Geoscience Reference
In-Depth Information
the SW velocity (Fig.
9.4
). In this reference frame, the mass conservation law reads
V
D
V
s
=s, where V is the velocity of matter just behind the SW front and s is the
shock compression, i.e., the ratio of the densities of the material behind and in front
of the SW. The bulk charge motion at the velocity V together with the matter gives
rise to convective current. The total current density caused both by the convective
and conductive current is given by
j
y
D
2
E
y
C
V
s
e
=s;
(9.22)
where
e
is the bulk charge density. The requirement of the current stationarity in
the form: j
y
D
0 allows us to find
e
e
D
s
2
E
y
=V
s
:
(9.23)
Substituting Eq. (
9.23
) into Poisson's equation (
9.10
) we obtain
dE
y
dy
D
sE
y
V
s
r
:
(9.24)
Integration of Eq. (
9.24
) under the condition E
.
0
/
D
E
m
D
†=
.
"
0
"
2
/
gives
(Zeldovich
1967
)
E
D
E
m
exp .
y=y
0
/;
0
D
V
s
r
=s:
(9.25)
Laboratory tests of the NaCl samples of 0.1-1 cm thickness under a pressure of
10 GPa have shown that the shock-compressed matter exhibits a conductivity of the
order of
2
10
3
-10
5
S/m (Mineev and Ivanov
1976
). Under these parameters
the relaxation length/typical size of the charged electric layer y
0
is of the order
or much smaller than the thickness of the sample. This means that the effect of the
stress-induced conductivity on the amplitude and shape of signals can be significant.
Since the load resistance of the external circuit is neglected, the potentials of
the capacitor plates could be considered to be equal. The potential difference, ',
and effective capacity, C
e
, formed by the front of the SW and the right plate of the
capacitor are of the order of
Z
V
c
†
s
2
"
1
"
0
S
l
V
c
t
;
'
D
E
y
dy
D
E
m
y
0
D
;
e
D
(9.26)
0
where S denotes the area of the plates. The current density in the external circuit is
then
"
1
"
0
V
c
†
s
2
.l
V
c
t/
2
:
'
S
dC
e
dt
D
j
D
(9.27)
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