WHAT do salad dressing and nuclear fusion have in common, and how can an electric motor further our understanding of both? More than one might suspect.
In both salad dressing and nuclear fusion, materials of different density will mix, which has a great bearing on such things as the uniformity of the dressing or how much energy will be achieved from an inertial confinement fusion (ICF) capsule.1 To investigate this mixing process, Lawrence Livermore has built a linear electric motor (LEM) that can provide selected acceleration profiles up to 1,000 times Earth's gravity.
"When friends ask what I do, I like to tell them that I'm particularly concerned with what happens when you turn a bottle of salad dressing upside down," quips Guy Dimonte, the Lawrence Livermore physicist who is leading the project to study instabilities in liquids of different densities when they are accelerated by a linear electric motor. "Actually, I'm only half joking, because the principle is the same, whether it's oil mixing with vinegar or a plastic shell mixing with thermonuclear fuel in inertial confinement fusion. We need to understand how hydrodynamic instabilities enhance the mixing of different materials because this information is very important to Lawrence Livermore's stockpile stewardship work," he says.

Perturbations Grow
When fluid of high density is supported against gravity by a less dense liquid, the system is unstable, and microscopic perturbations grow at the interface between the fluids. This phenomenon, called the Rayleigh-Taylor instability, also occurs when a bottle of oil-and-vinegar salad dressing is turned upside down. The instability causes spikes of the dense fluid to penetrate the light fluid, while bubbles of the lighter fluid rise into the dense fluid. The same phenomenon occurs when a light fluid is used to accelerate a dense fluid, causing the two fluids to mix at a very high rate. For example, during the implosion of an ICF capsule, this instability can cause enough mixing to contaminate, cool, and degrade the yield of the thermonuclear fuel.
The LEM is an excellent tool for studying this instability, but what is it? Think of a miniature high-speed electric train (the container) hurtling down a track (the electrodes) while diagnostic equipment (optical and laser) photographs it. The configuration is shown in Figure 1.2
The LEM, configured by Dimonte and his colleague, physicist Marilyn Schneider, consists of four linear electrodes, or rails, that carry an electrical current to a pair of sliding armatures on the container. A magnetic field is produced that works in concert with the rail-armature current to accelerate the container--just as in an electric motor, but in a linear fashion rather than in rotation. The magnetic field is augmented with elongated coils just as in a conventional electric motor. This configuration also helps hold the armatures against the electrodes to prevent arcing. The electrical energy (0.6 megajoules) is provided by 16 capacitor banks that can be triggered independently to produce different acceleration profiles (i.e., how the acceleration varies with time).
The container that holds the fluid is machined from a block of Delrin, a material that is corrosion-resistant, strong, and nonconducting. The container is 9 ¥ 9 ¥ 12 centimeters (about 4 inches on a side) and has 0.5-cm-thick Lexan windows in the front and back so the liquids can be backlit and imaged. High-resolution optical imaging diagnostics record the inter-fluid mixing. The optical source is either a flash backlighter for photography or a laser sheet for laser-induced fluorescence (Figure 2).
The container trajectory is measured with a laser position detector (LAPD) consisting of eight transverse, 1-milliwatt beams at different positions along the trajectory. When the container intersects these beams, photo diodes send electrical signals that are recorded by digitizers and then trigger the optical diagnostic system. The images are captured electronically using charge-coupled device (CCD) cameras and a desk-top computer using a LABVIEW program. Higher resolution images are taken with remote-controlled 35-millimeter cameras, and the images are digitized later with a photodensitometer. Electrical signals from the LAPD, current monitors, magnetic field loops, and crystal accelerometers are acquired on digitizing oscilloscopes and archived on another desk-top computer. Finally, the container is stopped by a mechanical brake with spring-loaded aluminum drums.
The key to successful operation of the LEM is the sliding armature because it must carry as much as 30,000 amperes of current without arcing. "When we first started, our armatures were flawed, and we melted a lot of copper electrodes with spectacular arcs. After several modifications, we developed an armature that is very reliable, capable of several hundred arc-free shots before the electrodes need to be replaced. The system now works great, but without the exciting fireworks of the early days," Dimonte says.
In a typical experiment, the container is filled with two fluids (such as freon and water) and inserted between the rail.3 The diagnostic equipment is activated, and the laboratory is then closed and interlocked. From an adjoining control room, the capacitors are charged and fired, sending the container down the rails with a final velocity of about 30 meters per second, depending on the needs of the experiment. Higher velocities are attainable with the energy available in the banks, but they are not required for most experiments. As the container intersects the laser beams, the imaging diagnostics are triggered and electrical signals are acquired. The container then enters the brake region and stops smoothly. "When we are in high gear, technicians Don Nelson and Sam Weaver can fire a shot as quickly as every 10 minutes," Dimonte explains.

Wide Range of Acceleration
"The beauty of using the LEM for these experiments is that we can take very high resolution images of the instabilities over a wide range of acceleration profiles," Dimonte says. "Most alternative drivers like compressed gas or rocket motors do not provide this flexibility. Mixing experiments are performed on Livermore's Nova laser under realistic conditions, but with less relative detail than on the LEM. The LEM is complementary to Nova and a very reliable and cost-effective tool for investigating the fine details of turbulent mixing."
In the example of Figure 2, the fluids have very little viscosity and the mixing is fast and turbulent. Here, scientists are interested in how the random bubbles of light fluid (on top) penetrate the heavy fluid (on bottom) and how the corresponding spikes of heavy fluid penetrate the light fluid. (Remember, gravity has been turned upside down because of the downward acceleration.) The amount of fluid mixing is indicated in Figure 3, which shows the bubble amplitude versus the distance traveled by the container for different acceleration profiles. From these data, Dimonte and Schneider can test turbulent mixing models and full hydrodynamic computer simulations.3

In another set of experiments, Dimonte and Schneider are investigating the mixing when the "fluids" have material strength. For example, when an aluminum plate is accelerated by high explosives, the driving pressure is comparable to the yield strength, or the point at which the material would become plastic. In this case, a smooth surface is expected to remain stable indefinitely, whereas a very rough surface would be unstable. They are testing this hypothesis by doing experiments using yogurt because it has enough yield strength to show the effect at the reduced g-forces of the LEM. Figure 4 shows an image of yogurt accelerated in the LEM when the initial undulations at the interface were about 1 millimeter in amplitude. The perturbations became very large because of the instability. When the experiment was repeated with a smooth interface, the instability was inhibited by the material strength.

Many more experiments are possible on the LEM with different fluids, diagnostics, and acceleration profiles. "Our strategy is to use small-scale experiments like the LEM, with high-quality optical diagnostics, to investigate the micro-physics of turbulent mixing. Over the next five years, we will test the mixing models with data of unprecedented resolution. When the National Ignition Facility becomes available, the mixing models can then be applied to more realistic conditions in an integrated sense, that is, including the other issues relevant to stockpile stewardship, such as radiation flow and material equation of state," Dimonte says.

--Sam Hunter

Key Words: acceleration, linear electric motor (LEM), Rayleigh-Taylor instability.

1. J. H. Nuckolls et al., "Laser Compression of Matter to Super-High Densities: Thermonuclear (CTR) Applications," Nature 239, 139 (1972).
2. G. Dimonte et al., "A Linear Electric Motor to Study Turbulent Hydrodynamics," Review of Scientific Instruments 67, 302 (1996).
3. G. Dimonte and M. B. Schneider, "Turbulent Rayleigh-Taylor Instability Experiments with Variable Acceleration," Physical Review E 54, 3740 (1996).

For further information contact Guy Dimonte (510) 423-0596 (dimonte1@llnl.gov).

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