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DOE OSTI2026

Particle Acceleration and Pitch-angle Evolution in Relativistic Turbulence

Synchrotron radiation detected from relativistic astrophysical objects such as pulsar-wind nebulae and jets from active galactic nuclei depends on the magnetic fields and the distribution functions of energetic electrons in these systems. Relativistic magnetically dominated turbulence has been recognized as an efficient mechanism for structure formation and nonthermal particle acceleration in these environments. Recent numerical simulations of relativistic turbulence have provided insights into the energy distribution functions of accelerated electrons. Much less is currently understood about their pitch angle distributions, which are crucial for accurately interpreting the spectra of synchrotron radiation. We perform a detailed case study of the pitch angle distributions formed during the process of turbulent acceleration for B 0 /δB 0 = 10 and $\tilde{σ}$ 0 ~40, where B0 is the uniform component of the magnetic field, δB0 is the fluctuating component, and $\tilde{σ}$ 0 is the plasma magnetization based on the magnetic fluctuations. We find that even minimal numerical noise can cause substantial pitch angle scattering, but we demonstrate techniques for overcoming the numerical challenges associated with the evolution of very small pitch angles. Our numerical results are consistent with the phenomenological considerations found in C. Vega et al. (2024a, 2025).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Development of an Ultrahigh-bandwidth Phase Contrast Imaging System for detection of electron scale turbulence and Gigahertz Radio-Frequency Waves

The study of waves and turbulence is vital to the development of future reactor-grade plasma devices developed in the quest for fusion energy. These fluctuations are responsible for moving heat and particles across the magnetic field, and a predictive understanding of them is needed to achieve the density and temperature required to sustain a plasma fusion reaction. While many techniques have been developed for measuring waves and fluctuations, every measurement method has limitations. There are relatively few techniques for measuring very high frequency fluctuations, such as radio frequency waves injected to heat the plasma, unstable waves driven by suprathermal particles, or short wavelength electrostatic waves driven by electron temperature or density gradients. The present project builds upon the proven phase contrast imaging (PCI) technique to extend the response of the diagnostic by orders of magnitude in frequency and almost a factor of ten in spatial resolution. PCI provides a measurement of electron density based on small angle scattering of a CO-2 laser beam by using optical techniques to render a phase shift as an intensity change on a detector. Due to the telecommunications revolution, technological development by manufacturers has focused on components in the near -infrared, so that high- quality lasers and detectors at 1.55 µm are readily available. Shifting PCI design to a new, shorter wavelength has numerous advantages and challenges. Similar detector performance is available with room-temperature arrays with GHz bandwidth, while the detector arrays for 10.6 µm required liquid nitrogen cooling and were therefore limited to a bandwidth of about 1 MHz. Shifting to a shorter wavelength reduces the angle at which the laser beam scatters off of plasma waves, allowing more such scattered components to pass through the aperture of the vacuum vessel port and be collected by the PCI, which increases the spatial resolution. Concomitant with these benefits, various questions of performance arise. At shorter laser wave- length, the sensitivity to mirror and lens quality is increased, the contribution of the laser to the overall system noise is increased, and the sensitivity to vibrations is increased. The custom optical components at the heart of the PCI technique were required to be properly scaled for the shorter wavelength, so fabrication technologies needed to be explored. This project was designed to show that a low noise, high response PCI system at 1.55 µm could be constructed and operated, and then to quantify potential issues to allow extrapolation to a full-size production system providing physics measurements on a large plasma device. The first stage, producing the custom optical component called a Phase Plate, was successfully achieved using two methods. First, an easily reproduced masking and coating technique was able to produce good phase plates with the required parameters. Second, a nanofabrication technique was found to produce extremely high quality phase plates at a competitive price. The PCI constructed with the new phase plates and 1.55 µm laser was found to provide excellent wavelength measurements with the theoretically expected response. The sensitivity to optical surface quality was found to be in line with previous measurements at 10.6 µm. The observed signal-to-noise ratio was similar to the theoretically expected value. The effect of vibrations on PCI was studied with the first measurement of the effect of beam motion on PCI response and comparison to theory, allowing for a quantitative prediction of the effect of vibrations on a production PCI system and the requirements for improved beam stabilization. PCI is an extremely cost-effective method to provide a low noise, absolutely calibrated measurement of plasma fluctuations across a wide spatial scale. This project has shown that a 1.55 µm PCI using modern techniques and components is less expensive than the 10.6 µm PCI of a few years ago, with the largest savings in phase plate fabrication and the infrared detector array.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Experimental Validation of a Kinetic Ballooning Mode in High-Performance High-Bootstrap Current Fraction Fusion Plasmas

We report the observation of a set of coherent high frequency electromagnetic fluctuations that leads to a turbulence induced self-regulating phenomenon in the DIII-D high bootstrap current fraction plasma. The fluctuations have frequency of 130~220kHz, the poloidal wave length and phase velocity are 16~30 m -1 and ~30 km/s, respectively in the outboard midplane with the estimated toroidal mode number n~5- 9. The fluctuations are located in the internal transport barrier (ITB) region at large radius and are experimentally validated to be kinetic ballooning modes (KBM). Furthermore, quasilinear estimation predicts the KBM to be able to drive experimental particle flux and non-negligible thermal flux, suggesting its significant role in regulating the ITB saturation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Feasibility Study: High-k Temperature (HiT) Fluctuation Diagnostic

The objective of the proposed research was to explore the feasibility of making measurements of high-k (electron-scale, ETG-relevant) electron temperature fluctuations in the core plasma of tokamaks and stellarators. We found that soft X-ray imaging combined with our novel pseudolocal tomographic algorithm enables local measurements of low-k (ion-scale, ITG/TEM and KBM/MTM relevant) electron temperature fluctuations in spherical tokamaks. The design parameters needed to consider deploying this new diagnostic are presented, and predictions for what the diagnostic would measure in L-mode and H-mode plasmas at NSTX-U, a high performance spherical tokamak in the USA, suggest that the new diagnostic can be used to study turbulence and transport over a wide range of plasma parameters, such as collisionality and plasma beta.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Observation of a reduced-turbulence regime with boron powder injection in a stellarator

Abstract In state-of-the-art stellarators, turbulence is a major cause of the degradation of plasma confinement. To maximize confinement, which eventually determines the amount of nuclear fusion reactions, turbulent transport needs to be reduced. Here we report the observation of a confinement regime in a stellarator plasma that is characterized by increased confinement and reduced turbulent fluctuations. The transition to this regime is driven by the injection of submillimetric boron powder grains into the plasma. With the line-averaged electron density being kept constant, we observe a substantial increase of stored energy and electron and ion temperatures. At the same time, the amplitude of the plasma turbulent fluctuations is halved. While lower frequency fluctuations are damped, higher frequency modes in the range between 100 and 200 kHz are excited. We have observed this regime for different heating schemes, namely with both electron and ion cyclotron resonant radio frequencies and neutral beams, for both directions of the magnetic field and both hydrogen and deuterium plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

A reduced-turbulence regime in the Large Helical Device upon injection of low-Z materials powders

Abstract Recently an improved confinement regime, characterized by reduced turbulent fluctuations has been observed in the Large Helical Device upon the injection of boron powder into the plasma (Nespoli et al 2022 Nat. Phys. 18 350–56). In this article, we report in more detail the experimental observations of increased plasma temperature and the decrease of turbulent fluctuations across the plasma cross section, on an extended database. In particular, we compare powders of different materials (B, C, BN), finding similar temperature improvement and turbulence response for the three cases. Modeling of the powder penetration into the plasma and of neoclassical electric field and fluxes support the interpretation of the experimental results. Additionally, we report evidence of the temperature improvement increasing with powder injection rates and decreasing for both increasing density and heating power. Though, plasma turbulence response varies depending on the initial conditions of the plasma, making it difficult to draw an inclusive description of the phenomenon.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

First Measurement of Drift-Alfvén Wave Polarization in Magnetically Confined Fusion Plasmas

Polarization of drift-Alfvén waves, defined as the ratio of electrostatic to electromagnetic fluctuations, has remained unmeasurable in fusion plasmas for decades, despite its pivotal role in understanding wave dynamics and their impact on plasmas. We report the first measurements of drift-Alfvén wave polarization in a hot, magnetically-confined plasma. Here, the breakthrough is enabled by a novel methodology developed from gyrokinetic theory, utilizing fluctuations of electron temperature and density. Analysis of data from the DIII-D tokamak reveals that the waves above the geodesic acoustic mode frequency exhibit dominant electromagnetic polarization, whereas lower frequency waves show a mix of electromagnetic and electrostatic polarization, indicating a strong coupling between shear Alfvén waves and drift-acoustic waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Kinetic theory of particle-in-cell simulation plasma and the ensemble averaging technique

Abstract We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlation at the start of the simulation between the statistical fluctuations of the weighted densities of macroparticle centers in the plasma particle phase-space. The fluctuations are associated with different initial conditions, typically due to the random initial conditions (in velocity space) of the macroparticles/simulation plasma, assigned according to their initial distribution of probability. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace–Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell’s equations for the fields, as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelation spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon (1970b Proc. 4th Conf. Numerical Simulation of Plasmas ) using a test macroparticle approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes using arbitrary macroparticle weights. Analytical estimates of statistical fluctuation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles. This method is illustrated by linear Landau damping uncovering (from noise, which is usually considered numerical) the physical fluctuations driven by a single small amplitude electrostatic wave perturbing a PIC simulation plasma in equilibrium.

fluctuations correlations↗
DOE OSTI2021

Observation of quasi-coherent density fluctuation in scrape-off layer enhancing boundary transport in high-βN hybrid plasmas on DIII-D

In this work, we report the observation of a quasi-coherent density fluctuation (QCF) by the Doppler backscattering system in the scrape-off layer (SOL) region of the DIII-D tokamak. This QCF is observed in high power, high performance hybrid plasmas with near double-null divertor (DND) shape during the electron cyclotron heating period. This mode is correlated with a steepened SOL density profile, and leads to significantly elevated particle and heat fluxes between ELMs. The SOL QCF is a long-wavelength ion-scale fluctuation (k θ ρ s ≈0.2-0.4 and k r ρ s ≈0.03), and propagates in the ion diamagnetic direction in the plasma frame. Its radial expanse is about 1.5–2 cm, well beyond the typical width of heat flux λ q on DIII-D. Also, the SOL QCF does not show any clear dependence on the effective SOL collisionality, and thus may raise issues on the control of plasma-material interactions in low collisionality plasmas in which the blob-induced transport is reduced. A linear simulation using BOUT++ with a 5-field reduced model is performed and compared with experimental observations. In simulation results, an interchange-like density perturbation can be driven by the SOL density gradient, and its peak location and the radial width of the density perturbation are in agreement with the experimental observations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Hyperdiffusion of dust particles in a turbulent tokamak plasma

In this work, the effect of plasma turbulence on the trajectories of dust particles is investigated for the first time. The dynamics of dust particles is computed using the ad hoc developed Dust Injection Simulator code, using a 3D turbulent plasma background computed with the TOKAM3X code. As a result, the evolution of the particle trajectories is governed by the ion drag force, and the shape of the trajectory is set by the Stokes number St∝a d /n 0 , with a d the dust radius and n 0 the density at the separatrix. The plasma turbulence is observed to scatter the dust particles, exhibiting a hyperdiffusive regime in all cases. The amplitude of the turbulent spread of the trajectories Δr 2 is shown to depend on the ratio Ku/St, with Ku∝u rms the Kubo number and urms the fluctuation level of the plasma flow. These results are compared with a simple analytical model, predicting Δr 2 ∝(Ku/St) 2 t 3 , or Δr 2 ∝(u rms n 0 /a d ) 2 t 3 . As the dust is heated by the plasma fluxes, thermionic emission sets the dust charge, originally negative, to slightly positive values. This results in a substantial reduction of the ion drag force through the suppression of its Coulomb scattering component. The dust grain inertia is then no longer negligible and drives the transition from a hyperdiffusive regime toward a ballistic one.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Hyperdiffusion of dust particles in a turbulent tokamak plasma

The effect of plasma turbulence on the trajectories of dust particles is investigated for the first time. The dynamics of dust particles is computed using the ad-hoc developed Dust Injection Simulator code, using a 3D turbulent plasma background computed with the TOKAM3X code. As a result, the evolution of the particle trajectories is governed by the ion drag force, and the shape of the trajectory is set by the Stokes number $St\propto a_d/n_0$, with $a_d$ the dust radius and $n_0$ the density at the separatrix. The plasma turbulence is observed to scatter the dust particles, exhibiting a hyperdiffusive regime in all cases. The amplitude of the turbulent spread of the trajectories $\Delta r^2$ is shown to depend on the ratio $Ku/St$, with $Ku\propto u_{rms}$ the Kubo number and $u_{rms}$ the fluctuation level of the plasma flow. These results are compared with a simple analytical model, predicting $\Delta r^2\propto (Ku/St)^2t^3$, or $\Delta r^2\propto (u_{rms}n_0/a_d)^2t^3$. As the dust is heated by the plasma fluxes, thermionic emission sets the dust charge, originally negative, to slightly positive values. This results in a substantial reduction of the ion drag force through the suppression of its Coulomb scattering component. The dust grain inertia is then no longer negligible, and drives the transition from a hyperdiffusive regime towards a ballistic one.

dust↗
DOE OSTI2025

Validation of a comprehensive first-principles-based framework for predicting the performance of future stellarators

This paper presents the validation of the GENE-KNOSOS-Tango framework for recovering both the steady-state plasma profiles in the considered radial domain and selected turbulence trends in a stellarator. This framework couples the gyrokinetic turbulence code GENE, the neoclassical transport code KNOSOS, and the transport solver Tango in a multi-timescale simulation feedback loop. Ion-scale kinetic-electron and electron-scale adiabatic-ion flux-tube simulations were performed to evolve the density and temperature profiles for four OP1.2b W7-X scenarios. The simulated density and temperature profiles showed good agreement with the experimental data using a reasonable set of boundary conditions. Equally important was the reproduction of observed trends for several turbulence properties, such as density fluctuations and turbulent heat diffusivities. Key effects were also touched upon, such as electron-scale turbulence and the neoclassical radial electric field shear. The validation of the GENE-KNOSOS-Tango framework enables credible predictions of physical phenomena in stellarators and reactor performance based on a given set of edge parameters.

Gyrokinetic simulations↗
DOE OSTI2024

Effects of Nonzero-frequency Fluctuations on Turbulence Spectral Observations

In situ observations of turbulence spectra in space plasmas are usually interpreted as wavenumber spectra, assuming that the fluctuation frequency is negligible in the plasma flow frame. We explore the effects of nonzero frequency in the plasma flow frame on turbulence spectral observations. The finite frequency can be caused by either propagating waves or nonlinear broadening of nonpropagating structures. We show that the observed frequency spectrum can be modified by the nonzero frequency of turbulent fluctuations in several ways. Specifically, (i) frequency broadening results in a minor modification to the observed spectrum, primarily acting as a smoothing kernel of the spectrum near the spectral break, while the asymptotic spectral index remains unchanged; (ii) wave propagation can affect the observed spectral index for anisotropic turbulence. The effect is significant at low frequencies and weaker at high frequencies, leading to a "concave" shape of the observed perpendicular spectrum; (iii) the Doppler shift for forward- and backward-propagating Elsasser modes can result in a nonzero cross helicity for critical-balanced turbulence since the effect of the Doppler shift favors outward-propagating waves systematically, resulting in an observed imbalance. These results may have important implications for the interpretation of solar wind flows observed by Parker Solar Probe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Spatial Intermittency of Particle Distribution in Relativistic Plasma Turbulence

Abstract Relativistic magnetically dominated turbulence is an efficient engine for particle acceleration in a collisionless plasma. Ultrarelativistic particles accelerated by interactions with turbulent fluctuations form nonthermal power-law distribution functions in the momentum (or energy) space, f ( γ ) d γ ∝ γ − α d γ , where γ is the Lorenz factor. We argue that in addition to exhibiting non-Gaussian distributions over energies, particles energized by relativistic turbulence also become highly intermittent in space. Based on particle-in-cell numerical simulations and phenomenological modeling, we propose that the bulk plasma density has lognormal statistics, while the density of the accelerated particles, n , has a power-law distribution function, P ( n ) dn ∝ n − β dn . We argue that the scaling exponents are related as β ≈ α + 1, which is broadly consistent with numerical simulations. Non-space-filling, intermittent distributions of plasma density and energy fluctuations may have implications for plasma heating and for radiation produced by relativistic turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

On the Effect of Beating during Nonlinear Frequency Chirping

Spectroscopic analyses of energetic particle (EP) driven bursts of MHD fluctuations in magnetically confined plasmas often exhibit chirps that occur simultaneously in groups of two or more. While the superposition of oscillations at multiple frequencies necessarily causes beating in the signal acquired by a localized external probe, self-consistent hybrid simulations of chirping EP modes in a JT-60U tokamak plasma have demonstrated the possibility of global beating, where the mode's electromagnetic field vanishes globally between beats and reappears with opposite phase [Bierwage et al., Nucl. Fusion 57, 016036 (2017)]. This implies that there can be a single coherent field mode that oscillates at multiple frequencies simultaneously when it is resonantly driven by multiple density waves in EP phase space. Conversely, this means that the EP density waves are mutually coupled and interfere with each other via the jointly driven field, a mechanism ignored in some theories of chirping. In this thesis-style treatise, we study the role of field pulsations in general and beating in particular using the Hamiltonian guiding center orbit-following code ORBIT with a reduced wave-particle interaction model in realistic geometry. Beating is found to drive the evolution of EP phase space structures. Additionally, a key mechanism is the pulsation of effective phase space islands combined with the alternation of their effective O- and X-points due to phase jumps between each beat. Observations: (1) Beating causes density wave fronts to advance radially in a pulsed manner and the resulting chirps become staircase-like. (2) The pulsations facilitate convective transfer of material between neighboring layers of phase space density waves. On the one hand, this may inhibit the early detachment of solitary phase space vortices. On the other hand, it facilitates the accumulation of hole and clump fragments into larger structures. (3) Long-range chirping is observed when massive holes or clumps detach and drift away from the turbulent belt around the seed resonance. It is remarkable that the detached vortices remain robust and,on average, maintain their concentric nested layers while being visibly perturbed by the field's continued beating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Applying Thomson scattering to diagnosing turbulent density and velocity fluctuations in a gas-puff z-pinch

The electron plasma wave feature (EPW) in the time-resolved Thomson scattering spectrum is used to obtain the local electron density in imploding high energy density gas-puff z-pinch plasmas. The optical setup was optimized to allow the relatively weak EPW feature obtained from 1 MA imploding neon gas-puff z-pinches to be seen above the continuum emission as well as the brighter ion acoustic wave (IAW) feature. Using a frequency-doubled Nd:YLF laser (E = 10 J, λ = 526.5 nm, Δt= 2.3 ns, spot size ~ 250 μm) and two visible light streak cameras, we determined the average electron density in the imploding plasma sheath 40 ns prior to stagnation to be n e = 2.5 × 10 18 /cm 3 . At pinch time, it reached n e = 1.7 × 10 19 /cm 3 . Here, the electron temperature during implosion measured via the IAW (approximately 50 eV) was four times lower than the implosion electron temperature measured via the EPW (approximately 200 eV), assuming that neither feature is affected by turbulent fluctuations in the plasma. In order for the electron temperatures inferred from the EPW and IAW spectral features to be self-consistent, we find that it is necessary to include velocity fluctuations in the analysis of the IAW feature peaks and corresponding density fluctuation in the peak widths of the EPW feature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Nature and Scalings of Density Fluctuations of Compressible Magnetohydrodynamic Turbulence with Applications to the Solar Wind

Abstract The solar wind is a magnetized and turbulent plasma. Its turbulence is often dominated by Alfvénic fluctuations and often deemed as nearly incompressible far away from the Sun, as shown by in situ measurements near 1 au. However, for solar wind closer to the Sun, the plasma β decreases (often lower than unity) while the turbulent Mach number M t increases (can approach unity, e.g., transonic fluctuations). These conditions could produce significantly more compressible effects, characterized by enhanced density fluctuations, as seen by several space missions. In this paper, a series of 3D MHD simulations of turbulence are carried out to understand the properties of compressible turbulence, particularly the generation of density fluctuations. We find that, over a broad range of parameter space in plasma β , cross helicity, and polytropic index, the turbulent density fluctuations scale linearly as a function of M t , with the scaling coefficients showing weak dependence on parameters. Furthermore, through detailed spatiotemporal analysis, we show that the density fluctuations are dominated by low-frequency nonlinear structures, rather than compressible MHD eigenwaves. These results could be important for understanding how compressible turbulence contributes to solar wind heating near the Sun.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Azimuthal and axial structures in 3D particle-in-cell simulation of Penning discharge

We report the results of a 3D particle-in-cell simulation of cylindrical Penning discharge with the axial magnetic field in the so-called reflex configuration, where the cathode and anti-cathode are biased to the same negative potential. The discharge is supported by thermal electron emission from the cathode. Electron and ion collisions, including ionization, are fully accounted for. The emphasis is on a specific regime in which the plasma potential at the center of the discharge is positive with respect to the chamber walls, serving as an anode. Spatial and temporal scales of the observed azimuthal and axial fluctuations and structures are characterized. It is suggested that azimuthal structures are caused by the dissipative gradient-drift instability. We find that the axial fluctuations related to the plasma-beam instabilities are weakly correlated with the azimuthal perturbations of the density, so that the azimuthal modes rotate as a whole and do not show any axial shear. The behavior of the electric potential is more involved, demonstrating intermittent standing wave and propagating structures in the axial direction that modulate the electron transport, producing the standing wave pattern (along the z-direction) in the radial electron flux.

3D PIC simulation of discharge↗