The Length of Critical Streamers

The concept of an equipotential length of a positive quasi-stationary streamer is introduced as a criterion for estimating the degree of its isolation. The equipotential length of positive critical streamers (streamers moving in the presence of an electric field of lowest magnitude sufficient for an unlimited propagation of a positive streamer) in normal atmosphere is determined for both individual streamers and streamers forming a thin bunch. The dependence of the equipotential length of positive quasi-stationary streamers on the magnitude of an external field, velocity, radius, and electron density in the streamer head is investigated. A criterion for analytical models of the quasi-stationary streamers that provides an additional independent equation for the system of equations describing the dynamics of a quasi-stationary streamer (applicable only to the critical streamer) is proposed. It is demonstrated that the influence of electrodes located at a distance from the streamer head larger than its equipotential length is low, which lends credence to using the equipotential length for estimating the degree of isolation of the positive streamers.