We found an analytical solution for the vortex structure in a rapidly rotating trapped Bose-Einstein condensate in the lowest Landau level approximation. This solution is exact in the limit of a large number of vortices and is obtained for the case of a condensate in a anisotropic harmonic potential. The solution describes as limiting cases both a triangle vortex lattice in the symmetric potential trap and a quasi-one-dimensional structure of vortex rows in an asymmetric case, when the rotation frequency is very close to the lower trapping potential frequency. The shape of the density profile is found to be close to the Thomas-Fermi inverted paraboloid form, except in the vicinity of edges of a condensate cloud.
We present results on the size, density, chemical potential, and lifetime of a Bose-Einstein condensate as a function of the number of condensate atoms for parameters appropriate to the time-averaged orbiting potential trap in which a Bose condensate of
87Rb atoms was recently formed [M. H. Anderson et al., Science 269, 198 (1995)]. These results were obtained by solving the time-independent nonlinear Schr\"odinger equation with anisotropic harmonic trapping potential. We also find vortex solutions for the trap and the critical rotation frequency required for their formation.