In warm dense matter and high energy density plasmas, the traditional Boltzmann description of a plasma begins to break down. In this regime, collisions are not determined by binary Coulomb collisions, but instead by many body Coulomb collisions. The Mean Force Kinetic Theory [S. D. Baalrud and J. Daligault, Phys. Plasmas 26, 082106 (2019)] provides an alternate closure to the BBGKY hierarchy based on expanding about a perturbation from equilibrium rather than about strength of correlations. One property of the Mean Force Kinetic Theory is it produces the same fluid equations, with altered transport coefficients, thus existing fluid codes would only need to update the transport coefficients. A code is presented to solve the Chapman-Enskog expansion for the Mean Force Kinetic Theory. Results show the self diffusion coefficient calculated for a Hydrogen plasma in
the warm dense matter regime. These plasmas contain degenerate electrons, whose screening effect are modeled by the potential of mean force. This potential is obtained using the Quantum Hyper Netted Chain Model (QHNC) [C. E. Starrett and D. Saumon, High Energy Density Phys. 10, 35 (2014)] developed by Starrett and Saumon. Future work intends to develop an independent version of the QHNC code to calculate ion-ion potentials of mean force necessary for the existing code, a module to expand transport coefficients to an arbitrary order in the Chapman-Enskog expansion, and a model for electron transport properties.

This material is based upon work supported by the US Department of Energy, National Nuclear Security Administration, under award No. DE-NA0003868.

The MJOLNIR (MegaJOuLe Neutron Imaging Radiography) dense plasma focus (DPF) at LLNL is a prototype source for performing neutron radiography of dynamic events. MJOLNIR’s driver can store up to 2 MJ stored energy and produce currents up to 4.5 MA (so far commissioned to >3 MA). The DPF consists of two coaxial electrodes, which generate a plasma sheath by ionizing deuterium gas. The sheath implodes on the axis in a z-pinch geometry. When the pinch breaks apart, it produces a beam of ions that impacts the “target”, a region of the sheath assembled on axis past the pinch (n_e ~1e19/cm^3). The “beam-target” interaction produces a neutron burst lasting on the order of tens of nanoseconds, which we use for radiography. We present our design of a laser interferometry diagnostic to measure the electron density of the pinch and target regions. It allows us to infer the ion density in the target region, study dynamics during implosion to optimize beam generation in the pinch region, and compare with hybrid fluid-kinetic particle-in-cell stimulations to benchmark models. The interferometer builds on an existing Schlieren imaging system, showing density gradients in the plasma and bounding the density. We compare the dynamics, instabilities, and structure of undoped deuterium, and argon- and neon-doped deuterium shots, using laser interferometry, visible self-emission imaging, neutron time-of-flight detectors, and EM probes. LLNL-ABS-848005

*Prepared by LLNL under Contract DE-AC52-07NA27344.

Axially ejected plasma shocks and plasma jets have been observed in dense plasma focus devices, leaving the electrodes at high velocity. For instance, in a plasma focus operating at 400J a plasma of ~ 10^-10 kg is ejected from the pinch with a velocity > 10⁵ m/s. These plasma conditions appear promising to be used as the base of a pulsed plasma thruster (PPT), particularly to develop a miniaturized propulsion device for orientation, capable of being integrated to a small-standardized satellite, such as the CubeSat. According to theoretical and scaling estimations, it is expected that for a pulsed plasma thruster operating with a stored energy of 1 J, a bit impulse in the range of fractions of μNs to some μNs per pulse would be obtained. It is important to take into consideration that a plasma focus works at milli bar pressures, and a PPT works in a space environment, i. e. vacuum, thus in the PPT the plasma will be generated from the ablation of the insulator material, PTFE for example. Thus, different experimental electrodes and insulators arrays must be studied in order to reproduce the plasma dynamics observed in a plasma focus.

This work presents the status of the pulsed micro energy propulsion research for nano satellites orientation developed by the P²mc Research Center of CCHEN and by SPEL of University of Chile. The report includes: a) design, construction and characterization of a miniaturized fast capacitor (2 kV, 2mF, ~ 40 nH, ~20 kA), b) design and construction of plasma guns with submillimeter internal and external radius, and PTFE insulator, c) electrical characterization of the miniaturized capacitor connected to the plasma gun operated at 1 to 2 J, d) measurements of the capacitor temperature operating at different repetition rate e) discussion and design of possible experimental arrays to measure the force produced by the miniaturized pulsed plasma thruster: optical measurements of the velocity and mass, torsional pendulum and thrust stand based on a single point load cell.

Supported by ANID FONDECYT Regular 1211695.

Commissioning MJOLNIR above 3.5 MA requires operational modifications to take advantage of the higher current to produce higher yields.

INTERLEAVING: So far, shots above 3.5 MA change the machine in a way that precludes back-to-back shots, requiring a low current (2.7 MA) “recondition shot” to reset the machine. Intermediate current shots at 3.2 MA did not recondition the machine. The yield on the highest current shots was independent of the yield of the recondition shot and the number of reconditioning shots performed. The 3.5 MA high yield shots, although interleaved, still exhibit suitable consistency in pinch time, yield, and neutron shape for time-gated flash neutron imaging.

FILL PRESSURE: The highest yield shots did not follow a constant drive parameter scaling for fixed anode. Fill-pressures above 12 Torr were associated with much lower dI/dt and yield. Measurements of rundown velocity and breakdown time for different fill pressures will be compared.

For interleaved shots below the critical pressure, the yield continues a favorable scaling (yet below I^4) from 2.7 MA above 3.5 MA. Without these changes, the yield diminishes or disappears above 3.5 MA. The interleaved shots are investigated to determine clues about what is different and how it reconditions the machine.

Prepared by LLNL under Contract DE-AC52-07NA27344.

A Dense Plasma Focus (DPF) is a coaxial plasma accelerator with a z-pinch as its final phase. An m = 0 instability leads to the break-down of the pinch column generating electric fields on the order of megavolts. These electric fields accelerate the ions and electrons in the pinch region in opposite directions. The ions are accelerated into plasma on axis resulting in beam-target fusion and neutron generation. The electrons are accelerated into the anode where they generate hard x rays via Bremsstrahlung radiation. A so-called step-wedge filter [1] is used to infer the x-ray temperature from the transmission of x rays through different tantalum thicknesses in the filter. This work will present the measurements of the high energy x-ray spectrum (higher than 62 keV) and corresponding neutron yields across various plasma conditions. Probing x rays provides a potential path to studying the electric fields and the underlying physics of ion beam generation in DPFs. These measures are taken on MJOLNIR which is a DPF located at LLNL being developed as a neutron source for flash neutron radiography.

This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory (LLNL) under Contract DE-AC52-07NA27344; LNL-ABS-848278

1. G. J. Williams et al, Rev. Sci. Instrum. 89, 10F116 (2018); https://doi.org/10.1063/1.5039383

This work describes the behavior of a plasma focus discharge of low energy and current, in an optimized regimen in X-ray and neutron production to high pressure of D₂ and H₂ (>10 mbar). The study was carried out in the multipurpose generator MPG (1.2 μF, 42 nH, 22-24 kV, ~100 kA, 290-345 J) under design and working conditions that extend to regimes with operating parameters out of the efficiency limits imposed by the similarities observed in PF discharges. In this direction, we considered the parameter space p-Z_eff, with Z_eff >> 2a (where Z_eff is the is the effective anode length, p is the fill pressure and a is the anode radius) and smaller anode radius, thus reducing the initial volume of discharge region and increasing the rise-rate of initial current density. The evolution of plasma sheath was characterized by Shadowgraphy technique at different discharge evolution times. For the characterization of the plasma density in the radial phase, digital interferometry was used. Both techniques were implemented, using picosecond laser source with a pulse duration of 170 ps Additionally, the electrical behavior of the discharge, as well as its performance, were monitored with conventional electrical diagnostics and neutron and X-ray detectors, respectively. From the refractive optical records, the appearance of plasma filaments is observed from an early stage of the discharge. During the evolution of the plasma sheath, the filaments remain confined in a region of the sheath, such as a toroidal plasma belt, without reaching the top of the anode nor participating in the radial compression phase [1]. On the other hand, from the records in the radial phase, the appearance of Rayleigh-Taylor type instabilities is observed. The measured total neutron yield exceeds the values predicted by scaling laws by a factor of five or higher at the same energy in the capacitor bank and pinch current. Additionally, we observe an increase in X-ray production and compression dynamics, as evidenced by a large amplitude dip in the current derivative signal, high compression velocity, and formation of instabilities.

Acknowledgments: C. Pavez acknowledges the financial support of the ANID-FONDECYT project N°1211885. G. Avaria acknowledges the financial support of the ANID-FONDECYT project No. 1211131.

References

[1] C. Pavez, M. Zorondo, J. Pedreros, A. Sepúlveda, L. Soto, G. Avaria, J. Moreno, S. Davis, B. Bora, and J.Jain. New evidence about the nature of plasma filaments in plasma accelerators of type plasma-focus. Plasma Physics and Controlled Fusion, 65(1), 015003 (2022).

LLNL’s Megajoule Neutron Imaging Radiography Dense Plasma Focus (MJOLNIR DPF) uses a plasma discharge in a deuterium gas to produce neutrons for the purpose of imaging. We have substantial interest in fine control of the intensity and the temporal and spatial distributions of the resulting neutron source. We have investigated the introduction of noble gas dopants (neon, argon, and krypton) to the deuterium gas with the intention of exercising such control. We present both experimental results and simulations of the effects of the dopants.
This work was prepared by LLNL under Contract DE-AC52-07NA27344.

Current measurements in Plasma Focus discharges are usually made with inductive probes such as Rogowskii coils, which present the disadvantage that it cannot determine the current circulating specifically through the plasma column. This indetermination makes it more difficult to estimate plasma characteristics such as the temperature inside the column through the Bennett relation.
Zeeman splitting, based on the spectral separation of optical emission lines, enables the estimation of the magnetic field in the plasma column when a high current is present. The emitted photons have a distinct polarization identified as σ⁺ and σ^-, possible to be separated by a λ/4 polarizing plate.

This work presents preliminary measurements of the magnetic field present at the plasma column of the PF-400J discharge in a high current density configuration (d_anode = 4.5 - 6.0 mm and z_eff = 10 - 20 mm), by using the Zeeman splitting spectroscopic technique of the Ar III emission at 330.18 nm. The measurements are spatially resolved in the radial direction, with the use of the combination of a polarizing crystal and a λ/4 plate, and a bifurcated fiber optic bundle focused on the entrance of a 0.5 m spectrometer with a 2400 l/mm grating.

With this experimental configuration a magnetic field of around 2 T is estimated at the pinch volume, when the maximum current (~100 kA) is achieved.

Authors acknowledge the finantial support from grants ANID FONDECYT Regular 1211131,

FONDECYT Regular 1211885 and FONDECYT Regular 1220533

A generalized Ohm’s law is derived to treat strongly magnetized plasmas in which the electron gyrofrequency significantly exceeds the electron plasma frequency. Strong magnetization of electrons causes the frictional drag between electrons and ions due to Coulomb collisions to shift, producing an additional transverse resistivity term in the generalized Ohm’s law that is perpendicular to both the current (J) and the Hall (JxB) direction. In the limit of very strong magnetization, the parallel resistivity is found to increase by a factor of 3/2 and the perpendicular resistivity by a logarithmic factor of the ion-to-electron mass ratio. These results suggest that strong magnetization significantly changes the magnetohydrodynamic evolution of a plasma. Regions of dense z-pinch plasmas can reach such strongly magnetized regimes, and the associated influence of strong magnetization may influence plasma dynamics in ways that are unexpected based on conventional transport theory of magnetized plasmas.

Strong magnetic fields in multi-MA accelerators can magnetize the electrons to a limit that their gyroradius becomes much smaller than the Debye length. These strongly magnetized plasmas exhibit novel transport properties that need to be better understood. Traditional theories are limited to weakly magnetized transport regimes where the gyroradius is much larger than the Debye length. Here, we develop a generalized kinetic theory that can treat Coulomb collisions in the strongly magnetized transport regime and which asymptotes to the traditional Boltzmann kinetic theory in the weakly magnetized limit. The theory also spans the weak to strong Coulomb coupling regimes by incorporating the mean force kinetic theory concept. To demonstrate the utility of the generalized theory, it is used to compute the friction force on a massive test charge moving through a strongly magnetized one-component plasma. It is shown that when the plasma is strongly magnetized, the friction force on a test charge shifts, obtaining components perpendicular to its velocity in addition to the typical stopping power component antiparallel to its velocity. Strong magnetization is also found to break the fundamental symmetry of independence of the sign of the charges of the interacting particles on the collision rate, commonly known as the “Barkas effect”. Strong magnetization in combination with oppositely charged interaction is found to increase the perpendicular resistivity and conductivity by an order of magnitude, which might have implications in the reduction of accelerator efficiency by diverting current away from the load.

Regions of the plasmas formed in multi-MA pinch implosions fall into the
very strongly magnetized regime, meaning that the electron gyrofrequency ex-
ceeds the electron plasma frequency and in the weak to moderate Coulomb
coupling regime denoting that the potential energy of interaction is on the or-
der of the kinetic energy. These regimes modify the Coulomb collision frequency
making traditional kinetic theories invalid.
Using a recently developed generalized Boltzmann kinetic theory for strongly
magnetized plasmas, the electron-ion temperature relaxation rates in both paral-
lel and perpendicular directions are calculated. It is shown that during the tem-
perature evolution electron-ion collisions can lead to a temperature anisotropy.
This work also studies how this developed temperature anisotropy relaxes via
Coulomb collisions in a strong magnetic field. These results have particular
relevance to the magnetically insulated transmission line where the plasma is
expected to be very strongly magnetized, and the current shunted in this region
is potentially a significant loss. The improved understanding of temperature
relaxation presented here will contribute to a more complete fluid model in
this novel plasma regime, which can in turn be used to inform improvements
in experimental Z-pinch techniques such as improving the efficiency of current
delivered to the load.