Still further back the field between the cathode and the
positive ions is enhanced again. The field distortion becomes noticeable with a
carrier number n > 106. For instance, in nitrogen with d D 2 cm, p D 760 torr,
˛ ³ 7 and E0/p ³ 40 V/torr cm, the field distortion is about 1 per cent, leading
to 5 per cent change in ˛. If the distortion of ¾D1 per cent prevailed in the entire
gap it would lead to a doubling of the avalanche size, but as the distortion is
only significant in the immediate vicinity of the avalanche head it has still an
insignificant effect. However, if the carrier number in the avalanche reaches
n ³ 108 the space charge field becomes of the same magnitude as the applied
field and may lead to the initiation of a streamer. The space charge fields play
an important role in the mechanism of corona and spark discharges in nonuniform
field gaps. For analytical treatment of space charge field distortion
the reader is referred to reference 12.