The major thrust of this proposal is in two separate experimental areas: 1) the flow of helium 2 between rotating concentric cylinders (Couette flow) and 2) the thermal expansion of liquid helium (which is closely related to the specific heat) near the lambda transition in a well-defined confined geometry. Questions concerning helium 2 Couette flow will be investigated: first the appearance of quantized vortices in the general case (both cylinders rotating), for which a new prediction exists; second, the stability of this array of quantized vortices, also a subject of recent theoretical work. The experiment for determining the thermal expansion of liquid helium consists of measuring the dielectric constant of helium confined between plates in a high Q superconducting LC cavity. Large scale computer simulations of vortex motion in helium 2 will be pursued. Experimental work suggests that ions may excite solitons on vortices in rotating helium 2. Simulation of a tangle of vortex lines, a subject of recent controversy, will also be made.
