Geoscience Reference
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F
fr
,
eV/cm
10
6
eE
th
10
5
10
4
F
min
10
3
e
min
e
*
10
2
10
0
10
2
10
4
10
6
10
8
e
, eV
Fig. 3.22
A schematic plot of dynamical friction force of electrons in the air versus electron
kinetic energy. The figure is partly adapted from Pasko (
2006
)
The generation of the runaway electrons is possible in the energy range from "
to "
min
where the fall off of the friction force dominates. It follows from Eq. (
3.17
)
that the runaway electrons can appear under the requirement
eE > F
fr
."/:
(3.20)
which means that the electric field will accelerate the electrons with such energies
continuously so that they become “runaway” electrons. The implication here is that
the increase of the electron energy in the electric field prevails over the energy losses
due to ionization of air. Conversely, if eE < F
fr
."/, then the electron energy falls
off quickly due to the ionization of air and other inelastic processes result in the
energy losses. The requirement given by Eq. (
3.20
) can be satisfied for the ambient
electric field E>E
r
D
F
min
=e. It follows from the detailed analysis that the
minimal value of the threshold electric field is given by (Gurevich and Zybin
2001
)
4e
3
Zn
m
a
m
e
c
2
E
r
D
;
(3.21)
where the dimensionless parameter a
11.
To satisfy Eq. (
3.20
), the runaway electron energy must be greater than the
threshold value, "
r
, which depends on the ambient electric field. Combining
Eqs. (
3.19
)-(
3.21
) we obtain that
m
e
c
2
E
r
2E
">"
r
:
(3.22)
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