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COMPACT EXPLOSIVE DRIVEN SHOCK WAVE FERROMAGNETIC
GENERATORS*
S. I. Shkuratov, E.F. Talantsev, M. Kristiansen, J. Dickens,
J.C. Hernandez, and A. Neuber
Pulsed Power Laboratory, Department of Electrical and Computer Engineering,
Texas Tech University, Lubbock, TX 79409-3102
Abstract
The results are presented of tests with compact,
explosively driven shock wave ferromagnetic generators.
The shock wave from high a explosive charge is passed
along the axis of a cylindrical, hard magnet. Two types of
permanent magnets were used in the experiments: rare-
earth NdFeB cylinders (D = 2.5 cm, L = 1.9 cm) and hard
ferrite BaFe
2
O
3
cylinders (D = 2.2 cm, L = 2.5 cm). The
shock wave demagnetizes the cylinder, reducing the flux
from the remnant value to zero. This change in flux
generates a voltage in the winding. The current generated
in the loads of the generators yielded a peak of 0.75 kA.
The operation of the shock wave ferromagnetic generators
was analyzed by the Maxwell 3D code. An analysis is
given on the specific features of pulse generation in a
system like this.
I. INTRODUCTION
The development of compact, explosive driven pulsed
power sources of initial energy is based on four
fundamental effects of solid state physics: the
piezoelectric effect (generation of electrical charge by a
material when it subjected to pressure forces), the
ferroelectric effect (depolarization of a material under the
action of a shock wave), the reverse magnetostrictive
effect (generation of magnetic field by a material when it
deformed) and ferromagnetic effect (demagnetization of
permanent magnet by a shock wave). In this paper the
results are presented of generation of electric pulses by
explosive-to-electric transducers that uses the remnant
magneto-static energy existing in hard ferromagnetic
materials.
II. PRINCIPLES OF THE OPERATION
AND DESIGN
The generation of electrical power is based on the fact
that the remnant magnetization of a ferromagnetic
material may be reduced or completely destroyed by a
shock wave, which randomly orients the magnetic
moments. When the alignment of magnetic moments is
randomized, there is a change in flux in the magnetic
________________________
Figure 1. Schematic diagram of the operation of the
shock wave ferromagnetic explosive-to-electric
transducer. (a) – initial stage of the system. (b) – shock
wave travels through the magnetic cylinder. (c) – shock
wave passes the winding.
* This work is solely funded by New World Vista Program in the Air Force Office of Scientific Research (AFOSR).
(a)
(b)
(c)
0-7803-7120-8/02/$17.00 © 2002 IEEE
core. If there are windings on the core there will be a rate
of change of flux linkages and thus a voltage induced in
the windings. The operation of the ferromagnetic
transducer is to destroy the remnant magnetization by a
shock wave from a high explosive, the destruction taking
place at the velocity of the shock wave in the magnetic
material.
Consider the cylindrical body of a permanent magnet of
circular cross section (Fig.1a) with one turn of a wire
wound on the cylinder. The cross section of the core has
the diameter D. The total flux, Φ
o
, in the turn of wire is
Φ
o
= B
o
π
D
2
/4 (where B
o
is the magnetic field at the turn
location).
As the shock wave travels through the magnetic
cylinder (Fig.1b) for the time ∆t, the remnant magnetic
field in the cylinder will be destroyed in the length ∆l =
∆tV (where V is the velocity of a shock wave). Since the
velocity V of a shock wave in the solid is essentially
constant, the voltage generated in the single turn, EMF,
will be
EMF = dΦ/dt = d (B
o
π
D
2
/4)/dt = π
D
2
B
o
V/4d, (1)
where d is the diameter of the wire. The voltage
generated in a single turn for this geometry is a square
wave of magnitude π
D
2
B
o
V/4d with a time width, T
p
, of
d/V. If a coil has N turns of wire the width of the pulse
produced is T
p
= N d/V .
The magnitude of the voltage is proportional to the
diameter of the magnetic cylinder and inversely
proportional to the diameter of the wire used. The
duration is proportional to the number of turns and the
wire thickness.
The equivalent circuit of the ferromagnetic generator is
shown in Fig. 2. The induced voltage, EMF, is in series
with the inductance, L
c
, and the resistance, R
c
, of the
pulse-generating coil and the load, Z
l
.
Figure 2. Equivalent circuit of the shock wave
ferromagnetic generator.
Figure 3 presents the schematic diagram of the
explosive driven ferromagnetic generator (EDFMG). In
all shock wave experiments type C-4 high explosive was
used. In this set of shock wave experiments we used a
flyer plate design. We used axial detonation of the high
explosive. The semispherical impactor (flyer plate) is
responsible for the initiation of a shock wave in the
ferromagnetic body. The detonation velocity for C-4 is
8.37 km/s. The impactor speed has to reach 3-4 km/s to
initiate a shock wave in the active element. The shapes of
the flyer plates were precisely calculated so that a plane
shock wave was generated in the ferromagnetic active
element.
Explosive tests were performed in the explosive
facilities of the Pulsed Power Laboratory, Texas Tech
University. The measuring circuit is shown in Fig. 4.
Figure 3. Schematic diagram of the EDFMG.
Pulsed current was measured with commercial Pearson
Electronics current monitor, model 411. The pulsed high
voltage was measured with a Tektronix high voltage
probe, model P6015. All measuring devices were placed
in a protecting steel box.
Figure 4. Measuring circuit for experimental studies of
EDFMGs.
We performed shock wave experiments with two
different types of ferromagnetic active elements: rare-
earth NdFeB cylinders, D = 2.5 cm, L = 1.9 cm, and hard
ferrite BaFe
2
O
3
cylinders, D = 2.2 cm, L = 2.5 cm. Figure
5a shows the EFMFG in the charged state mounted in the
Figure 5. The EDFMG in the charged state (a) (the device
is pointed out by the white arrow). The EDFMG after the
test (b).
a
b
explosive tank. Figure 5b shows the EDFMG after the
test. The device was completely destroyed.
III. EXPERIMENTAL RESULTS
The current pulse waveform produced by the EDFMG
with an NdFeB active element is given in Fig. 6. The
current amplitude is about 0.75 kA. The FWHM of the
pulse is about 15 µs. The rise time is about 5 µs.
Figure 6. Operation of the EDFMG. Waveform of the
current pulse. The active element is an NdFeB cylinder (D
= 2.5 cm, L = 1.9 cm). The load resistance is 9 mΩ. The
load inductance is 1.7 µH.
The voltage pulse waveform is given in Fig. 7. The
duration of the voltage pulses is about 7 µs. The pulse
waveform has a multi-peak structure. The differences in
the shape and in the width of the voltage and the current
pulses produced are under investigation.
Figure 7. Waveform of the voltage pulse. The active
element is an NdFeB cylinder (D = 2.5 cm, L = 1.9 cm).
The load resistance is 9 mΩ. The load inductance is 1.7
µH. Attenuation 10 dB.
The generators are absolutely destroyed after the
explosive tests (Fig. 5b). In a few cases we recovered the
remainders of an NdFeB ferromagnetic active elements
after the tests. The pieces of NdFeB possess weak
magnetic properties that are not comparable with the
magnetic properties of the NdFeB before the test. A shock
wave demagnetizes of the NdFeB magnets almost
completely. The photo of one of the sets of the remainders
is shown in Fig. 8.
We performed series of tests with EDFMG having the
same active element (NdFeB) but with different inductive
load (7 µH, 22 mΩ). The current waveform has no
significant distinctive features from the current waveform
across the 1.7 µH load. The only difference is the lower
current amplitude: 260 A.
Figure 8. The remainders of an NdFeB ferromagnetic
active element after an explosive test. There is practically
no the attraction between pieces.
We carried out a series of explosive tests with shock
wave generators having hard ferrite BaFe
2
O
3
active
elements. The design of the generators in these
experiments was identical to the design of the generator
with NdFeB active elements. The current pulse waveform
of the generator is given in Fig. 9. The current amplitude
is about 130 A and the pulse width is about 30 µs.
Figure 9. Operation of the EDFMG. Waveform of the
current pulse. The active element is a BaFe
2
O
3
hard ferrite
cylinder (D = 2.2 cm, L = 2.5 cm). The load resistance is
9 mΩ. The load inductance is 1.7 µH.
IV. MAGNETIC FLUX IN AN OPEN
CIRCUIT
In the series of experiments described we used an open
ferromagnetic circuit design. An open ferromagnetic
circuit is a ferromagnetic system (magnetic cylinders,
discs, bars) having unclosed N-S poles and where the
magnetic flux closes through a nonferromagnetic medium
or through the space surrounding the two magnetic
poles. The amplitude of the pulse produced in the pulse-
generating coil depends on the rate of variation of the
magnetic flux inside the coil and the parameters of the
coil (Eq. (1)).
The manufacturers of magnets provide information
about properties of the materials in a closed circuit. A
closed ferromagnetic circuit is a ferromagnetic system
(magnetic toroids, rectangular cores, etc.) having closed
poles and in which the magnetic flux circulates inside the
circuit with little flux in the surrounding
nonferromagnetic space. Characteristics for NdFeB and
BaFe
2
O
3
in a closed circuit are given in Table 1.
Table 1. Characteristics of NdFeB and BaFe
2
O
3
in a
closed ferromagnetic circuit.
Material
B
r
(T)
H
c
(A-
turn/m)
H
ci
(A-
turn/m)
B
.
H
max
(T
.
A-
turn/m)
Max.
Oper.
Tem.(C)
NdFeB
1.23
9x10
5
1.1x10
6
2.8x10
5
150
BaFe
2
O
3
0.4
2x10
5
2x10
5
2.9x10
4
300
B
r
is the residual flux density; H
c
is the coercive force;
H
ci
is the intrinsic coercive force (the point at which the
hysteresis curve crosses the H axis); BH
max
is the
maximum energy product, and Max. Oper. Tem. is the
maximum operating temperature of the magnet.
We performed a simulation of the magnetic flux density
B and the magnetic intensity H of NdFeB and BaFe
2
O
3
in
an open circuit using the Maxwell 3D code. Figure 10
presents a schematic diagram of the ferromagnetic active
element with the winding for magnetic field and eddy
current simulations.
Figure 10. Schematic diagram for magnetic field and
eddy current simulations. Magnetic field is oriented along
Z axis.
Figure 11 presents the magnetic flux density inside and
outside the NdFeB cylinder having a diameter of 2.5 cm
and length of 1.9 cm. The magnetic flux in the winding
near the cylinder strongly depends on the distance and on
the position along the cylinder body. The flux near the top
and the bottom is significantly lower than the flux near
the middle of the cylinder.
Figure 11. Magnetic flux density inside and outside an
NdFeB cylinder (D = 2.5 cm, L = 1.9 cm).
V. EDDY CURRENTS
When a shock wave propagates in a solid magnetic
cylinder, there occurs disorientation of the magnetic
moments resulting in a decrease or complete disappe-
arance of residual magnetization. As this takes place,
some accompanying processes occur. The magnetic flux
in the cylinder, rapidly varying under the action of the
shock wave, induces eddy currents which in turn induce a
magnetic field of strength H directed to keep the magnetic
flux at its initial level. In the coil wound on the cylinder a
current is generated which induces a magnetic field
directed, like the field created by eddy currents, to keep
the magnetic flux at its initial level. The operating point
on the magnetization curve then moves to the right. We
performed a simulation of eddy currents in the core using
the Maxwell 3D code.
As it follows from the simulation results, eddy current
amplitude in the NdFeB body reaches a significant value,
950 A. The generation of eddy currents in the magnetic
cylinder reduces the efficiency of the generation of a
current pulse in the pulse-generating coil. The amplitude
of the pulse generated in the coil is directly proportional
to the resulting change in the magnetic flux density in the
active element ∆
∆∆
∆B = B
r
- B
0
, where B
r
is the initial
magnetic flux density in the core and B
0
is the flux density
remaining in the core. The resulting change in magnetic
flux density in the active element is responsible for the
generation of the current pulse. To estimate the resulting
change in magnetic flux density in the ferromagnetic
cylinder responsible for the generation of the current
pulse, we have performed a simulation of the processes
occurring in the ferromagnetic core with the use of the
Maxwell Simulator and experimental data of explosive
tests. The estimation of the resulting change in magnetic
flux in a pulse-generating system with the NdFeB active
elements gives ∆
∆∆
∆B = 0.05-0.1 T. This is less than 40% of
the magnetic flux of the NdFeB cylinders in an open
circuit.
VI. SUMMARY
The demagnetization of hard rare-earth intermetallic
compounds by a shock wave from high explosive and the
generation of high current pulses in compact explosive
driven ferromagnetic system is demonstrated
experimentally. The analysis of the processes in the
generator shows the significant effect of eddy current on
the efficiency of the generation. To suppress eddy currents
in the ferromagnetic active element and to increase the
efficiency of the shock wave ferromagnetic generator it is
necessary to redesign the pulse-generating unit, to split it
into separate parts insulated from each other.
VII. ACKNOWLEDGEMENT
The authors thank Dr. P. Worsey and J. Baird for their
technical contribution to the explosive test performance
and useful discussions. They also thank Dr. H. Krompoltz
for helpful discussions.