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Fig. 3.24 A signature of “early/fast” VLF event associated with a sprite which was observed in
Crete on August, 29 during the 2003 EuroSprite campaign (Neubert et al. 2005 ). Typically these
events are characterized by an abrupt onset and a signal recovery ranging from 10-300 s. Adapted
from Haldoupis et al. ( 2009 )
recombination with positive ions, the majority of which compose O 2C and NO C
while Ǜ d is the effective coefficient of recombination of electrons with positive
cluster ions which are produced from positive ions via a hydration chain reaction.
Notice that the interaction between electrons and negative ions due to electron
attachment and detachment does not enter this simplified equation.
Taking into account that the dissociative recombination of electrons and single
positive ions dominates above 80-85 km (Glukhov et al. 1992 ; Haldoupis et al.
2009 ); that is, in the altitude range of interest, one may ignore the last term on
the right-hand side of Eq. ( 3.25 ). Additionally, taking the notice of plasma quasi-
neutrality one should substitute n i n e into Eq. ( 3.25 ). Let n e0 be the electron
number density arising after the short-term stage of electron production. Taking this
value as the initial one and performing integration of this equation we come to the
following usual law for binary plasmas
n e0
1 C Ǜ d n e0 t :
n e D
(3.26)
Substituting n e D n e0 =2 into Eq. ( 3.26 ) we obtain the rough estimate of the
plasma relaxation time t r d n e0 / 1 . In the altitude range of interest the numeri-
cal values of the parameters are as follows: Ǜ d D .1 3/ 10 7 cm 3 s 1 (Lehtinen
and Inan 2007 ) and n e0 D 6 10 4 cm 3 (Haldoupis et al. 2009 ). Substituting these
values into the above relationship gives the estimate t r .2 5/ 10 2 s which is
compatible with the recovery time of early VLF events.
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