Kinetics of electrohydrodynamic instability of a charged liquid helium surface

Two-dimensional (2D) electron layers floating on the surface of bulk liquid helium have been studied extensively over the last few decades as platforms for studying phase transitions in 2D, and recently, due to their relevance to quantum technologies. The maximum density of the electron layer is limited by the electrohydrodynamic (EHD) instability of the charged liquid helium surface, beyond which the electrons leave the surface in the form of multielectron bubbles (MEBs). Here, we report the experimental observation and analysis of the kinetics of EHD instability both above and below the $\ensuremath{\lambda}$ point of liquid He-4 to directly measure the instability length and time scales. The measurements agree with theoretical estimates and can inspire new experiments to reach ultrahigh electron densities above liquid helium.