  The one dimensional one component plasma has applications to one dimensional
particle systems with logarithmic interactions such as charges in a single
channel wire or vortex filaments in a fluid convection stream. The exact
integral of this plasma in the canonical ensemble with a gaussian confining
potential has already been computed. In this paper, I compute the exact volume
of the phase space of the plasma of N particles at fixed energy without a
confining potential using a microcanonical ensemble and show that, as in the
two-dimensional case, it has negative temperature states, suggesting that one
dimensional turbulence can occur from vortex/electron clustering.
