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At least 73 records · Page 4

Statistical analysis of non-Maxwellian electron distribution functions measured with angularly resolved Thomson scattering

Angularly resolved Thomson scattering is a novel extension of Thomson scattering, enabling the measurement of the electron velocity distribution function over many orders of magnitude. Here, details of the theoretical basis of the technique and the instrument designed for this measurement are described. Angularly resolved Thomson-scattering data from several experiments are shown with descriptions of the corresponding distribution functions. A reduced model describing the distribution function is given and used to perform a Monte Carlo analysis of the uncertainty in the measurements. The electron density and temperature were determined to a precision of 12% and 21%, respectively, on average, while all other parameters defining the distribution function were generally determined to better than 20%. It was found that these uncertainties were primarily due to limited signal to noise and instrumental effects. Furthermore, measurements with this level of precision were sufficient to distinguish between Maxwellian and non-Maxwellian distribution functions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fusion yield of plasma with velocity-space anisotropy at constant energy

Velocity-space anisotropy can significantly modify fusion reactivity. The nature and magnitude of this modification depends on the plasma temperature, as well as the details of how the anisotropy is introduced. For plasmas that are sufficiently cold compared to the peak of the fusion cross section, anisotropic distributions tend to have higher yields than isotropic distributions with the same thermal energy. At higher temperatures, it is instead isotropic distributions that have the highest yields. However, the details of this behavior depend on exactly how the distribution differs from an isotropic Maxwellian. Therefore, this paper describes the effects of anisotropy on fusion yield for the class of anisotropic distribution functions with the same energy distribution as a 3D isotropic Maxwellian and compares those results with the yields from bi-Maxwellian distributions. In many cases, especially for plasmas somewhat below reactor-regime temperatures, the effects of anisotropy can be substantial.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Measurement of Thomson-scattering spectra with continuous angular resolution (invited)

Here, a novel Thomson-scattering diagnostic with continuous angular resolution over a span of 120° was developed for the characterization of plasmas produced at the Omega Laser Facility. Spectrally resolving light scattered from electron plasma wave features as a function of emission angle provides a means to efficiently probe a large range of plasma frequencies and k vectors. Together, these spectra contain critical constraints on the plasma-physics models used to interpret the data and enable experimental measurements of the electron-velocity distribution function over several orders of magnitude without assumptions about its mathematical form. Major components of the instrument include (1) a reflective collection objective that gathers light over a range of 120° × 12°; (2) a spatial-filter image relay for measurement localization; (3) cylindrical optics for producing a line image of the collection aperture; (4) a transmission grating spectrometer; and (5) a time-gated, image-intensified camera. Thomson-scattered light collected from an ~(50 – μM) 3 volume of plasma is recorded with 0.8-nm spectral and 1° angular resolution. Initial experiments examined the properties of the electron-velocity distribution in gas-jet-produced plasmas in the presence of heating via inverse bremsstrahlung absorption.

47 OTHER INSTRUMENTATION↗

Theory, observations, and simulations of kinetic entropy in a magnetotail electron diffusion region

In this work, we examine velocity-space kinetic entropy, a spatially local measure of entropy for systems out of thermal equilibrium, during an encounter of an electron diffusion region at a magnetic reconnection site in Earth’s magnetotail by the Magnetospheric Multiscale (MMS) mission. We start by generalizing the theory of kinetic entropy to the case of non-uniform velocity space grids and transforming the equations into spheri- cal energy coordinates useful to experimental plasma detectors. The theory is then applied to MMS data and compared to particle-in-cell simulations of reconnection. We demonstrate that the entropy-based non-Maxwellianity measure from the MMS data is of sufficiently high precision to reliably identify non-Maxwellian distributions and therefore the measurements when kinetic effects are most significant. By comparing two different non-Maxwellian measures, we show that total entropy density suffers from “information loss” because it lacks a dependence on the velocity space grid, and so has lost information about how well a distribution function is resolved. Local velocity-space kinetic entropy density recovers this information. We quantify information loss and argue that the considerations needed to minimize it are crucial for instruments designed to measure distribution functions in situ.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Molecular beam scattering from flat jets of liquid dodecane and water

Abstract Molecular beam experiments in which gas molecules are scattered from liquids provide detailed, microscopic perspectives on the gas–liquid interface. Extending these methods to volatile liquids while maintaining the ability to measure product energy and angular distributions presents a significant challenge. The incorporation of flat liquid jets into molecular beam scattering experiments in our laboratory has allowed us to demonstrate their utility in uncovering dynamics in this complex chemical environment. Here, we summarize recent work on the evaporation and scattering of Ne, CD 4 , ND 3 , and D 2 O from a dodecane flat liquid jet and present first results on the evaporation and scattering of Ar from a cold salty water jet. In the evaporation experiments, Maxwell–Boltzmann flux distributions with a cos θ angular distribution are observed. Scattering experiments reveal both impulsive scattering (IS) and trapping followed by thermal desorption (TD). Super‐specular scattering is observed for all four species scattered from dodecane and is attributed to anisotropic momentum transfer to the liquid surface. In the IS channel, rotational excitation of the polyatomic scatterers is a significant energy sink, and these species accommodate more readily on the dodecane surface compared to Ne. Our preliminary results on cold salty water jets suggest that Ar atoms undergo some vapor‐phase collisions when evaporating from the liquid surface. Initial scattering experiments characterize the mechanisms of Ar interacting with an aqueous jet, allowing for comparison to dodecane systems. Key Points Molecular beam scattering from flat liquid jets is a powerful technique to elucidate mechanistic detail at the gas–liquid interface. Previous dodecane scattering experiments have uncovered angularly‐resolved thermal desorption fractions and energy transfer at the interface for several small molecule scatterers. Preliminary results on scattering from cold salty water reveal mechanisms of interaction between argon and an aqueous jet.

Yang, Walt↗

Discrete generative diffusion models without stochastic differential equations: A tensor network approach

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a “score function” that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such “discrete diffusion models” (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the d = 1 constrained Fredkin chain and the d = 2 Ising model. Published by the American Physical Society 2025

Causer, Luke (ORCID:0000000194243473)↗

Collisionless adiabatic afterglow

In this work, we study, by numerical and analytical means, the evolution of a collisionless plasma initiated between absorbing walls. The ensuing flow is described by rarefaction waves that travel inward from the boundaries, interact, and eventually vanish after crossing through, leading up to the asymptotic stage of the decay. Particle simulations indicate that the kinetic evolution strongly resembles one found in isentropic gas dynamics. Namely, a very gradual density profile forms in the expanding central region where the rarefaction waves interact, with an accompanying linear velocity profile. Asymptotically, the density falls off as 1/t. The density and the flux at the boundary show little variation over the period when rarefaction waves still exist. Plasma potential, on the other hand, drops quite rapidly (on the underlying ion-acoustic timescale) to less than initial electron temperature Te when over 70% of the particles still remain in the system. This is due to electron kinetics being governed by conservation of adiabatic invariant in a slowly varying potential well. Analytical model of the velocity distribution is presented to explain the simulations. The results have implications for afterglow plasmas used in material processing and also for ion-extraction devices. One property of potential interest is good uniformity of the decaying plasma that occurs after approximately one ion-acoustic time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A physics-informed deep learning description of Knudsen layer reactivity reduction

A physics-informed neural network (PINN) is used to evaluate the fast ion distribution in the hot spot of an inertial confinement fusion target. The use of tailored input and output layers to the neural network is shown to enable a PINN to learn the parametric solution to the Vlasov–Fokker–Planck equation in the absence of any synthetic or experimental data. As an explicit demonstration of the approach, the specific problem of Knudsen layer fusion yield reduction is treated. Here, the predictions from the Vlasov–Fokker–Planck PINN are used to provide a non-perturbative solution of the fast ion tail in the vicinity of the hot spot, thus allowing the spatial profile of the fusion reactivity to be evaluated for a range of collisionalities and hot spot conditions. Excellent agreement is found between the predictions of the Vlasov–Fokker–Planck PINN and the results from traditional numerical solvers with respect to both the energy and spatial distribution of fast ions and the fusion reactivity profile, demonstrating that the Vlasov–Fokker–Planck PINN provides an accurate and efficient means of determining the impact of Knudsen layer yield reduction across a broad range of plasma conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Characterization of thermal transport and evolution of Au plasma in ICF experiments by Thomson scattering

Here, this paper demonstrates the capability of optical Thomson scattering (OTS) to measure thermal transport, and provides support to radiation hydrodynamic and kinetic simulations of electron thermal transport and plasma evolution. OTS theory and plasma simulations are applied to the interpretation of experimental measurements of laser-produced plasma from spherical gold targets on the OMEGA laser facility. The dynamical form factor, S($\vec{k}$, ω), of electron density fluctuations that is used in the fitting of Thomson scattering spectra includes ion–ion collisions and effects of non-Maxwellian distribution functions. OTS measurements and their interpretation are consistent with the nonlocal transport model in radiation hydrodynamic simulations as well as with kinetic simulations in the second half of the probe pulse duration. In particular, the reversal of heat transport during cooling is observed to be consistent with simulations, while some discrepancies are noted during the initial heating of the Au targets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Multi-dimensional incoherent Thomson scattering system in PHAse Space MApping (PHASMA) facility

A multi-dimensional incoherent Thomson scattering diagnostic system capable of measuring electron temperature anisotropies at the level of the electron velocity distribution function (EVDF) is implemented on the PHAse Space MApping facility to investigate electron energization mechanisms during magnetic reconnection. This system incorporates two injection paths (perpendicular and parallel to the axial magnetic field) and two collection paths, providing four independent EVDF measurements along four velocity space directions. For strongly magnetized electrons, a 3D EVDF comprised of two characteristic electron temperatures perpendicular and parallel to the local magnetic field line is reconstructed from the four measured EVDFs. As a result, validation of isotropic electrons in a single magnetic flux rope and a steady-state helicon plasma is presented.

47 OTHER INSTRUMENTATION↗

Electron cyclotron emission measurements and modeling in optically semi-transparent plasma on the HSX stellarator

On the Helically Symmetric Experiment (HSX), electron cyclotron emission (ECE) at the second harmonic of the electron gyrofrequency is measured with a 16-channel heterodyne receiver. An ECE radiometer diagnostic has been calibrated with a broadband frequency source, allowing independent measurements of the electron temperature. The antenna pattern has a significant impact on the measurements, and modeling its effect is necessary to produce an ECE radiation temperature spectrum. Measurements, calibration results, and modeling of the ECE data are presented in this paper. At a relatively high plasma density, HSX plasmas are thermal, and the radiation temperature measured by the radiometer is in good agreement with the electron temperature measured by a Thomson scattering diagnostic. At a relatively low plasma density, the deviation from a Maxwellian distribution is large, and asymmetry in the radiation temperature profile is measured. These measurements are supported by single-pass and multi-pass ray tracing calculations of the electron cyclotron emission using the TRAVIS ray tracing code. Thermal and nonthermal electron populations exist in HSX, and the effect of these populations on the asymmetry in the measured emission is presented.

Cyclotron radiation↗

Verification of an energy-conserving semi-implicit electrostatic particle-in-cell scheme for modeling high-density plasma at scale

A verification study of a semi-implicit energy-conserving electrostatic particle-in-cell algorithm is presented. The algorithm relaxes the time-step and mesh-size constraints that require resolution of the plasma period and Debye length associated with traditional explicit momentum-conserving particle-in-cell algorithms. Physical implications and applicability of using the semi-implicit scheme for modeling high-density plasmas are discussed. Where possible, numerical results are compared against analytical solutions. The simulation results indicate that the algorithm is stable at time steps larger than twice the inverse plasma frequency and cell sizes larger than the Debye length. It is found that the algorithm gives adequate results, provided that the distribution function and the spatiotemporal scales dictating the physics of the problem are resolved. As such, the algorithm may provide a robust method for kinetic modeling of high-density plasmas at scale.

Cyclotron resonance↗

Modeling the electron cyclotron emission radiation signature from suprathermal electrons in a tokamak

An Electron Cyclotron Emission (ECE) modeling code has been developed to model ECE radiation with an arbitrary electron momentum distribution, a small oblique angle, both ordinary (O-mode) and extraordinary polarizations (X-mode), and multiple cyclotron frequency harmonics. The emission and absorption coefficients are calculated using the Poynting theorem from the cold plasma dispersion and the electron–microwave interaction from the full anti-Hermitian tensor. The modeling shows several ECE radiation signatures that can be used to diagnose the population of suprathermal electrons in a tokamak. First, in an n = 2 X-mode (X2) optically thick plasma and oblique ECE view, the modeling shows that only suprathermal electrons, which reside in a finite region of the velocity and space domains, can effectively generate cyclotron emissions to the ECE receiver. The code also finds that the O1 mode is sensitive to suprathermal electrons of both a high v ⊥ and v || , while the X2 mode is dominantly sensitive to suprathermal electrons of a high v ⊥ . Finally, the modeling shows that an oblique ECE system with both X/O polarization and a broad frequency coverage can be used to effectively yield information of the suprathermal electron population in a tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Electron-only reconnection and associated electron heating and acceleration in PHASMA

In this work, using incoherent Thomson scattering, electron heating and acceleration at the electron velocity distribution function (EVDF) level are investigated during electron-only reconnection in the PHAse Space MApping (PHASMA) facility. Reconnection arises during the merger of two kink-free flux ropes. Both push and pull type reconnection occur in a single discharge. Electron heating is localized around the separatrix, and the electron temperature increases continuously along the separatrix with distance from the X-line. The local measured gain in enthalpy flux is up to 70% of the incoming Poynting flux. Notably, non-Maxwellian EVDFs comprised of a warm bulk population and a cold beam are directly measured during the electron-only reconnection. The electron beam velocity is comparable to, and scales with, electron Alfvén speed, revealing the signature of electron acceleration caused by electron-only reconnection. The observation of oppositely directed electron beams on either side of the X-point provides “smoking-gun” evidence of the occurrence of electron-only reconnection in PHASMA. 2D particle-in-cell simulations agree well with the laboratory measurements. The measured conversion of Poynting flux into electron enthalpy is consistent with recent observations of electron-only reconnection in the magnetosheath [Phan et al., Nature 557, 202 (2018)] at similar dimensionless parameters as in the experiments. The laboratory measurements go beyond the magnetosheath observations by directly resolving the electron temperature gain.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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↗

Molecular beam scattering of ammonia from a dodecane flat liquid jet

The evaporation and scattering of ND 3 from a dodecane flat liquid jet are investigated and the results are compared with previous studies on molecular beam scattering from liquid surfaces. Evaporation is well-described by a Maxwell–Boltzmann flux distribution with a cos θ angular distribution at the liquid temperature. Scattering experiments at E i = 28.8 kJ mol -1 over a range of deflection angles show evidence for impulsive scattering and thermal desorption. Further, at a deflection angle of 90°, the thermal desorption fraction is 0.49, which is higher than that of other molecules previously scattered from dodecane and consistent with work performed on NH 3 scattering from a squalane-wetted wheel. ND 3 scattering from dodecane results in super-specular scattering, as seen in previous experiments on dodecane. The impulsive scattering channel is fitted to a “soft-sphere” model, yielding an effective surface mass of 55 amu and an internal excitation of 5.08 kJ mol -1 . Overall, impulsively scattered ND 3 behaves similarly to other small molecules scattered from dodecane.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dimension-free path-integral molecular dynamics without preconditioning

Convergence with respect to imaginary-time discretization (i.e., the number of ring-polymer beads) is an essential part of any path-integral-based molecular dynamics (MD) calculation. However, an unfortunate property of existing non-preconditioned numerical integration schemes for path-integral molecular dynamics—including essentially all existing ring-polymer molecular dynamics (RPMD) and thermostatted RPMD (T-RPMD) methods—is that for a given MD time step, the overlap between the exact ring-polymer Boltzmann–Gibbs distribution and that sampled using MD becomes zero in the infinite-bead limit. This has clear implications for hybrid Metropolis Monte Carlo/MD sampling schemes, and it also causes the divergence with bead number of the primitive path-integral kinetic-energy expectation value when using standard RPMD or T-RPMD. We show that these and other problems can be avoided through the introduction of “dimension-free” numerical integration schemes for which the sampled ring-polymer position distribution has non-zero overlap with the exact distribution in the infinite-bead limit for the case of a harmonic potential. Most notably, we introduce the BCOCB integration scheme, which achieves dimension freedom via a particular symmetric splitting of the integration time step and a novel implementation of the Cayley modification [R. Korol et al., J. Chem. Phys. 151, 124103 (2019)] for the free ring-polymer half-steps. More generally, we show that dimension freedom can be achieved via mollification of the forces from the external physical potential. The dimension-free path-integral numerical integration schemes introduced here yield finite error bounds for a given MD time step, even as the number of beads is taken to infinity; these conclusions are proven for the case of a harmonic potential and borne out numerically for anharmonic systems that include liquid water. The numerical results for BCOCB are particularly striking, allowing for nearly three-fold increases in the stable time step for liquid water with respect to the Bussi–Parrinello (OBABO) and Leimkuhler (BAOAB) integrators, while introducing negligible errors in the calculated statistical properties and absorption spectrum. Importantly, the dimension-free, non-preconditioned integration schemes introduced here preserve ergodicity and global second-order accuracy, and they remain simple, black-box methods that avoid additional computational costs, tunable parameters, or system-specific implementations.

Korol, Roman (ORCID:0000000193076351)↗

Response of a charged particle in contact with a chaotic thermostat to an oscillating electric field

A numerical investigation is made of the response of a thermalized charge in contact with a chaotic thermostat to an externally applied, oscillating electric field, with and without a confining magnetic field. This study is based on the recent theoretical development of a chaotic thermostat [G. J. Morales, Phys. Rev. E 99, 062218 (2019)] for which the static properties of a thermalized charge (spatial diffusion and mobilities) were previously established. It is found here that in the unmagnetized case, to extract significant power from the oscillating electric field requires that the oscillatory velocity be larger than the thermal velocity. The spatial diffusion caused by the self-consistent, chaotic fluctuations is shown to be reduced, and even suppressed, by the coherent oscillations. The frequency-dependent mobilities, including cyclotron resonance, are determined, and the nonlinear modifications produced by large electric fields are explored. The value of the mobilities and the modifications to the diffusion coefficient exhibit non-monotonic dependencies on the control parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗