by Brian Fishbine
Small-scale laboratory experiments are helping to validate computer
simulations of nuclear weapon performance.
The goal of stockpile stewardshipand Los Alamos' core missionis
to ensure the safety, reliability, and performance of the nuclear stockpile.
The current ban on underground nuclear testing, however, severely limits
the options for carrying out this mission. As a result, we now rely heavily
on simulations produced by computer programs, or codes, to predict the
performance of a nuclear weapon under various conditions.
Simulations provide far more diagnostic information than a nuclear test
does. Using models of the physical processes that occur in a nuclear detonation,
a computer can calculate variables such as temperature and pressure for
any point in the calculational space of the simulated explosion with high
spatial resolutionfrom the time the virtual bomb goes off (or before)
to any time later.
New visualization tools can then present the huge volumes of information
produced by a weapon simulation in ways scientists can quickly grasp.
(A complete simulation produces nearly fifty times the information contained
in the Library of Congress.) For example, one of the new Los Alamos PowerWallswhich
each provides a 4- by 2-meter stereo displaycan immerse weapon scientists
in a full-color, three-dimensional movie of, say, the temperature field
of a simulated thermonuclear fireball.
But these stunning displays pose a daunting question: do they show what
will really happen? A simulation is only as good as the equations, algorithms,
and computer hardware that go into it, no matter how striking the display.
If the computer models are wrong, inappropriate, or incorrectly implemented
or executed, the simulation will be flawedwhich is unacceptable
for stockpile stewardship.
To help ensure that the predictions of weapon simulations are as accurate
as possible, experimenters and code users at Los Alamos are using data
from a variety of small-scale experiments to validate some of the physics
models in the codes. The laboratory experiments discussed in this article
focus on one of several fluid instabilities that have been studied by
weapon scientists for decades. (Nearly sixty years ago, the Manhattan
Project scientists who built the first atomic bomb realized that fluid
instabilities could prevent a successful detonation.) However, these small-scale
experiments occur at temperatures and pressures far removed from those
in a nuclear weapon explosion and use materials quite different from those
in nuclear devices. To fully validate a weapon code also requires the
use of data from nuclear tests performed before the test ban went into
effect as well as data from other experiments, as we discuss later in
The fluid instability of primary interest in these small-scale experiments
is the Richtmyer-Meshkov instability, which occurs when the interface
between two fluids with different densities is accelerated by a shock
wave striking the interface perpendicularly. The instability was first
predicted in 1960 by R. D. Richtmyer, a Los Alamos theorist, and first
experimentally observed in 1969 by E. E. Meshkov, a Russian experimentalist.
The instability develops whether the shock travels from a dense fluid
to a less-dense fluid or vice versa. For flat or spherical interfaces,
the instability causes slight disturbances at the interface to grow into
large ripples that breach the interface and mix the fluids. The instability
has been observed in inertial confinement fusion (ICF) experiments, in
which intense laser or particle-beam pulses heat and compress small, layered
metal spheres filled with deuterium and tritium in order to produce fusion
reactions. It is also believed to occur in supernova explosions.
Only in recent years, however, have researchers been able to produce the
Richtmyer-Meshkov instability in small-scale experiments that yield high-quality
data, which is essential for good code validation. Some of these experiments
have been performed at Los Alamos by Robert Benjamin and his research
team. Related research has also been performed at other national labs,
at several universities, and by private industry.
Some of the recent simulations of the Los Alamos experiments were done
by Cindy Zoldi, who completed her Ph.D. in applied mathematics at the
State University of New York at Stony Brook this past spring, then joined
the technical staff at Los Alamos. Zoldi's graduate work involved validating
the RAGE code, one of several unclassified codes used to improve physics
models through comparison of code results with experimental data.
Gas Column Experiments
In these small-scale experiments, the Richtmyer-Meshkov instability is
produced, along with other instabilities, when a planar shock wave propagating
in air strikes a small column of sulfur hexafluoride gas, which is five
times denser, or heavier, than air. [figure: Vorticity
in Shocked-Gas Experiments] The experiments are designed to produce
results that are as two-dimensional (flat) as possible in order to validate
the RAGE code in two dimensions. Three-dimensional validation efforts
are possible in the future.
For these experiments the quantities of interest
are the gas density and velocity. Seven sequential snapshots of the density
show the shock wave first distorting the column of sulfur hexafluoride,
then producing finer and finer swirling motion that eventually mixes the
gases turbulently. [figure: Density Snapshot]
The gas velocity late in the instability's evolution (750 microseconds
after the shock wave has left the downstream edge of the column) is also
determined from two successive high-resolution snapshots of the evolving
column. The velocity is then used to determine the vorticity, a measure
of the intensity of the gas swirling.
To measure the gas density and velocity, the experimenters uniformly mix
microscopic glycol/water droplets with air and/or sulfur hexafluoride
before piping the gas mixture(s) to the experimental chamber. The droplets,
generated by a fog machine like those used in theaters for special effects,
are about 0.5 micrometer in diameter. Because they're much larger than
gas molecules, the droplets scatter light much more efficiently, enabling
the gas density to be measured by photographing the brightness of the
gas/droplet mixtures. By measuring how groups of the droplets move, the
researchers can also produce maps of the gas velocity within and near
the shocked gas column.
gas column is formed by slowly and smoothly piping the dense sulfur hexafluoride
through a circular nozzle into the air already present in the experimental
chamber. By lighting up cross sections of the column with short laser
pulses, the experimenters photographically record the column's density
or velocity. Before each laser pulse slices through the gas column, it
is spread into a horizontal, fan-shaped sheet about 1 millimeter thick.
The experimenters determine the gas velocity by measuring how far and
in what direction groups of the glycol/water droplets move between two
successive laser-pulse snapshots. Pattern-recognition software ensures
that the velocity is determined for the same group of droplets in two
successive frames. Los Alamos was the first to measure high-velocity flow
in a shocked gas using this combination of "tracer particles"
and pattern-recognition software. The technique was a breakthrough for
shocked-gas studies and has greatly enhanced the quality and completeness
of the code validation work discussed here.
The first section of the shock tube in which the
shock wave is generated contains nitrogen pressurized to about three times
atmospheric pressure. [figure: Shocked-Column
Experiment] This section is separated by a polypropylene membrane
from a second region of the shock tube that contains air (which is mostly
nitrogen) at atmospheric pressure. Rupturing the membrane abruptly releases
the nitrogen into the second region, producing a shock wave with a speed
of about 400 meters per second, or 900 miles per hour. Although polypropylene
looks like the clear plastic used to wrap food, it has the unique property
of shattering when ruptured, making it ideal for generating high-quality
After leaving the shock generator, the shock wave encounters the gas column
formed within the experimental chamber. The chamber has windows through
which the laser pulses pass and through which three cameras view the column's
initial state and later distortion and breakup.
The experiment is fairly compactthe basic apparatus fits on a 6-
by 2- meter "tabletop"; the gas column is about 6 millimeters
in diameter and 7.5 centimeters tall. However, these small experiments
produce big results, as the doctoral dissertations and publications flowing
from the research confirm. In addition, four postdoctoral researchers
who originally worked in Benjamin's research team were later hired at
Los Alamos as technical staff members.
Collaboration is Key
But the validation work has not been easy. Once the experiments began
to produce useful data, it took about two years to get the RAGE code results
and the experimental data to agree quantitatively. The effort involved
close collaboration between the code users and the experimentersthe
key to good code validation, says Tim Trucano, a code validation expert
at Sandia National Laboratories in Albuquerque, NM. Trucano is a member
of the Validation and Verification Program for the Department of Energy's
Advanced Simulation and Computing (ASC) program, which involves Los Alamos,
Sandia, and Lawrence Livermore National Laboratories. The ASC program,
formerly called the Accelerated Strategic Computing Initiative (ASCI),
focuses on simulations for stockpile stewardship.
Initially, the simulation showed the shock wave
distorting the column generally as seen in the early stages of the experimental
shock-wave/column interaction. However, quantitative comparisons of the
simulated and experimental results for the distorted column's outer dimensions
as functions of time and for the velocity and vorticity fields at a single
time were poor. In particular, the simulated peak velocities were about
two times larger than the experimentally observed ones. [figure: Experiment
and Simulation Comparisons]
There were several sources of error. For one, Zoldi was able to obtain
better agreement with the experiment by using an initial boundary between
the sulfur hexafluoride and the surrounding air that was more diffuse
than that indicated by initial measurements. Subsequent measurements confirmed
that the boundary was indeed more diffuse. In addition, the velocity and
vorticity comparisons improved when the experimenters (1) mixed the fog
with both the sulfur hexafluoride and the air to obtain velocity data
for both gases and (2) used a higher-resolution camera to take the photos
used to measure the velocity.
There was also a problem with the way the predicted and experimentally
observed velocities were initially compared. In addition to the large
velocity produced by the shock wave's impact, the column receives a small
velocity induced by the pair of large vortices generated in the shock
wave's wake. The effect of this added velocity had not been taken into
account. When it was, together with the other improvements, the experimental
and simulated values for the fluid's peak velocity agreed to within 10-15
percent. The various fixes substantially improved the velocity comparison.
In Trucano's view, this work is a perfect example of the give and take
between experimenters and code users that is required for good code validation.
And the collaboration paid off with good agreement between the simulation
and the experiment for the larger-scale structure. But at present the
RAGE code cannot reproduce the later experimental phases when submillimeter
ripples form that lead to turbulent gas mixing. The ripples are quite
clear in the laser-pulse photos (see cover photo, for example) but not
in the simulations.
A major purpose of code validation is in fact to determine the ranges
of experimental parameters for which the code produces accurate results.
(It's not mathematically, physically, or economically possible for a code
to exactly reproduce the experimental results.) For this particular experiment
the code is now valid for the larger-scale structure, although efforts
are ongoing to reproduce the fluid's late-time smaller-scale behavior
Although the agreement obtained thus far gives confidence in the code's
ability to correctly model complex fluid flow, the validation technique
itself can be made even more quantitative. Other Los Alamos researchers
are using advanced mathematical toolsfractals, wavelets, and structure
functionsto quantitatively compare the simulated and experimentally
observed complexity of the turbulent fluid's late-time structure. Their
research is at the forefront of the new science of code validation.
Regarding the importance of using experiments to validate codes, Los Alamos
Director John Browne says, "Code-validation experiments are the foundation
of predictive capability."
Other Validating Data
In fact, weapon code users at Los Alamos currently use data not only from
small-scale experiments like Benjamin's but also from nuclear tests performed
before the Comprehensive Test Ban Treaty went into effect and from a variety
of large-scale experiments as well, including hydrotests, subcritical
tests, and magnetic-compression and ICF experiments.
Hydrotests help code users interpret the results of some codes that simulate
the implosion of a nuclear weapon. During implosion, shock waves produced
by high explosives compress nuclear materials to supercritical mass. (The
term hydrotest comes from the fact that, during implosion, the high pressures
and temperatures generated by the high explosives cause metals and other
materials to flow like liquids.) By imploding nonnuclear surrogate materials
with properties similar to those of nuclear materials, hydrotests simulate
weapon implosion without producing a nuclear explosion. In contrast, data
on nuclear materials without implosion is obtained from subcritical tests
performed at the Nevada Test Site.
At present, Los Alamos has two hydrotest facilities. PHERMEX, the Lab's
hydrotest workhorse for nearly forty years, takes x-rays of implosion
from a single direction at two times. When fully operational in 2004,
the second facility, DARHT, will take x-rays of implosion from two perpendicular
directions at up to four times.
More recently, protons instead of x-rays have also been used to image
implosions. Proton radiography has the potential to take tens or hundreds
of images per hydrotest, providing implosion movies and possibly three-dimensional
images as well. Using protons produced by the 800-million-electronvolt
accelerator at the Los Alamos Neutron Science Center, preliminary proton-radiography
experiments are being used to test concepts for "advanced hydrotest
Ranging from small shocked-gas experiments like those in Benjamin's lab
to large hydrotests, a wide variety of experiments are providing the data
scientists need to validate the physical models in the weapon codes. John
Browne puts the importance of code validation in a national perspective.
In a statement to Congress this past June, he observed that a major component
of the stockpile stewardship mission is "predictive science,"
which will allow the weapons complex "to evaluate how any issue in
the stockpile, or any change that we might consider, will affect system
safety, reliability, and performance."
Validation and Stockpile Stewardship
By Ray Juzaitis, Associate Director, Weapons Physics
The goal of stockpile stewardship is to ensure that the weapons
in the enduring nuclear stockpile, both today and in the future,
are safe and reliable and will perform as expected—including
those weapons that may have undergone changes due to aging, refurbishment,
or other required modification. To meet this goal, we must sustain
our existing expertise in weapon physics, engineering, and manufacturing,
as well as sustain the technologies and facilities that support
our mission. To meet the challenge potentially posed by future changes
in requirements, we must also explore and develop new expertise
and new support capabilities.
Because stewardship activities must occur without nuclear testing,
we now rely heavily on computers to simulate nuclear weapon performance.
Indeed, some of the most powerful computers and computer programs
in existence are currently used to assess, in astonishing detail,
the performance of complete nuclear weapon systems.
But decisions about the stockpile based on simulations will be
well founded only if the simulations' physical models are validated
with experimental data. The accompanying article describes validation
work at Los Alamos that draws on data from elegant and precise small-scale
experiments with shocked gas columns. These experiments are helping
us explore and understand hydrodynamic instabilities, which play
a significant role in nuclear weapon performance. These experiments
also provide an excellent example of the experimental science needed
to validate the simulations upon which stockpile stewardship vitally
New visualization tools such as the Los Alamos PowerWalls help scientists
grasp the huge volumes of information produced in a computer simulation
of a nuclear explosion. The scientists here are viewing a three-dimensional
simulation of a fluid instability. The code-validation experiments discussed
in the article produce a two-dimensional version of a similar fluid instability.
Internal reflections produced this kalaidoscopic image of the shock tube
used in the shocked-gas experiments. The end of the tube, whose internal
dimensions are 7.5 by 7.5 centimeters, is the small black square at the
Los Alamos researchers Paul Rightley (left) and Kathy Prestridge (right)
prepare to take shocked-gas data that can be used for code validation.
Robert Benjamin received a B.S.
in engineering physics from Cornell University and a Ph.D. in physics
from M.I.T. Since joining the Lab in 1973, he has done x-ray and
optical imaging for ICF experiments, developed diagnostics for pulsed
magnetic-compression experiments, and conducted fluid-instability
experiments. Benjamin received the 1994 Los Alamos Fellows Prize
for outstanding research and became a Laboratory Fellow in 1997.
He has three patents and over thirty publications.
Cindy Zoldi received a B.S. in electrical engineering
from the University of Maine and an M.S. and Ph.D. in applied mathematics
from the State University of New York at Stony Brook. She joined
the Lab in 2002 as a technical staff member. A member of the Society
for Industrial and Applied Mathematics, the American Physical Society,
and the Association for Women in Mathematics, Zoldi has presented
her research on fluid instabilities at various national and international
<The gas column is formed by piping sulfur hexafluoride,
a gas five times denser than air, through a circular nozzle into