Electromagnetic Effects Resulted from Explosions - Ultra and Extremely Low Frequency Electromagnetic Fields - page 428

that in the ground the free path lengths of the gamma-quantums and electrons are
significantly shorter than those in the air. In the case of Compton interaction the
mean free path of quantum with energy on the order of 1 MeV is D b = where
b 1:5 10 2 kg=m 2 and is the medium density. For example, one can find that
100 m at the sea level in the atmosphere and 0:1 m in the ground with
the density D 1:7 10 3 kg=m 3 . The free path length of the Compton electrons in
the ground is e D b e = 1 mm (b e 2 kg=m 2 ), i.e. this value is small too. Based
on these simple estimates one may expect that the ratio of linear sizes of the electric
dipoles caused by underground and atmospheric explosions with the same energy
is inversely proportional to the ratio of densities of the corresponding media, i.e. 1-
10 3 . For the more accurate estimate we should take into account radiation-induced
conductivity of the rock around the underground chamber.
One more significant factor which may greatly decrease the EMP of an under-
ground explosion is the natural conductivity of the rock. The gamma-quantum pulse
originated from the nuclear fission has a duration about 0:1s, which corresponds
to the characteristic frequency ! 10 7 Hz. Taking a typical value of the rock
conductivity D 10 2 -10 3 S=m, we obtain the estimate of the corresponding
skin-depth in the ground r s . 0 e !/ 1=2

3-9 m. To illustrate this strong
attenuation, we note that if the explosion point is situated at the depth of 500 m,
then this short signal can attenuate 10 24 times or larger.
One more effect can be associated with the neutrons produced by explosions and
by secondary gamma-radiation. The deceleration of these neutrons down to thermal
energy is basically due to the interaction of the neutrons with nuclei of the light
elements such as hydrogen. This seemed entirely possible since the ground usually
contains about 16 % of hydrogen, 57 % of oxygen, 19 % of silicon, and 8 % of
aluminum (Straker 1971 ). The duration of the deceleration process is on the order of
10 ns, whereas the life time of the thermal neutrons in the ground is about 0.1-1 ms
that is significantly greater than the duration of primary gamma-quantum pulse. The
inelastic scattering and capture of the thermal neutrons by the nuclei of aluminum
and silicon causes the secondary gamma-radiation followed by the generation of
electric current. The characteristic frequencies of this process are ! D 10 3 -10 4 Hz.
This means that this effect could be observed in principle since the corresponding
skin-depth is about 90-900 m, that is compared with the explosion depth.
The high-temperature plasma in the underground explosion cavity is believed to
be one of the main sources for the EMP generation during a nuclear detonation. In
the nuclear device the fission reaction is completed for the times about 10 8 -10 7 s.
By this moment the matter still occupies the volume of about several cubic
centimeters. Since the temperature of fissioned matter reaches 10 7 K, the atoms of
light elements are completely ionized. This indicates that the electron-ion collisions
prevail in the plasma. In such a case the conductivity p of two-component plasma
can be written in the form (e.g., Lifshitz and Pitaevskii 1981 ):

4 p 2
3=2

T 3=2
Ze 2 m 1= e L

p D : (11.3)