Wave-Radiation Model for the Onset of Dissipation at the Roton Critical Velocity in Superfluid Helium

A linearized form of the Gross-Pitayevski (GP) equation is used to calculate the rate at which quasiparticles are created by a small sphere moving through a superfluid at a velocity greater than ${\left(\frac{{\omega }_k}{k}\right)}_{min}$, the Landau roton critical velocity. Because the excitations described by the linearized GP equation can be given a hydrodynamic interpretation, the qualitative features of the model porposed here for the roton critical velocity are analogous to the many critical-velocity phenomena of classical physics. The quantitative results of the model indicate that energy dissipation sets in so rapidly that, once the creation of quasiparticles is allowed kinematically, it should be impossible experimentally to force a negative-ion complex to move observably faster than the roton critical velocity. An investigation of the meaning of the linearized GP equation is also given.