Vortex patterns and energies in a rotating superfluid

The two-dimensional vortex patterns that occur in a rotating cylinder of superfluid 4He are systematically ordered for numbers of vortices N=1,2,...,30,37,50 using a prescription for their free energy that is independent of angular velocity and is based upon the justified omission of images. Barrier energies between patterns of the same N and of neighboring N are discussed. A new derivation of the vortex free energy for perfect square and triangular lattices gives the result in terms of GAMMA (x). Patterns that are expected to display high triangular symmetry are studied up to N=217, but circular distortion strongly reduces the region of triangular symmetry even in an unbounded fluid, as shown by the scattering structure factor. According to calculations on arrays containing over one-million vortices, the destabilizing velocity at the vortex position R in a finite circular region of a perfect triangular lattice is proportional to (R/R0)5, where R0 is the radius of the circular region