  We study the long time evolution and stationary speed distribution of N point
particles in 2D moving under the action of an external field E, and undergoing
elastic collisions with either a fixed periodic array of convex scatterers, or
with virtual random scatterers. The total kinetic energy of the N particles is
kept fixed by a Gaussian thermostat which induces an interaction between the
particles. We show analytically and numerically that for weak fields this
distribution is universal, i.e. independent of the position or shape of the
obstacles or the nature of the stochastic scattering. Our analysis is based on
the existence of two time scales; the velocity directions become uniformized in
times of order unity while the speeds change only on a time scale of O(|E|^-2).
