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The behavior of the time dependences of the volt- The experimental dependence of the voltage on the
age and electric field depends strongly on the position front side of the specimen (Fig. 3b) is not in complete
of the measurement electrodes. For the present model, agreement with the calculated curve. The electric field
in which the shock front has a zero thickness, shock- in this model should increase only at the late stages of
wave penetration leads to an instantaneous decrease in shock-wave motion. The further behavior of the elec-
the electric field at the back side of the specimen. The tric field depends strongly on the parameter s (increase
current density remains finite. After that, the electric or decrease). The voltage increase in the experiment
field increases monotonically. This behavior is caused begins earlier than that predicted by the model. Qual-
by the formation of a current countercurrent system in itatively, the experimental curve is more similar to the
the conductor and by spatial extension of this system in equilibrium dependence Ee(t)/E0. This behavior may
the course of shock-front motion. The experimental and be related to non-one-dimensionality of the magnetic
calculated dependences (see Fig. 3a) are significantly field. The registered signal depends strongly on the
different in the first 10 15 nsec. A smoother variation point of connection of the electrodes. Connection of
of the registered voltage may be attributed to the finite the electrodes at the foil edges is sensitive to electro-
thickness of the shock front in the experiments and also magnetic field nonuniformity. In Fig. 3b, the value of s
to a certain deviation of the shock wave from the pla- may be roughly evaluated as s H" 0.8 0.9.
Application of the Electromagnetic Model for Diagnosing 235
As a whole, the agreement between our experi- the model may be used for diagnosing shock-wave pro-
mental and numerical dependences may be estimated cesses in metals.
as satisfactory. In any case, the dependences V (t)/V0 This work was supported by the Russian Foun-
and E(t)/E0 have an identical character. The values dation for Fundamental Research (Grant No. 99-02-
s H" 0.9 0.95 found from Fig. 3a do not contradict 16807).
the known data. Extrapolation of the results of [5] to
the shock-wave pressure p = 43 GPa yields the value
s H" 1.08 1.12. The difference in these values may be
REFERENCES
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2. S. D. Gilev,  Shock-induced conductivity waves in a
The experimental information obtained confirms
conductor placed in an external magnetic field, Fiz.
that the electric conductivity of Constantan varies
weakly under shock compression. For this reason, Con- Goreniya Vzryva, 32, No. 6, 116 122 (1996).
3. S. D. Gilev and T. Yu. Mikhailova,  Electromagnetic
stantan is the best material to be used as a shunt
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in the method of electric conductivity measurement in
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dielectric metal junctions [4]. The voltage oscillations
36, No. 6, 153 163 (2000).
registered (see Fig. 2) are manifestations of electromag-
4. S. D. Gilev and T. Yu. Mikhailova,  The development of
netic nonequilibrium in the conductor and may be taken
a method of measuring a condensed matter electrocon-
into account in interpretation of experimental data in
ductivity for investigation of dielectric metal transitions
the measurement cell including the Constantan foil and
in a shock wave, J. Physique IV, 5, C3-211 216 (1997).
the specimen under study. The first increase in voltage,
5. A. N. Dremin and G. I. Kanel ,  Dependence of elec-
which corresponds to shock-wave propagation in Con-
tric conductivity of MNMts 3-13 manganin and MNMts
stantan, is a convenient time marker and may be used
Constantan 40-1.5 on pressure under shock compression,
to determine the delay of the emergence of conductivity
Fiz. Goreniya Vzryva, 8, No. 1, 147 149 (1972).
in the substance considered.
6. S. D. Gilev,  Electromagnetic effects in a measure-
The disagreement between the experimental and
ment cell for investigating the electrical properties of
numerical dependences may be caused by the effect of
shock-compressed substances, Fiz. Goreniya Vzryva,
the finite thickness of the shock front, the deviation
30, No. 2, 71 76 (1994).
of the shock wave from the planar form, and the elec-
7. D. D. Bloomquist, G. E. Duvall, and J. J. Dick,  Electri-
tromagnetic field nonuniformity. These factors are not
cal response of a bi-metallic junction to shock compres-
taken into account in the model. With these allowances,
sion, J. Appl. Phys., 50, No. 7, 4838 4849 (1979).
the present model may be applied for diagnosing shock-
8. L. C. Chhabildas and J. R. Asay,  Rise-time measure-
wave processes in metals. This experimental technique
ments of shock transitions in aluminum, copper, and
has a number of advantages. Thus, for example, the
steel, J. Appl. Phys., 50, No. 4, 2749 2756 (1979).
electric conductivity of metals is measured under con-
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high pressures, in: P. Caldirola and H. Knoepfel (eds.),
the classical method of thin foils [9]. This allows a cor-
Physics of High Energy Density, Academic Press, New
rect description of the state of the substance for high
York (1971).
energy densities. In particular, it seems of interest to
study the defects of the crystalline structure of metals
under conditions of a controlled loading rate.
CONCLUSIONS
Numerical [1, 2], analytical [3], and experimental
studies performed in the present work allow us to jus-
tify the electromagnetic model of shock compression of
a conductor in a magnetic field. The electromagnetic
model proposed describes experimental data on shock
compression of Constantan. With the above allowances, [ Pobierz całość w formacie PDF ]