  We investigate the nature of the plasma analogy for the Laughlin wave
function on a torus describing the quantum Hall plateau at $\nu=\frac{1}{q}$.
We first establish, as expected, that the plasma is screening if there are no
short nontrivial paths around the torus. We also find that when one of the
handles has a short circumference -- i.e. the thin-torus limit -- the plasma no
longer screens. To quantify this we compute the normalization of the Laughlin
state, both numerically and analytically. For the numerical calculation we
expand the Laughlin state in a Fock basis of slater-determinants of single
particle orbitals, and determine the Fock coefficients of the expansion as a
function of torus geometry. In the thin torus limit only a few Fock
configurations have non-zero coefficients, and their analytical forms simplify
greatly. Using this simple limit, we can reconstruct the normalization and
analytically extend it back into the 2D regime. We find that there are geometry
dependent corrections to the normalization, and this in turn implies that the
plasma in the plasma analogy is not screening when in the thin torus limit.
Further we obtain an approximate normalization factor that gives a good
description of the normalization for all tori, by extrapolating the thin torus
normalization to the thick torus limit.
