CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
RECENT ADVANCES IN QUASMSENTROPIC COMPRESSION
EXPERIMENTS (ICE) ON THE SANDIA Z ACCELERATOR
C. A. Hall, J.R. Asay, M.D. Knudson, D.B. Hayes, R.L. Lemke,
J.P. Davis, C. Deeney
Sandia National Laboratory, Albuquerque, NM87185-1181*
Abstract. The Z Accelerator is a pulsed power machine capable of delivering currents to loads of
-20 MA over times of 100-300 ns. This current produces smoothly increasing, time dependant
magnetic pressures that can be applied to specimens allowing quasi-isentropes for these materials
to be inferred. A new load design has been developed that allows this pressure to be uniformly
applied to as many as 8 samples simultaneously. Diagnostics have recently been fielded that have
resulted in an increased understanding of the magneto-hydrodynamic effects and our confidence
in the utility of this experimental configuration for EOS measurements. Efforts are also underway
on Z to provide a capability for shaping the pressure profile applied to the samples which should
increase useful sample thicknesses to > 1mm by eliminating the formation of low-level shocks. In
addition to direct measurements of quai-isentropic material response, the impulse from this loading technique has been demonstrated to launch macroscopic flyer plates to velocities of-21 km/s
for high-pressure Hugoniot studies. Results of ICE measurements on 6061-T6 aluminum to -1
Mbar will be discussed.
study aluminum to a stress state of -1 Mbar, constituitive properties2, optical effects in interferometer windows3, phase changes4'5, and energetic
material response6. Strictly speaking, compressive
isentropic material response implies that the compression is both adiabatic and reversible. Ramp
loading of solids over the timescales of these experiments (typically 100-300 ns) is adiabatic but
not perfectly reversible. Viscosity, strength effects, and phase transition kinetics, if present, are
dissapative terms that produce entropy and are
present to some degree in all solids. Therefore,
ICE is actually quasi-isentropic, but ramp loading
of solids has historically been referred to as isentropic and this convention will be used throughout
the remainder of the paper.
The ramp loading capability on Z can also be
used to make high-pressure Hugoniot measurements with accuracies approaching that of conventional gas gun data. Macroscopic aluminum flyers
of -12 mm width and -0.5 mm thickness have
been launched to velocities of 21 km/s allowing
INTRODUCTION
A principal goal of the Sandia shock physics
program is to establish a capability to make accurate equation of state (EOS) measurements using
the Z pulsed power machine. Early efforts centered on use of high energy x-rays from Z-pinches
to produce ablativly driven shocks. Difficulties
with steady shock durations, fiber-coupled diagnostics, and the ability to achieve 1-D loading hindered our efforts. However, recognition by Asay
that pressure acting on samples from the smoothly
increasing magnetic fields generated as the machine discharged could produce high magnitude,
shockless ramp waves led to the development of
isentropic compresion experiments (ICE) on Z1.
Recent advancements in this technology have enhanced the quality of EOS information that can be
obtained through improvements to loading conditions, our understanding of MHD effects, and the
ability to field accurate, complex targets as required. This capability has recently been used to
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kbar (26 mm wide panels) to a peak of-1.5 Mbar
(15 mm wide panels).
A major advance in the panel arrangement is
the ability to create 1-D planar loading over a
large portion of the panel face, thus allowing
large, nonconductive samples to be studied. Static
electromagnetic simulations using the code
QUICKSILVER9 indicate that for the 26 mm wide
panels, an 11 mm region with 1% horizontal
loading uniformity exists in the center of the
panel, and covers its entire height. When the
panel is decreased to 15 mm in width, the 1% uniformity region is reduced to ~6 mm. These results
have been experimentally validated using a spatially resolved line imaging interferometer10 to the
light-limited resolution of the diagnostic. Results
indicated that uniformity over this region was in
agreement with the simulations.
symmetric impact studies of aluminum to pressures
approaching 5 Mbar. These flyers have also been
used as a high-pressure, constant drive input for
the Sandia National Laboratories effort to obtain
the EOS of liquid deuterium.
SQUARE PANEL GEOMETRY
The Z Accelerator7 is a low inductance pulsed
power generator capable of capacitively storing
11.6 MJ of electrical energy. The accelerator uses a
combination of fast switches and transmission lines
to deliver a 20-MA, 100 - 300 ns risetime current
pulse to generate time-varying magnetic fields
between the anode and cathode that continuously
load planar specimens under study. Low inductance loads designed for the Z accelerator are
fielded at the center of Z's radially converging
magnetically-insulated transmission lines.
When first attempted on Z, ICE samples were
limited to material disks pressed into stainless
steel conductors1. This limited the ability to assemble multiple material layers either before or
after the pressing process due to sample distortions. In addition, magnetic pressure was not constant across the samples due to the radial, converging geometry or varying vacuum gap between
the current carrying conductors at the point where
they were mounted.
These limitations led to the development of the
"square panel geometry" as shown in Figure 1
which is now the standard experimental configuration used for ICE on Z8. In this arrangement,
four seperate panels are manufactured independently, with one side used to carry the current during the experiment (power flow surface), and the
other containing one or more counterbores with
prescribed conductor thicknesses for gathering
experimental data. Both the powerflow surface
and counterbore floors are diamond machined to
tightly constrain both surface figure and parallelism. Because magnetic pressure scales with the
square of current density, and current density at
the sample location is simply the current divided
by the current carrying perimeter, loading pressure
can easily be affected through changes in panel
width. Several panel widths have been successfully used to produce loading from a peak of ~500
FIGURE 1: The newly developed "square panel
geometry "for conducting ICE on Z.
Symmetry of loading between panels has also
been characterized8. VISAR11 was used to record
surface motion at the same points on both the upper and lower portions of counterbores on multiple
panels. Results show that, in general, loading is
the same to approximately 1.5-2% between panels.
Efforts are underway to improve this with more
careful panel placement relative to the cathode.
MHD EFFECTS
When obtaining material response information
from observing ramp wave evolution, it is essential
1164
rately characterized along the Hugoniot to stresses
greater than 1 Mbar14.
The experiment, shot Z575, used 15 mm wide
6061-T6 aluminum panels with 10 mm diameter
counterbores with 400 jiim, 498(im, and 851jim
floor thicknesses, backed by nominally 1 mm
thick, 6 mm diameter LiF interferometer windows.
Epoxy was used to bond the windows to the aluminum with a typical thickness of - 2 jum. The
interface surface of each window was coated with
Ijim of aluminum prior to bonding to provide a
specular reflector for the interferometer (VISAR).
Velocity was recorded for each of the material
thicknesses at the aluminum-LiF interface with
resulting wave profiles shown in Figure 2.
that the material be at a known initial state. This is
an area of concern when the ramp waves are generated through pulsed magnetic loading because
magnetic field can potentially diffuse through the
sample under investigation causing joule heating
and density variations. This effect could lead to
systematic errors in the resulting inferred pressurevolume material response.
An effort to characterize, and be able to accurately model, this field diffusion was undertaken.
Data was taken at specific material depths in both
copper and aluminum where diffusion was predicted to occur (using Lee-Moore conductivity
models in an MHD code) during the ramp compression. Both time resolved rear surface velocity
measurements using VISAR and time resolved
field intensity measurements using Bdot probes12
were taken. The resulting records were overlayed
to define a minimum material thickness where diffusion does not occur during compression for both
copper and aluminum at given current densities
and profiles useful for ICE.
In addition, this and other data was modeled
with ALEGRA, an MHD code under development
at Sandia National Laboratories, to compare predicted diffusion rates to data13. In general, predictions were consistently overestimating diffusion
rates by approximately 35%. It was determined
that the existing conductivity models were inadequate over the range of conditions encountered on
the power flow surface in a typical Z firing. Modifications to the model were made in the description
of conductivity at the onset of melt. Comparisons
between simulations and data after the modifications were made indicate good agreement.
0.75
0,8
0.85
0.9
Time, microseconds
0.95
FIGURE 2: Velocity profiles (shot Z575)from
which the aluminum isentrope to -1 Mbar was
inferred
Z575 was analyzed using the method of characteristics15'8. For this approach, the Lagrangian
sound speed (CL) was obtained as a function of
particle velocity (up) at 0.01 km/s increments.
Stress and specific volume were then inferred from
the relations dp = p0(CL)dup and dv = l/v0(dUp/CL).
The material must be assumed to be rate independent for these relationships to apply. To validate this
assumption, arrival times for characteristics at 0.5
km/s increments were plotted versus initial material thickness for each of the three samples and
found to be straight within experimental error. The
stress-volume curve that resulted from this analysis
is shown in Figure 3 compared to published Hugoniot data and a prediction for the isentrope using a
1.0 Mbar ICE ON ALUMINUM
Previous ICE studies on aluminum and copper
were limited to stress states of ~300kbar8'2 In these
materials, as with many, there is little difference in
P-v response between the isentrope and Hugoniot.
This is useful when validating the technique, but it
was desired to extend ICE to a stress level where
deviation between the two curves could easily be
seen. Aluminum was chosen to be investigated
because it is a standard panel material for ICE, it is
reasonably well understood, and it has been accu1165
simple model with a linear Us-up relationship and
y/v held constant,
PULSE SHAPING
As has been discussed, there is a minimum material thickness required to prevent magnetic field
diffusion from influencing the data during compression. This requirement, in combination with
the need to keep wave reflections from influencing
the results when samples are bonded to the aluminum or copper counterbore floors, defines the
minimum sample thickness for ICE. For accuracy
in material response inferences using characteristic
analysis, a large seperation (AX) in sample thickness is needed for accuracy in determineing CL.
Therefore, it is desirable to have an ability to
shocklessly load thicker samples.
In many materials, Lagrangian sound speed (CL)
varies more for a given increment of stress where
compression is the greatest (i.e. before the material
response stiffens in the P-v plane). When the pressure characteristics associated with their respective
Lagrangian sound speeds are plotted in a material
thickness vs. time plot (X-t plot), it can be seen
that intersection of the early characteristics occurs
before those arriving later in time for a linearly
increasing input pressure profile. This is shown
schematically in Figure 4. The result of the intersection of these characteristics is a low level shock
that forms early in time and grows, as was typically seen when the "standard" pressure profile
available on Z was used early in ICE development.
Z575, aluminum ICE data
0.20
0.25
0.30
0.35
0.40
specific volume, cm3/gm
FIGURE 3: the inferred aluminum isentrope to
~1 Mbarfrom shot Z575 compared to the Hu~
goniot and a predicted isentrope using y/v as a
constant
It appears there is good agreement between current data and the simple theory used to predict the
isentropic response of 6061-T6 aluminum to this
stress level. Error bars on the IMbar data are determined from accuracy in relative timing between
velocity profiles, accuracy in mass velocity measurements from VISAR, and sample characterization.
With all VISAR measurements made through
LiF interferometer windows in these experiments,
effects of ramp loading on the strain-dependant
index of refraction window calibration must be
considered. Recent theory reported by Hayes16 and
supported by data in sapphire3 indicate that when a
linear index of refraction vs. density relationship
describes a window material, the calibration factor
used to infer interface velocity information through
the window is the same for ramp loading as for
shock loading. Recent reanalysis of published
shock data on LiF17 indicate that a linear relationship does represent the material to within experimental error. Therefore, it is assumed that the
window correction used to obtain the velocity data
in these experiments is adequate. Experiments are
currently underway to validate this assumption.
Pressure characteristics
jUnshocked
Region
dt
Formation of premature shock
Material thickness
FIGURE 4: A figurative X-tplot showing how
pressure characteristics intersect early in time
for a nonlinear material and linear ramp
loading
Figure 5 shows this effect when LiF was loaded to
-IMbar using ICE on Z with 0.25, 0.5, and 1.0
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mm thick LiF samples backed by LiF interferometer windows. Each sample/window assembly
was mounted on a 400^im aluminum conductor.
The interface velocity between the common conductor and a LiF window is labeled as "input",
2.5
Z737, aluminum
2-
1.50,8mm
1 -
Ice on LiF
0.5-
0
0.5
0.75
0,85
0.9
0.7
0,9
Time, microseconds
1.1
FIGURE 6: Shot Z737, -500 kbar aluminum
with pulse shaping applied. Shockless loading
seen at a thickness of 1.5 mm
0.95
Time, microseconds
FLYER PLATES
FIGURE 5: Shot Z576, -1 Mdar 0.25,
0.5, and LO mm thick LiF backed by LiF windows
showing formation and growth of shock,
In addition to studies of material properties along
the isentrope, the impulse from ramp loading can
be used to impart momentum to plates for impact
studies giving material response along the Hugoniot. Initial attempts at launching plates on Z18 of
~10 mm diameter and on order 0.5 mm thickness
resulted in velocities of 10 km/s for copper, 12
km/s for titanium, and 13 km/s for aluminum.
Plate motion was continuously monitored throught
the launch cycle with VISAR. In addition, diagnostics were fielded to investigate plate integrity
and state. For these launches, the 1.5 Mbar panel
configuration was used with a partial machine
charge.
Recently, an aluminum flyer was succesfully
launched to a terminal velocity of 21 km/s19 on Z
using a similar configuration, but with an increased
current density acting on the panels. Two 1.5
Mbar square load panels (15 mm wide) were
seperated by two 8 mm wide spacers forming a
rectangle instead of a square. In addition, the entire panel was machined to an initial thickness of
725 pm except for a 2.0 mm perimeter which gives
the panel structural integrity. Because of the current density increase, the loading pressure increased to -2.5 Mbar. The standard, essentially
linear current profile was used causing a high
loading rate during launch. The result is an ~700
To extend shockless loading using ICE to
higher stresses in many materials, or to investigate
more compressible materials at lower stresses, the
time-dependent loading rate for a given nonlinear
material needed to be controlled. An effort was
undertaken on Z to institute a method for shaping
the input magnetic pressure pulse. This was accomplished by discharging one forth of the machine's stored energy 100-200 ns prior to the main
pulse, and has been demonstrated on multiple firings, In addition to the prepulse, the risetime of the
main discharge can be extended to ~240 ns. A
combination of these two capabilites was used to
investigate aluminum to -SOOkbar. The resulting
velocity profiles for the 0.8 and 1.5 mm thick samples are shown in figure 6. As can be seen, there is
no evidence of a shock in the thicker profile, but it
appears that a large amplitude shock would form in
the velocity range of 0.2 — 1.75 km/s range if the
wave were propagated into a thicker sample. This
is in stark contrast to shots where pulse shaping
was not used and smaller shocks formed much
earlier in time.
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kbar shock causing initial plate motion as shown in
the velocity profile of Figure 7, This launch capability has been used to investigate the Hugoniot
response of aluminum to, and release from, ~5
Mbar20.
2
D.B. Reisrnan, A. Toor, R.C. Cauble, C.A. Hall,
J.R. Asay, M.D. Knudson, and M.D. Furnish, J.
Appl Phys., 89, 3, pp 1625-1633, (2001),
3
C.A. Hall, D.B. Hayes etal., to be published.
4
J.P. Davis, D.B. Hayes, "Investigation of Liquid™
Solid Phase Transition Using Isentropic Compression Experiments (ICE)99, this proceedings.
5
J. R. Asay, C.A. Hall, etal, in Shock Compression of Condensed matter-1999, edited by M.D.
Furnish, L.C. Chhabildas, and R.S. Hixon, AIP
Conference Proceedings, Melville, NY, pp.
11514154.
6
D.B. Reisman, J.W. Forbes, etal., "Isentropic
Compression of LX-04 on the Z Accelerator",
this proceedings,
1
M.K. Matzen, Phys. Plasmas. 4 (5), 1519-1527
(1996).
8
C.A. Hall, J.R. Asay, etai, Rev. Sci Instrum., 72,
9, Sept 2001
9
D.B Seidel, MX. kiefer, R.S. Coats, T.D. Pointoin, J.P. Quintenz, and W.A. Johnson, Proceedings of CP90 Europhysics Conference on
Computational Physics, edited by A. Tenner
(World Scientific, Singapore), pp. 475-482
(1991)
10
W.M. Trott, M.D. Knudson, etal, in Shock
Compression of Condensed matter-1999, edited
by M.D, Furnish, L.C. Chhabildas, and R.S.
Hixon, AIP Conference Proceedings, Melville,
NY, pp. 993-998.
11
L.M. Barker and R.E. Hollenbach, J. Appl Phys.
43,4669(1972).
12
G. Sharp, Dissertation, Univ. New Mex., Oct.
2001
13
Lemke, this proceedings
14
A.C. Mitchell and W.J. Nellis, /. Appl Phys.,
52, 5, pp. 3363-3374, (1981).
15
J,B. Aidun and Y.M. Gupta, J. Appl Phys. 69,
6998-7014(1991).
16
D.B. Hayes, /, Appl Phys., 89, 11, pp. 64846486, (2001)
17
J.L. Wise, and L.C. Chhabildas, in Shock Waves
in Condensed Matter, Edited by Y.M. Gupta
(plenum, New York, 1986), P. 441.
18
C.A. Hall, M.D. Knudson, etal., Intl. J. Impel
Eng, 2001,
19
M.D. Knudson, to be published.
20
M.D. Knudson, to be published.
20
0
50
100
150
Time (ns)
200
250
FIGURE 7: Time resolved velocity profile of a
21 km/s aluminum flyer launched on Z.
SUMMARY
Ramp loading experiments to obtain material
response measurements along the quasi-isentrope
to -1 Mbar have been demonstrated in aluminum
using pulsed magnetic loading on the Z accelerator. These results were obtained with improvements in experimental configuration over earlier
attempts. These improvements provided uniform
pressure loading over large diameter samples with
attached interferometer windows. Results show
deviation from the Hugoniot in agreement with
theoretical predictions using a simple material
model.
The ability to shape the input loading profile to
minimize low-level shock formation and an increased understanding of MHD effects will lead to
the design of more accurate experiments in the
future.
Macroscopic aluminum flyer plates have also
been launched on Z to velocities of 21 km/s with
dimensions that are useful for accurate material
response measurements.
REFERENCES
1
J. R. Asay, in Shock Compression of Condensed
matter-1999, edited by M.D. Furnish, L.C
Chhabildas, and R.S, Hixon, AIP Conference
Proceedings, Melville, NY, pp. 261-266.
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