Mathematicalhyphen;physical model of the streamer in nonuniform fields

摘要

The initial electron avalanche created in the high nonuniform fields near an anode leaves behind it a space charge of positive ions that enhance the field farther away from the anode and, hence, produce the necessary conditions for successive electron avalanches to produce the streamer. A mathematical model of these processes has been derived and the minimum anode voltage required to satisfy these equations has been computed for different geometrical parameters. This streamer onset voltage agrees well with measured values. The conditions for streamer onset are found to exist whenever the average gradient of the field is higher than a certain value specified by the initial avalanche length.