Biermann suggested that ionized gas clouds in comet tails are accelerated by collision with a stream of solar particles. The field-free case is discussed to establish conditions for which cometary plasma acceleration may be enhanced by plasma instability. A general criterion for instability of plasmas of arbitrary ionic composition and velocity distribution is derived. This result is applied to determine the stability of combinations of cometary gas densities and solar particle densities and temperatures. Electron-ion instability grows briefly if the solar electrons are cool enough. This is a transient effect. As soon as the electrons lose their translational velocity, their temperature becomes high enough to restore plasma stability, even for succeeding generations of inflowing electrons. The total momentum transfer is negligibly small compared with the momenta of cometary-tail ions. Plasma instability does not appreciably contribute to tail plasma acceleration. (auth)