The two-dimensional one-component plasma at the special coupling \beta = 2 is
known to be exactly solvable, for its free energy and all of its correlations,
on a variety of surfaces and with various boundary conditions. Here we study
this system confined to a spherical annulus with soft wall boundary conditions,
paying special attention to the resulting asymptotic forms from the viewpoint
of expected general properties of the two-dimensional plasma. Our study is
motivated by the realization of the Boltzmann factor for the plasma system with
\beta = 2, after stereographic projection from the sphere to the complex plane,
by a certain random matrix ensemble constructed out of complex Gaussian and
Haar distributed unitary matrices.Comment: v2, typos and references corrected, 24 pages, 1 figur