Messanae Universitas Studiorum: No conditions. Results ordered -Date Deposited. 2019-10-16T08:24:09ZEPrintshttp://cab.unime.it/images/sitelogo.pnghttp://cab.unime.it/mus/2005-04-21Z2012-09-14T11:31:26Zhttp://cab.unime.it/mus/id/eprint/282This item is in the repository with the URL: http://cab.unime.it/mus/id/eprint/2822005-04-21ZMathematical study of the runaway process in particle swarmsIn this article we study two linear Boltzmann equations which describe the time evolution of the electron distribution in a weakly ionized gas, both of them one-dimensional in the velocity and any spatial variable, and one of them spatially homogeneous. We present two mathematical definitions of electron runaway, one based on travelling wave phenomena and the other one involving the average speed asymptotics. Under suitable assumptions on the collision frequency, we prove electron runaway according to the average speed definition in the spatially homogeneous as well as the spatially dependent case. For constant collision frequency v0 the average speed is shown to relax to a/v0 where a is the electrostatic acceleration.Giovanni FrosaliCornelis Van Der Mee