  The two-dimensional one-component plasma, i.e. the system of point-like
charged particles embedded in a homogeneous neutralizing background, is studied
on the surface of a cylinder of finite circumference, or equivalently in a
semiperiodic strip of finite width. The model has been solved exactly by
Choquard et al. at the free-fermion coupling $\Gamma=2$: in the thermodynamic
limit of an infinitely long strip, the particle density turns out to be a
nonconstant periodic function in space and the system exhibits long-range order
of the Wigner-crystal type. The aim of this paper is to describe, qualitatively
as well as quantitatively, the crystalline state for a larger set of couplings
$\Gamma=2\gamma$ ($\gamma=1,2,...$ a positive integer) when the plasma is
mappable onto a one-dimensional fermionic theory. The fermionic formalism,
supplemented by some periodicity assumptions, reveals that the density profile
results from a hierarchy of Gaussians with a uniform variance but with
different amplitudes. The number and spatial positions of these Gaussians
within an elementary cell depend on the particular value of $\gamma$. Analytic
results are supported by the exact solution at $\gamma=1$ ($\Gamma=2$) and by
exact finite-size calculations at $\gamma=2,3$.
