The collision of two ionized streams

Abstract

It is shown that the interpenetration of two ionized streams is arrested, as a rule, not because of individual collisions between particles belonging to opposite streams, but because the whole system of charged particles is unstable. The smallest wavelength of an unstable oscillation is λ_min where $\lambda_{min} = \surd \left(\frac {\pi m_0 U^2}{2N \epsilon^2}\right) \left(1 - \frac {U^2}{c^2} \right) ^{-\frac {3}{4}}$ Here ± U are the velocities of the undisturbed streams, and N is the density of electrons in each.

A further calculation for the non-relativistic case deals with the amplification of the plasma oscillations present in two colliding streams. It is shown that these grow rapidly and that $\tau_{crit} \surd (m_0 U^2|\pi N \epsilon^2$ is the distance of interpenetration achieved before the counterstreaming of the electrons is brought to a halt. The value of τ_crit depends only insensitively on the ratio of the internal plasma energy densities Tpl to the kinetic energy densities T_kin in the streams. For example, τ_crit = 9·0 when T_pl:T_kin = 1:10, and τ_crit = 19·0 when T_pl : T_kin = 1:10⁵.