Theory for the critical ionization velocity phenomenon

A theoretical consideration is given to the critical ionization velocity. A macroscopic theory is constructed, assuming that (1) the newly born ions have an unstable velocity distribution and (2) the resultant fluctuating electric field heats the electrons. For the critical ionization velocity to operate in the case of $\text{m}{}_{\mathrm{a}}\text{V}{}^2\text{2}\text{> eφ}{}_{\mathrm{<mtext>ion</mtext>}}$, the initial values of high speed ion (or newly ionized ion) density and suprathermal electron energy density should be above a certain threshold. This threshold depends upon the velocity diffusion co-efficient and the collisional loss rate of the newly ionized ion.