^3 $). In the most representative interval $10^{-1}\,{\rm cm} > d > 10^{-4}\,$cm $\tau $ varies in the range $10^{-3}\,{\rm s} \le \tau \le 10^{+8}$ s. The situation is most intriguing in the vicinity of the critical point (at the critical point, the charged helium film becomes unstable). As it is approached, $\tau$ increases to infinity.