Experimental and Theoretical Analyses of ExplosivelyFormed Fuse (EFF) Opening Switches
ABSTRACT The EFF is used at Los Alamos as the primary opening switch for high current applications. It has interrupted currents from ~10 kA to 25 MA, thus diverting the current into low inductance loads. To understand and optimize the performance of fullscale experiments, many parameters were studied in a series of smallscale experiments, including: electrical conduction through the explosive products; current density; explosive initiation; insulator type; conductor thickness; conductor metal; metal temper; and on. The results show a marked inverse correlation of peak EFF resistance with current density. In this paper we postulate and refute a simple extrusion mechanism of EFF operation; demonstrate that the EFF switch has a nearideal profile for producing flattopped voltage profiles; and explore possible mechanisms for the degradation of small scale switch performance.
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ABSTRACT: A series of 1D isentropiccompression experiments (ICE) has been initiated using the highexplosive pulsedpower (HEPP) system. Accurate highstress isentropic equationofstate (EOS) data had been reported using the HEPPICE system. A number of important advantages of the system were demonstrated, including higher stresses, higher accuracy, and larger sample sizes than those of other methods. Several potential design improvements have since been identified and tested. The storage inductor was eliminated, and the experiment was performed before the output of the plate flux compression generator could shortcircuit itself. This eliminated the loss of current that occurs when the generator plates bounce apart. A new design of explosively formed fuse opening switch was employed with a multipoint initiation system that reduced the explosive mass, significantly reduced the timing jitter by eliminating air gaps, and minimized flux losses. In addition, with this new switch, the resistanceversustime profile may be adjusted by controlling the initiation times of its four quadrants. Anomalous results were obtained with the new switch. The results of using this switch in an EOS experiment on pure tantalum are reported.IEEE Transactions on Plasma Science 09/2010; · 0.87 Impact Factor
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EXPERIMENTAL AND THEORETICAL ANALYSES OF
EXPLOSIVELYFORMED FUSE (EFF) OPENING SWITCHES
Douglas G. Tasker, James H. Goforth, Henn Oona,
Los Alamos National Laboratory, Los Alamos, NM, USA
Gerald Kiuttu, Matthew Domonkos,
Air Force Research Laboratory, Albuquerque, NM, USA.
ABSTRACT
The EFF is used at Los Alamos as the primary opening switch for high current
applications. It has interrupted currents from ~10 kA to 25 MA, thus diverting the
current into low inductance loads. To understand and optimize the performance of full
scale experiments, many parameters were studied in a series of smallscale experiments,
including: electrical conduction through the explosive products; current density;
explosive initiation; insulator type; conductor thickness; conductor metal; metal temper;
and on. The results show a marked inverse correlation of peak EFF resistance with
current density. In this paper we postulate and refute a simple extrusion mechanism of
EFF operation; demonstrate that the EFF switch has a nearideal profile for producing
flattopped voltage profiles; and explore possible mechanisms for the degradation of
small scale switch performance.
INTRODUCTION
The EFF used in high explosive (HE) pulsed power circuits at Los Alamos is a
cylindrical switch. The cylindrical design simplifies HE initiation, reduces electrical
breakdown problems, and produces a compact device. However, these cylindrical
devices are too expensive and complex to use for routine and frequent testing. A small
scale EFF (SSEFF) is used instead for simplicity, and economy. These SSEFFs were
designed to match the electrical and physical conditions of the fullscale EFFs. The anvil
patterns are identical, and the current densities in most tests are matched to 87 kA/cm.
The effects of varying a wide array of parameters have been studied, including: the HE
type; the metal foil thickness [1]; the metal type; the metal temper; the current density
[2]; the addition of Teflon between the HE and the aluminum; the type of die plastic [1];
the cavitydepth in the plastic die; the cavity shape; the surface finish of the plastic; the
time of switch initiation relative to the peak current; and the load inductance [1]. The
effects of transient magnetic pressures on SSEFFs will be discussed in this paper.
ANALYSIS
The SSEFF design comprises the Teflon die, the HE, the aluminum foil, return conductor
and insulation, Figure 1. The die is a 19.05 x 165.1 x 165.1.mm Teflon block. A series
of 12.7 mm deep, 6.0 mm wide grooves are cut across the block with a center to center
spacing of 7.5 mm. This leaves a series of 1.5mm wide Teflon teeth. The foil is the
same as in the large scale EFF, i.e., 812.8µm thick 6061T6 aluminum; it is 6.35cm
wide in the SSEFF. The return conductors are 0.5in. thick, and 6.5in. wide.
Page 2
The EFF Resistance Profile
We refer to a number of features in the resistance profile in this paper, in particular first
motion, the knee, and the peak; see Figure 1. First motion is the time when the shock
wave from the detonating HE arrives at the interface between the foil and the plastic die;
the time axes are normalized to this. The knee is a saddle point in the resistance rise and
occurs ~3 µs after first motion. The structure of the resistance rise from the knee to the
peak determines the shape of the voltage profile across the switch. The peak is the
maximum resistance of the switch at ~4.5 µs after first motion.
Knee
First
motion
Peak
HE
PTFE
PE
C
C
PWL
C
PEPE
T
G
C
Figure 1. Left: SSEFF. T: teeth, C: conductors, HE: explosive, PE: insulation, PTFE:
die, G: gaps, PWL: plane wave lens. Right: Typical resistance plot.
Knee to peak profile, and the flattopped voltage
The EFF can produce a flattopped voltage pulse; for this there is an optimum resistance
time profile R(t) for any given inductance, L. Consider the series LR(t) circuit, where
R(t), the EFF, shares the same current I(t) as a fixed inductor, L. Using Kirchoff’s
( )
( ) ( )0
L I t R t
dt
voltage law,
dI t
+
=
. Given the initial current, I0, the general solution for
the voltage across the resistor is
( )
L
0
( )( ) ( )
I t R t
( )
R tdt
V tI R t e
−
==
∫
. For a flattopped
voltage pulse,
( )
L
( )
R tdt
R t e
−∫
is constant. Then,
2
( 0)
Rdt
L
dR
dt
R
L
e
−
=
∫
≠
. If tinf is the time
when R(t) would go to infinity, the solution is
inf
t
( )
L
R t
t
=
−
(1)
If t0 is the time when the resistance reaches the knee, and I0 = I(t0), the voltage is
, which is clearly a constant with time while the resistance obeys
(
0 inf0
( )
V tI Ltt
=÷
(1). We have fitted Equation (1) to typical resistance data, shown on the left of Figure 2.
The best fit is L = 213.1 nH and tinf = 4.468 µs. Clearly, from the knee to the peak the
concave upward slope of the resistance fitted the equation well. The voltage is from a
circuit calculation for a 213.1 nH parallel inductance and I0 = 415 kA; note the flat top
from ~2.8 µs to ~3.8 µs. So, the EFF is wellsuited to the generation of flattopped
voltage pulses. Ideally, the resistance before the knee should rise quickly to minimize
flux loss; however, the actual rise is parabolic.
− )
Page 3
0
50
100
150
200
250
300
350
1.5 2.5 3.54.5
µs
R
mohm
0
10
20
30
40
50
60
70
V
kV
Metal extrusion model
Assuming two dimensional flow of the foil, it is extruded and stretched around the teeth
of the Teflon die. The foil resistance along the side walls is
length, w the width is a constant, d its thickness, and η its resistivity. As the pressures in
the gas cavity are low (~1 GPa), we assume that the volume, v, is approximately constant.
Combining equations we have
stretches into the cavity, and η is a function of the temperature T; T is estimated to be
~600K, due to shock heating, see below. We also assume that the length of the sidewall
/
Rl wd
η=
where l is the
. The length is a function of time, t, as it
conductors increases approximately linearly with time,
2( )/
t
l
η
t
RTv
=
0
()
0
t
dl
dt
lltt
≈+−
, where l0 is the
initial length at first motion, t0, and the shape of the resistance time profile is initial length at first motion, t
⎧
≈+
⎨
⎩
Comparing the typical R(t) profile on the right of Figure 2, the initial rise has a similar
parabolic shape to (2). The fit to the data is
3.2714×10
this metal extrusion model accurately describes the resistance rise of the EFF, but, when
we quantify the fit the model is inadequate. Comparing with the fit, b should equal
dl
Tv
dt
typical SSEFF, so the initial length l0 = 60 mm; w = 63.5 mm, d = 812.8 µm, and v0 =
3.1 µm3. Typical velocities of metal jets formed by HEs are ≤8 km/s, so we assume dl/dt
dl
T
dt
(3.2714×105). Hence, metal extrusion alone cannot account for the magnitude of the
resistance rise.
Correlation of SSEFF performance with various parameters
To understand and control switch performance, we plotted and tabulated various switch
performance parameters for the SSEFF against a range of controlling parameters. Of the
comparisons, the best correlations were between resistivity, and current density or
magnetic pressure Pb [2]; these were
and
0.966. Here the calculated magnetic pressure was not corrected for the geometry of the
e
0, and the shape of the resistance time profile is
2
()
t
Rltt
dt
⎭
00
( )/
T
η
dl
⎫
⎬
−
v (2)
where a = 0.59, b =
2
0
( ){( )}
R ta b tt
=+−
5, t0 = 4.79 ns; the correlation coefficient is 0.999. The good fit suggests that
( )/ .
η
Now η(600K) = ~100 nS/m; there are ten gaps, each 6 mm long for a
= 8 km/s. From these data,
( )/
η
1466;
v
≈
this is much smaller than b
with correlation coefficients of 0.968 and
2
(/) 319.02 1.5303
−
/(/)
R
(
cmgap I W kA cm
Ω=×
2
(/)286.22.0416)
B
RcmgapP MPa
Ω=−×
V
R
t0
tinf
Fit
0
50
100
150
200
250
300
1.52.53.5 4.5
t µs
R
mohm
Fit
Figure 2. Left: R(t) fit above the knee, and voltage V. Right: Fit to R(t)below knee.
Page 4
EFF electrodes and the return conductor; it was defined as
permeability of free space (4π×107) and J is the linear current density (I/W) current (the
actual pressures are given below). If the fits were extrapolated, the resistivity would
intersect the zero resistivity axis at either a J of 208 kA/cm, from the current density
correlation (equivalent to 272 MPa), or at a pressure of 140 MPa from the pressure
correlation, which is equivalent to 150 kA/cm. To test these predictions, an experiment
was fired at 157 kA/cm and the SSEFF failed to open, thus supporting the prediction of a
150kA/cm limit (magnetic pressure) as opposed to the 208kA/cm limit. The correlation
with magnetic pressure was therefore deemed to be more appropriate. Later, large scale
experiments were performed at current densities of 157 kA/cm and no degradation of
performance was observed. Consequently, the degradation was determined to be peculiar
to the design of the SSEFF.
Mechanisms for EFF performance degradation
The inverse correlation of resistivity vs. pressure begged the question of what mechanism
degraded SSEFF performance. Candidates considered included Joule heating leading to
thermal softening of the metal; Joule heating leading to thermal expansion and
deformation of the foil; shock melting; uniform and nonuniform magnetic loading of the
foil; magnetic deadpressing of the HE [2]; and electric breakdown [2] or conduction in
the product gases at the higher applied fields. In a typical SSEFF experiment, the current
rises to a peak according to the LCR resonance of the circuit, and the EFF is usually
opened at the time of the first peak; i.e., after approximately one quarter cycle. From
tabulated resistivities, the rise in temperature, of a 32mil thick 6061T6 foil, due to
Joule heating is estimated to be 23 K for a current density rising sinusoidally to a peak of
74 kA/cm in 35 µs. We can compare the temperature rise due to Joule heating to that due
to shock heating.
The theory of shock reflection at a boundary is based on the fact that the stresses and
particle velocities either side of the boundary are equal [3,4]. From the JWL adiabatic
for HE PBX9501 [5], and the shock Hugoniot of 6061T6 [6], we calculate that the
detonating HE initially shocks the aluminum to a pressure of 40.33 GPa and a density of
3553 kg/m3. From the LANL thermodynamic tables [7], we calculate that T rises from
300 K to 981K under shock loading, or ~30 times the rise due to Joule heating; it then
falls isentropically to ~600K as the detonation gases expand. Shock melting can be
discounted because the phase diagram of aluminum [8] clearly shows that the aluminum
remains in the FCC phase at this temperature and pressure. Of course, the large scale
EFF would undergo the same shocked loading as the SSEFF, so shock heating cannot
explain the differences in their performances.
Magnetic pressures under typical conditions – uniform current density
The magnetic pressure pushes the foil against the HE, and it can compress the HE and
reduce its sensitivity to the point that it may not initiate. This HE deadpressing depends
on the current density and the strain rate [2]. It was shown that deadpressing is a
feasible mechanism for failure, but only uniform magnetic loading across the width of the
foil was considered in that study. Unlike the large scale EFF, the magnetic loading on a
SSEFF is very nonuniform, as we will see.
2
1
0
2
bPJ
μ=
where µ0 is the
Page 5
In a typical SSEFF experiment, the sinusoidal current reaches a peak current density of
86.6 kA/cmwidth at 32 µs. At this peak, dI/dt is zero, so the current densities across the
width of the conductors are uniform, but the magnetic pressures are not. From field
calculations [9], the corresponding magnetic pressure applied to the foil is 42 MPa at the
inside edges nearest the return conductor, and 19.5 GPa at the inside center, see Figure 3.
(Under dynamic conditions, an even greater proportion of the current flows on the outside
edges.) As PB (42 MPa) does not exceed the compressive strength of the HE (60 MPa) at
the foil edges, the foil will deform elastically and compress the HE before the arrival of
the detonation wave and may force a crack to propagate. A corresponding compressive
strain of ~0.1% has been estimated [2].
Pore collapse in explosive – uniform current density
A typical PBX9501 HE charge is pressed to a density of 1840 kg/m3 compared with its
theoretical maximum density of 1855 kg/m3; it therefore has a pore volume of 0.8%.
Consequently under standard conditions (550 kA peak), a 0.1% bulk compression will
reduce the void volume by 14% to 0.7%, which will reduce the sensitivity of the HE
[10], but probably not prevent it from detonating.
Magnetic pressures at higher current densities
Consider the EFF at the time of peak current, again when dI/dt is zero, but this time with
a peak current density of 150 kA/cmwidth, instead of the standard 86.6 kA/cmwidth.
As before, the current is perfectly uniform across the width of the foil. From the plot of
resistance versus pressure, we can predict that the switch will fail to open at this current
density. The pressure at the foil’s edge will then be 126 MPa and 58.5 MPa at the center.
As the compressive strength of the HE is 60 MPa, the HE will be plastically deformed
(crushed) over the entire surface under the foil, so the HE will be compressed to zero
porosity across the entire width, i.e., to >1855 kg/m3. This elimination of HE voids will
prevent detonation, i.e., it will deadpress the HE [10]. Note that the compression is
isentropic (shock less) and of relatively low pressure, so the HE will not be initiated
during this compression process. Consequently, there will be a compressed layer of HE,
that may be cracked, that will not detonate and will act as a dead weight against the foil.
The acceleration of the foil will therefore be reduced, and the EFF performance will be
degraded. The nonuniform magnetic loading of the foil across its width will cause it to
bow as it compresses the HE. Therefore, the center of the foil would be separated from
the HE in the center, and it would be separated from the Teflon die at the edges, see
Figure 3. This will reduce the extrusion of the foil into the Teflon die by the HE gases.
Figure 3. Left: Magnetic pressure at current peak. Right: Explosive deformation.
Page 6
The separation of the foil from the HE will relieve the magnetic pressure to zero in the
center, and concentrate it at the edges. So the deadpressing would be confined to the
edges of the HE.
SUMMARY AND CONCLUSIONS
We have derived the ideal resistance profile for an opening switch to produce a flat
topped voltage output, and have shown that the EFF is wellsuited to this purpose. A
theoretical metal extrusion model was proposed to account for the resistance rise in the
EFF, and the form of the predicted rise matched the experimental closely; but the
predictions values were wrong. Therefore, metal extrusion alone does not describe the
EFF behavior; the true mechanism has not been established. An inverse correlation of
peak resistance with magnetic pressure was observed for the SSEFF. We have concluded
that these effects are due to nonuniform magnetic loading of the foil in the SSEFF.
Metal fusing, especially along the edges of the foil in the SSEFF is also possible.
(Studies of the resistance of large scale EFFs show a small dependence on current
density.) Metal fragmentation and subsequent conduction in the HE’s product gases are
also possibilities. In unpublished work, we have shown that the switch resistance is
strongly dependent on the temper of the metal foil. More brittle foils reach higher
resistances faster. And, in other work we have shown that the switch resistance is
reduced when HEs with high conductivity product gases are used to drive the foil.
ACKNOWLEDGMENT
We wish to acknowledge Dennis Herrera, Dave Torres, and Jim King for their excellent
experimental work. This study was funded by the US Department of Energy (LAUR
066087) and the US Air Force Research Laboratory.
REFERENCES
1. D.G. Tasker et al., Eighth International Conference on Megagauss Magnetic Field
Generation and Related Topics, Tallahassee, FL, USA, Oct 1823, 1998, p.619.
2. D.G. Tasker et al., IEEE International Pulsed Power Conference, 2005, Monterey, CA.
3. Ya. B. Zel’dovich and Yu. P. Raizer, Physics of Shock Waves and HighTemperature
Hydrodynamic Phenomena, Academic Press, New York, 2002, Chapter XI.
4. G.E. Duvall, Procs. Response of metals to high velocity deformation, 1960, 9, p.165.
5. B. M. Dobratz, P.C. Crawford, “LLNL Explosives Handbook,” UCRL52997, 1985.
6. “Selected Hugoniots,” Los Alamos Scientific Lab., May 1, 1969, LA4169MS.
7. “Sesame: The Los Alamos National Laboratory Equation of State Database,” LAUR
923407, Editors Stanford P. Lyon and James D. Johnson., 1992. Sesame Table 3715.
8. David A. Young, Phase diagrams of the elements, Univ. of California Press, 1991.
9. Calculated with FlexPDE Professional Version 4.2.16.2D.
10. A.W. Campbell et al., 8th Symp. on Detonation, Albuquerque, NM, 1985, p.1057.