Double layers and electrostatic shocks

It is shown that it is useful to define double layers and shocks so that the ion phase spaces of double layers are the mirror image (about zero ion velocity) of the ion phase spaces for laminar electrostatic shocks. The distinguishing feature is the direction of the free ion velocity. It is also shown that double layers can exist without the presence of trapped ions. The Bohm condition for double layers, that the ion drift velocity on the high potential side must be greater than the ion sound velocity, is shown to be related to a requirement of a lower limit on the Mach number of laminar electrostatic shocks