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DOE OSTI2026

Measurements of the electron energy distribution function in partially magnetized low temperature plasmas

While Langmuir probes (LPs) are relatively simple and inexpensive plasma diagnostics for the electron density, temperature, and the electron energy distribution function (EEDF), the interpretation of the measured current–voltage (I–V) characteristic is complicated considerably by the presence of a magnetic field. In regimes where the electron gyroradius is comparable to the probe radius, the electron flux to the probe surface is retarded by reduced mobility across field lines and can no longer be described by a thermal model. Predicting the current collected by the probe in these regimes requires accurate estimates of the plasma diffusion coefficients, which are usually difficult to obtain. In this work, we measure electron energy distribution functions in E×B plasmas with magnetized electrons and non-magnetized ions in argon and krypton gases, using both a LP and laser Thomson scattering (LTS) at various magnetic fields. Using the LTS measurements to provide a robust benchmark for comparison, we compare existing theories describing the flux to the probe under magnetized conditions. We find that even when the electron gyroradius associated with the effective electron temperature is small compared to the probe radius, the EEDF computed using classical probe theory is still robust at energies higher than the energy at which the gyroradius becomes larger than the probe size. For plasmas that are not strongly non-Maxwellian, we formulate a method to extract robust density and temperature measurements using physics-informed fitting techniques to analyze EEDFs computed using classical theory.

Devin, E. G. [Princeton Plasma Physics Laboratory ↗

DOE OSTI2022

Time-resolved electron energy distribution functions at the substrate during a HiPIMS discharge with cathode voltage reversal

Abstract The time-dependent plasma properties of a high-power impulse magnetron sputtering plasma are investigated which include a positive ‘kick’ pulse on the sputtering target 2 μ s after the main negative pulse, this reversing the voltage on the cathode. At a substrate 15 cm distant from the magnetron, the time-dependent electron energy distribution function (EEDF), plasma potential, potential commute time and plasma diffusion properties are measured using a single Langmuir probe. Results show that the positive pulse on the target expels plasma and raises the plasma potential across the chamber on the order of 1 to 2 μ s, which is the time scale of the electron diffusion. The EEDF at the substrate fits a Druyvesteyn distribution during the main negative pulse rising slightly in average energy over time. The distribution is still Druyvesteyn and at the very start of the positive pulse, but then loses the higher energy electrons and drops in average electron energy as the positive pulse progresses. A Boltzmann equation solver, BOLSIG+, was used to predict the EEDF at the substrate during the positive pulse and it agrees best with the measurements assuming a value of 0.2 Td for the E / N (electric field/gas number density).

Physics↗

DOE OSTI2023

Kinetic simulation of a 50 mTorr capacitively coupled argon discharge over a range of frequencies and comparison to experiments

The effect of driving frequency in the range of 13.56–73 MHz on electron energy distribution and electron heating modes in a 50 mTorr capacitively coupled argon plasma discharge is studied using 1D-3V particle-in-cell simulations. Calculated electron energy probability functions exhibit three distinct “temperatures” for low-, mid-, and high-energy electrons at all the studied driving frequencies. When compared to published experimental data, the calculated probability functions show a reasonable agreement for the energy range resolved in the measurements (about 2–10 eV). Discrepancies due to limitations in experimental energy resolution outside this range lead to differences between computational and experimental values of the electron number density determined from the distribution functions, and the predicted effective electron temperature is within 25% of experimental values. The impedance of the discharge is interpreted in terms of a homogeneous equivalent circuit model, and the driving frequency dependence of the inferred combined sheath thickness is found to obey a known, theoretically derived, power law. The average power transferred from the field to the electrons (electron heating) is computed, and a region of negative heating near the sheath edge, particularly at higher driving frequencies, is identified. Analysis of the electron momentum equation shows that electron inertia, which on temporal averaging would be zero in a linear regime, is responsible for negative values of power deposition near the sheath edge at high driving frequencies due to the highly nonlinear behavior of the discharge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Characterization of an RF-driven argon plasma at atmospheric pressure using broadband absorption and optical emission spectroscopy

Atmospheric pressure plasmas in argon are of particular interest due to the production of highly excited and reactive species enabling numerous plasma-aided applications. In this contribution, we report on absolute optical emission and absorption spectroscopy of a radio frequency (RF) driven capacitively coupled argon glow discharge operated in a parallel-plate configuration. This enabled the study of all key parameters including electron density and temperature, gas temperature, and absolute densities of atoms in highly electronically excited states. The space and time-averaged electron density and temperature were determined from the measurement of the absolute intensity of the electron-atom bremsstrahlung in the visible range. Considering the non-Maxwellian electron energy distribution function, an electron temperature (T e ) of 2.1 eV and an electron density (n e ) of 1.1 × 10 19 m –3 were obtained. The time-averaged and spatially resolved absolute densities of atoms in the metastable (1s 5 and 1s 3 ) and resonant (1s 4 and 1s 2 ) states of argon in pure Ar and Ar/He mixture were obtained by broadband absorption spectroscopy. The 1s 5 metastable atoms had the largest density near the sheath region with a maximum value of 8 × 10 17 m –3 , while all other 1s states had densities of at most 2 × 10 17 m –3 . Here, the dominant production and loss mechanisms of these atoms were discussed, in particular, the role of radiation trapping. We conclude with a comparison of the plasma properties of the argon RF glow discharges with the more common He equivalent and highlight their differences.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Establishing criteria for the transition from kinetic to fluid modeling in hollow cathode analysis

Hollow cathodes for plasma switch applications are investigated via 2D3V particle-in-cell simulations of the channel and plume region. The kinetic nature of the plasma within the channel is dependent on the thermalization rate of electrons, emitted from the insert. When Coulomb collisions occur at a much greater rate than ionization or excitation collisions, the electron energy distribution function rapidly relaxes to a Maxwellian and the plasma within the channel can be described accurately via a fluid model. In contrast, if inelastic processes are much faster than Coulomb collisions, then the electron energy distribution function in the channel exhibits a notable high-energy tail, and a kinetic treatment is required. This criterion is applied to hollow cathodes from the literature, revealing that a fluid approach is suitable for most electric propulsion applications, whereas a kinetic treatment can be more critical to accurate modeling of plasma switches.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Double-sided electron energy analyzer for measurement of non-Maxwellian electron energy distributions

Here, a double-sided electron energy analyzer is developed for studies of magnetic reconnection. It can measure electron energy distribution functions along two directions opposite to each other at the same time. Each side is composed of a floating reference grid, an energy selector grid, and a collector plate. The voltage of the selector grid is swept from –40 to 0 V with respect to the reference grid with a frequency of 1 MHz. This fast sweeping is required to resolve sub-Alfvénic changes in plasma quantities of the Magnetic Reconnection Experiment, where the typical Alfvénic time is a few microseconds. The reliability of the energy analyzer is checked in Maxwellian plasmas away from the reconnection region. In this case, the electron temperature computed from the electron energy distribution function agrees with measurements of a reference triple Langmuir probe. When it is located near the reconnection region, the temperatures of the tail electron population from both sides, facing into the electron flow and facing away from it, exceed the bulk electron temperature measured by the Langmuir probe by a factor of about 2.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Benchmark of the KGMf with a coupled Boltzmann equation solver

The Kinetic Global Model framework (KGMf) is an open-source general-purpose global model (spatially averaged) simulation code developed to explore the reaction kinetics and pathways in plasma discharge systems. It contains species continuity and electron energy balance equations, with a time-dependent evaluated electron energy distribution function (EEDF) for electron impact reactions. The EEDF is utilized to determine the rate coefficients for electron impact reactions, which can have profound impact on the temporal evolutions of plasma parameters. Previously, the EEDF was commonly assumed as Maxwellian or an analytical function of the effective electron temperature. In this work, the KGMf is coupled with a Boltzmann equation (BE) solver to self-consistently compute the EEDF. The EEDF evolution frequency is determined based on relative changes of the reduced electric field. The KGMf is benchmarked with the ZDPlasKin code based on high-pressure low-temperature argon plasma discharge cases. Additionally, the temporal evolutions of reduced electric field, electron temperature, EEDF, reaction rates, and species densities, are obtained and compared under different discharge conditions, showing good agreement between the KGMf and the ZDPlasKin simulations. The application of the KGMf for predicting breakdown times in high power microwave discharges is also presented, which shows qualitative agreement with particle-in-cell simulations. The KGMf can be further applied for more complicated plasma discharge systems, where the reaction kinetics are more intricate (e.g., plasma-assisted combustion systems).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Streamer self-focusing in an external longitudinal magnetic field

The numerical simulation of the development of a streamer discharge in a gap with an external longitudinal magnetic field was used to demonstrate the self-focusing of such discharges. Self-focusing is caused by a sharp deceleration of the radial ionization wave due to a change in the electron energy distribution function, a decrease in the average electron energy, the rate of gas ionization, and the electron mobility in crossed electric and magnetic fields as compared to the case of the discharge development without a magnetic field. The self-focusing effect of a streamer discharge in an external longitudinal magnetic field is observed for both positive and negative pulse polarities. The work proposes an estimate of the critical value of the magnetic field, which makes it possible to control the development of pulsed high-voltage discharges at various gas pressures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Kinetic simulations of ignited mode cesium vapor thermionic converters

Cesium vapor thermionic converters are an attractive method of converting high-temperature heat directly to electricity, but theoretical descriptions of the systems have been difficult due to the multi-step ionization of Cs through inelastic electron–neutral collisions. This work presents particle-in-cell simulations of these converters, using a direct simulation Monte Carlo collision model to track 52 excited states of Cs. Here, these simulations show the dominant role of multi-step ionization, which also varies significantly based on both the applied voltage bias and pressure. The electron energy distribution functions are shown to be highly non-Maxwellian in the cases analyzed here. A comparison with previous approaches is presented, and large differences are found in ionization rates due especially to the fact that previous approaches have assumed Maxwellian electron distributions. Finally, an open question regarding the nature of the plasma sheaths in the obstructed regime is discussed. The one-dimensional simulations did not produce stable obstructed regime operation and thereby do not support the double-sheath hypothesis.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2022

Characterization of sub-picosecond laser-produced fast electrons by modeling angularly resolved bremsstrahlung measurements with 3D hybrid particle-in-cell code

Hard x-rays produced by intense laser-produced fast electrons interacting with solids are a vital source for producing radiographs of high-density objects and implosion cores for inertial confinement fusion. Accurate calculation of hard x-ray sources requires a three-dimensional (3D) simulation geometry that fully models the electron transport dynamics, including electron recirculation and the generation of absolute photon yields. To date, 3D simulations of laser-produced bremsstrahlung photons over tens of picoseconds and code benchmarking have not been performed definitively. In this study, we characterize sub-picosecond laser-produced fast electrons by modeling angularly resolved bremsstrahlung measurements for refluxing and non-refluxing targets using the 3D hybrid particle-in-cell (PIC), Large Scale Plasma code. Bremsstrahlung radiation and escaped electron data were obtained by focusing a 50-TW Leopard laser (15 J, 0.35 ps, 2 × 10 19 W/cm 2 ) on a 100-μm-thick Cu foil and a Cu with a large plastic backing (Cu–CH target). Data for both the Cu and Cu–CH targets were reproduced for simulations with a given set of electron parameters. Comparison of the simulations revealed that the hard x-ray emission from the Cu target was significantly longer in duration than that from the Cu–CH target. Here, the benchmarked hybrid PIC code could prove to be a powerful tool in the design and optimization of time- and angular-dependent bremsstrahlung sources for flash x-ray and gamma-ray radiography.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Similarity-based scaling networks for capacitive radio frequency discharge plasmas

We demonstrate similarity-based scaling networks for capacitive radio frequency (RF) plasmas, which extensively correlate discharge characteristics under varied conditions, incorporating the transition from original to similarity states. Based on fully kinetic particle-in-cell simulations, similar RF discharges in argon are demonstrated with three external control parameters (gas pressure, gap distance, and driving frequency) simultaneously tuned. A complete set of scaling pathways regarding fundamental discharge parameters is obtained, from which each plasma state finds its neighboring node with only one control parameter tuned. The results from this study provide a promising strategy for plasma multi-parameter mapping, enabling effective cross-comparisons, prediction, and manipulation of RF discharge plasmas.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Investigating the effects of electron bounce-cyclotron resonance on plasma dynamics in capacitive discharges operated in the presence of a weak transverse magnetic field

Recently, Patil et al. [Phys. Rev. Res. 4, 013059 (2022)] have reported the existence of an enhanced operating regime when a low-pressure (5 mTorr) capacitively coupled discharge (CCP) is driven by a very high radio frequency (60 MHz) source in the presence of a weak external magnetic field applied parallel to its electrodes. Their particle-in-cell simulations show that a significantly higher bulk plasma density and ion flux can be achieved at the electrode when the electron cyclotron frequency equals half of the applied radio frequency for a given fixed voltage. In the present work, we take a detailed look at this phenomenon and further delineate the effect of this “electron bounce-cyclotron resonance (EBCR)” on the electron and ion dynamics of the system. We find that the ionization collision rate and stochastic heating are maximum under resonance condition. The electron energy distribution function also indicates that the population of tail-end electrons is highest for the case where EBCR is maximum. Formation of electric field transients in the bulk plasma region is also seen at lower values of applied magnetic field. Finally, we demonstrate that the EBCR-induced effect is a low-pressure phenomenon and weakens as the neutral gas pressure increases. The potential utility of this effect to advance the operational performance of CCP devices for industrial purposes is discussed in this report.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Single-shot ultrafast dynamics of nanosecond pulsed plasmas: Transition from ps–ns nonequilibrium to near-full ionization

The ultrafast multi-stage evolution of state-defining properties in atmospheric-pressure nanosecond pulsed plasmas is quantified using single-discharge, jitter-free, continuous streak-sweep spectroscopy of N 2 (C → B) molecular and N + /O + ionic species with a single-shot time resolution as short as ∼160 ps. An early period of extreme nonequilibrium is observed with vibrational temperatures [T V (C)] dropping from ∼8000 K at <200 ps after plasma breakdown to <4000 K within ∼1 ns, with near-ambient rotational temperatures [T R (C)] ∼ 300 K due to limited collisional energy transfer. This early-time T V (C) trend is representative of a direct and unquenched look into the high-energy tail of the electron energy distribution function; thus, it tracks real-time changes in the mean electron energy via the N2(C) emission signatures. This is followed by the rapid onset of N + /O + ionic emission after a distinct time delay of ∼14.9 ns due to multistep chemical kinetics. The ionic emission enables determination of electron densities (n e ) >2 × 10 19 cm −3 and electron temperatures (T e ) >36 000 K, indicating the transition to a nearly fully ionized regime. The ps–ns temporal dynamics are also compared between air and N 2 plasmas to assess the influence of collisional partners, as well as across the anode, cathode, and central gap regions to identify spatial variations in plasma behavior. Finally, this work demonstrates versatile continuously probing approach capable of spectro-temporal and spatially resolved single-shot measurements of key state variables in the ps–ns evolution of atmospheric-pressure nanosecond pulsed plasmas.

Electric discharges↗

DOE OSTI2023

Variable magnetic field electron spectrometer to measure hot electrons in the range of 50–460 keV

Resonance absorption (RA) occurs when a p-polarized electromagnetic wave, obliquely incident on an inhomogeneous plasma, tunnels past its turning point and resonantly excites an electron plasma wave (EPW) at the critical density. This phenomenon is important, for instance, in the direct drive approach to inertial fusion energy and is a particular example of a wider phenomenon in plasma physics known as mode conversion, which is crucial for heating magnetic fusion devices, such as tokamaks, via RF heating. Direct measurement of these RA-generated EPW accelerated hot electrons, with energy in the range of a few tens to a few hundreds of keV, is a challenging task due to the relatively low deflecting magnetic fields needed. The solution described here is a magnetic electron spectrometer (MES) with a continually changing magnetic field, lower at the entrance of the MES and gradually increasing toward the end, that enables the measurement of a wide spectral range of electrons with energies between 50 and 460 keV. Electron spectra taken in a LaserNetUS RA experiment were acquired from plasmas generated by irradiating polymer targets with the combination of an ~300 ps pulse followed by a series of ten high intensity 50–200 fs duration laser pulses from the ALEPH laser at Colorado State University. In conclusion, the high intensity beam is designed as spike trains of uneven duration and delay pulses in order to modify the RA phenomenon.

47 OTHER INSTRUMENTATION↗

DOE OSTI2026

Partially Ionized Plasma Physics and Technological Applications

Partially ionized plasma physics has attracted increased attention recently due to numerous technological applications made possible by the increased sophistication of computer modelling, the depth of the theoretical analysis, and the technological applications to a vast field of manufacturing for computer components. Partially ionized plasma is characterized by a significant presence of neutral particles in contrast to the fully ionized plasma. The theoretical analysis is based upon solutions of the kinetic Boltzmann equation, yielding the non-Maxwellian electron energy distribution function (EEDF), thereby emphasizing the difference with a fully ionized plasma. The impact of the effect on discharges in inert and molecular gases is described in detail, yielding the complex nonlinear phenomena resulting in plasma selforganization. A few examples of such phenomena are given, including the non-monotonic EEDFs in the discharge afterglow in a mixture of argon with the molecular gas NF3; the explosive generation of cold electron populations in capacitive discharges, hysteresis of EEDF in inductively coupled plasmas. Recently, highly advanced computer codes were developed in order to address the outstanding challenges in plasma technology. These developments are briefly described in general terms.

non-Maxwellian electron energy distribution functi↗

DOE OSTI2024

Helium metastable density determination in the COST reference source by absolutely calibrated optical emission spectroscopy

Helium metastable densities in the COST Reference Microplasma Jet are estimated for a variety of He/N2 admixtures and dissipated powers by applying a collisional-radiative model to absolutely calibrated optical emission spectroscopy measurements. This is accomplished by delineating the excitation mechanisms that result in the N2(C–B) and N2+(B–X) emission bands, the latter of which is strongly coupled to the presence of helium metastables. A number of other plasma parameters are established and discussed for each operating condition including the electron energy distribution function, reduced electric field, rate constants, and electron density. With these parameters, the reaction rates for the primary ionization pathways are also calculated, emphasizing the importance of helium metastables for discharge sustainment. Good agreement with the existing literature is found for most plasma parameters and for helium metastable densities, in particular. A clear [N2]−1 relationship between the nitrogen concentration and density of helium metastables is demonstrated, as has been identified in previous studies in analogous atmospheric pressure plasma jets. This validates the efficacy of this optical technique for determining helium metastable densities and establishes it as a viable, and in many cases, more accessible alternative to other means of quantifying helium metastables in low-temperature plasmas.

Physics↗

DOE OSTI2023

Electron kinetics in a positive column of AC discharges in a dynamic regime

Abstract We have performed hybrid kinetic-fluid simulations of a positive column in alternating current (AC) argon discharges over a range of driving frequencies f and gas pressure p for the conditions when the spatial nonlocality of the electron energy distribution function (EEDF) is substantial. Our simulations confirmed that the most efficient conditions of plasma maintenance are observed in the dynamic regime when time modulations of mean electron energy (temperature) are substantial. The minimal values of the root mean square electric field and the electron temperature have been observed at f/p values of about 3 kHz Torr −1 in a tube of radius R = 1 cm. The ionization rate and plasma density reached maximal values under these conditions. The numerical solution of a kinetic equation allowed accounting for the kinetic effects associated with spatial and temporal nonlocality of the EEDF. Using the kinetic energy of electrons as an independent variable, we solved an anisotropic tensor diffusion equation in phase space. We clarified the role of different flux components during electron diffusion in phase space over surfaces of constant total energy. We have shown that the kinetic theory uncovers a more exciting and rich physics than the classical ambipolar diffusion (Schottky) model. Non-monotonic radial distributions of excitation rates, metastable densities, and plasma density have been observed in our simulations at pR > 6 Torr cm. The predicted off-axis plasma density peak in the dynamic regime has never been observed in experiments so far. We hope our results stimulate further experimental studies of the AC positive column. The kinetic analysis could help uncover new physics even for such a well-known plasma object as a positive column in noble gases.

Physics↗

DOE OSTI2024

Spectral analysis and kinetic modeling of radioluminescence in air and nitrogen

Here, in this article we present a quantitative analysis of the second positive system of molecular nitrogen and the first negative system of the molecular nitrogen cation excited in the presence of ionizing radiation. Optical emission spectra of atmospheric air and nitrogen surrounding 210 Po sources were measured from 250 to 400 nm. Multi-Boltzmann and non-Boltzmann vibrational distribution spectral models were used to determine the vibrational temperature and vibrational distribution function of the emitting N 2 (C 3 Π u ) and N 2 + (B 2 Σ + u ) states. A zero-dimensional kinetic model, based on the electron energy distribution function (EEDF) and steady-state excitation and de-excitation of N 2 (X 1 Σ + g ), N 2 + (B 2 Σ + u ), N 2 + (X 2 Σ + g ), N 4 + , O 2 + , and N 2 (C 3 Π u , v), was developed for the prediction of the relative spectral intensity of both the N 2 + (B 2 Σ + u → X 2 Σ + g ) emission band and the vibrational bands of N 2 (C 3 Π u → B 3 Π g ) for comparison with the experimental data.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗