Bounds on the mobility of electrons in weakly ionized plasmas

We obtain exact upper and lower bounds on the steady-state drift velocity, and kinetic energy of electrons, driven by an external field in a weakly ionized plasma (swarm approximation). The scattering is assumed to be elastic with a simplified velocity dependence of the collision cross sections. When the field is large the bounds are close to each other and to the results obtained from the conventional approximation of the Boltzmann equation in which one keeps only the first two terms of a Legendre expansion. The bounds prove rigorously that it is possible to increase the electron mobility by the addition of suitably chosen scatterers to the system as predicted by the Druyvesteyn approximation and found in experiments.