Laboratory Study of Rock Deformation and Fracture - Ultra and Extremely Low Frequency Electromagnetic Fields - page 340

9.1.4 Phenomenological Models of Shock

Polarization in Dielectrics

In phenomenological models of shock polarization effect, the structure of SW front
is not considered and a jump/discontinuity of polarization at the SW front is usually
assumed. The relaxation of shock polarization behind the front was supposed to be
due to the thermal and mechanical relaxation (Allison 1965 ). The relaxation can
also be a by-product of conductivity arising in the dielectric behind the SW front
(e.g., Zeldovich 1967 ).
Now we consider a simple phenomenological model of the polarization current
in the circuit of a shorted capacitor shown in Fig. 9.1 and try to explain the pattern
of oscillogram displayed in Fig. 9.2 . Following Zeldovich ( 1967 ) we first ignore the
relaxation process due to the conductivity induced by the SW in the compressed
medium. Then the electric charge has to be situated on the SW front and on the
plates of a capacitor as schematically shown in Fig. 9.4 .Let † 1 and † 2 be
the surface charge densities on the right and left plates, respectively, while " 1 and
" 2 are the dielectric permittivities of the medium in front of and behind the SW
front, respectively. The plane SW is considered to be an extremely narrow layer or
discontinuity of the medium parameters. If a load resistance of the external circuit is

ʣ 2

ʣ ʣ 1

x = V c t

l

y

Fig. 9.4 A schematic plot of charge distribution in the shock-compressed sample and on plates of
shorted capacitor. Here † 2 ,and† are the surface charge densities on the plates and SW

front, respectively. The arrows show the direction of SW propagation in the sample

† 1 ,