  We study a basic plasma physics model--the one-fluid Euler--Poisson system on
the square torus, in which a compressible electron fluid flows under its own
electrostatic field. In this paper we prove long-term regularity of periodic
solutions of this system in 2 spatial dimensions.
  Our main conclusion is that on a square torus of side length $R$, if the
initial data is sufficiently close to a constant solution, then the solution is
wellposed for a time at least $R/\epsilon^2(\log R)^{O(1)}$, where $\epsilon$
is the size of the initial data.
