Tkachenko waves

The existence of Tkachenko waves in rotating superfluid⁴He has been confirmed experimentally. Tkachenko waves are displacement waves in the vortex line array that exists in a rotating superfluid. The waves were excited and detected in resonant cavities formed by a stack of closely spaced parallel plates. The dispersion relation, studied as a function of rotation speed, disk spacing (which fixed one component of the wave vector), and temperature, is compared with existing theories and found to be in good agreement at low temperatures. The theories predict peaks in the density of states associated with a lattice of vortices; the resonant responses observed are found to correspond to these peaks. The need for a more complete theory is presented in the light of the behavior of the vortex resonances at elevated temperatures.This work was supported by NSF grant DMR-78-25409.