Development of the Electrohydrodynamic Instability of Charged Liquid Helium Surface

The surface electron density on the surface of bulk liquid helium is limited by the classical electrohydrodynamic (EHD) instability. Due to the EHD instability, the surface electrons enter the liquid helium and form Multielectron Bubbles (MEBs). This instability is not an instantaneous process; in fact, it extends over a period of time. A detailed analysis of the dynamics of the instability and its dependency on factors like charge density and electric field can be crucial in effectively manipulating the instability to obtain a stable high-density state. Though there are a few previous experimental studies on the onset of EHD instability on charged liquid helium-4 surface, the temporal dynamics of the EHD instability has not been studied yet. In this work, we present the experimental investigation of the temporal dynamics of the instability as a function of charge density and electric field. The unstable wave vectors are determined using image analysis of the acquired images and found to be matched with the theoretically expected values. The growth rate of unstable wave vectors is studied in detail and found to be limited by the kinematic viscosity of the medium.