Superfluidity in liquid \(^4\) He is characterized by the absence of viscosity, and the critical velocity marks the transition from a non-dissipative to a dissipative flow state. In past experiments, the critical velocity was observed for a pool of positive ions trapped below a free surface, which was attributed to the nucleation of a quantized vortex associated with the macroscopic quantum tunneling. To study the problem further, here we consider a novel ion pool design in which a channel is connected to reservoirs at both ends and examine the response of the system in both linear and nonlinear regimes (i.e., below and above the critical velocity, respectively) using finite element method (FEM) simulations. We find that the velocity in the channel is uniform within 5% and that the response of the system is well described by the lumped constant circuit model in both linear and nonlinear regimes. These features allow well-controlled investigations of the transport properties of the ions even above the critical velocity, which enables us to quantitatively understand the vortex nucleation process and the vortex state above the critical velocity.
