The Z-pinch is a plasma configuration that occurs when a pulsed high current arc discharges between two electrodes, causing a plasma column to implode under its own self-generated magnetic pressure. Over the years, researchers have had difficulty predicting and understanding its behavior.
DARPA is interested in using Z-pinches to make compact neutron sources. However, DARPA’s applications require more neutrons than are produced by the current state-of-the-art dense plasma focus (DPF) experiments.
To increase the neutron yield on these devices, Schmidt’s team in the Lawrence Livermore National Laboratory’s Engineering Directorate is using a model of the DPF Z-pinch to optimize the electrode design. Previous Z-pinch modeling took a fluid approach that averaged physical quantities over many particles, washing out beam formations and other important effects. Instead of using a fluid approach, the team developed the first fully kinetic model of a DPF plasma that enables physical quantities to be tracked at the particle level. This model predicts more accurate neutron yields, allowing it to be used as a design tool.
“Modeling these plasmas fully kinetically was a real breakthrough in understanding how they work and predicting their behavior,” said Schmidt, an applied plasma physicist working in the Engineering Directorate. “DARPA’s $1 million award will allow us to apply this new simulation capability to a larger DPF and to push the neutron yield on these devices to even higher levels.”
Team members will model various DPF electrode designs and optimize the design for high neutron yield. They also will conduct experiments in North Las Vegas using a National Security Technologies DPF that has 1 megajoule of stored energy, 250 times greater than the one they are currently using at LLNL.
This time-lapsed rendering illustrates the formation of an umbrella-shaped plasma sheath (purple) being pushed down the length of a cylindrical electrode, eventually collapsing inward on itself to create a tremendously dense region (white). Simultaneously, an ion beam (green) is timed to pass through the device as the plasma collapses in on itself, which accelerates the beam particles. Image: Kwei Chu/LLNL
Dense plasma focus Z-pinch devices are sources of copious high energy electrons and ions, x rays, and neutrons. The mechanisms through which these physically simple devices generate such high-energy beams in a relatively short distance are not fully understood. We now have, for the first time, demonstrated a capability to model these plasmas fully kinetically, allowing us to simulate the pinch process at the particle scale. We present here the results of the initial kinetic simulations, which reproduce experimental neutron yields (∼10^7) and high-energy (MeV) beams for the first time. We compare our fluid, hybrid (kinetic ions and fluid electrons), and fully kinetic simulations. Fluid simulations predict no neutrons and do not allow for nonthermal ions, while hybrid simulations underpredict neutron yield by ∼100x and exhibit an ion tail that does not exceed 200 keV. Only fully kinetic simulations predict MeV-energy ions and experimental neutron yields. A frequency analysis in a fully kinetic simulation shows plasma fluctuations near the lower hybrid frequency, possibly implicating lower hybrid drift instability as a contributor to anomalous resistivity in the plasma.
The most advanced application would be the use of Z-pinch devices as acceleration stages for particle accelerators. In addition to being compact, the devices are technologically simple, which means less cost and potentially less to go wrong. They also produce gradients much higher than those obtained with today’s standard radio-frequency stages. Some near-term applications might include using Z-pinch devices to produce well-defined particle beams for nuclear forensics, radiography, oil exploration, and detection of special nuclear materials.
The team also compared its results with those from simulations performed with fluid codes and with hybrid codes that combine aspects of kinetic and fluid codes. “The fluid simulations predicted zero neutrons and were not capable of predicting ion beams, says Schmidt. The hybrid simulations underpredicted the experimental neutron yield by a factor of 100 and did not predict ions with energies above 200 kiloelectronvolts. The more complex, fully kinetic simulation was necessary to get the physics right.”
The team also designed, fabricated, and assembled a tabletop DPF experiment to directly measure the acceleration gradients inside the Z-pinch. The first gradient recorded was a time-of-flight measurement of the DPF’s self-generated ion beam using a Faraday cup. “These measurements, made during subkilojoule DPF operation, now hold the record for the highest measured DPF gradient in that energy class,” says Ellsworth.
A second and more sophisticated measurement of the gradient is now under way. The team has refurbished a radio-frequency-quadrupole accelerator to make an ion probe beam for the pinch plasma. (See the figure below.) The accelerator produces a 200-picosecond, 4-megaelectronvolt ion probe beam, which is injected into the hollow center of the DPF gun just as the pinch occurs. The researchers will use this tool to measure the acceleration of the probe beam through the Z-pinch. From that, they will deduce the acceleration gradient of the plasma and demonstrate the possibility of using the Z-pinch as an acceleration stage. “The probe-beam experiments will directly measure for the first time the particle acceleration gradients in the pinch,” says Tang.
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