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DOE OSTI2017

A prospectus on kinetic heliophysics

Under the low density and high temperature conditions typical of heliospheric plasmas, the macroscopic evolution of the heliosphere is strongly affected by the kinetic plasma physics governing fundamental microphysical mechanisms. Kinetic turbulence, collisionless magnetic reconnection, particle acceleration, and kinetic instabilities are four poorly understood, grand-challenge problems that lie at the new frontier of kinetic heliophysics. The increasing availability of high cadence and high phase-space resolution measurements of particle velocity distributions by current and upcoming spacecraft missions and of massively parallel nonlinear kinetic simulations of weakly collisional heliospheric plasmas provides the opportunity to transform our understanding of these kinetic mechanisms through the full utilization of the information contained in the particle velocity distributions. Several major considerations for future investigations of kinetic heliophysics are examined. Furthermore, turbulent dissipation followed by particle heating is highlighted as an inherently two-step process in weakly collisional plasmas, distinct from the more familiar case in fluid theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

Electron parallel transport for arbitrary collisionality

Integral (nonlocal) closures [J.-Y. Ji and E. D. Held, Phys. Plasmas 21, 122116 (2014)] are combined with the momentum balance equation to derive electron parallel transport relations. For a single harmonic fluctuation, the relations take the same form as the classical Spitzer theory (with possible additional terms): The electric current and heat flux densities are connected to the modified electric field and temperature gradient by transport coefficients. In contrast to the classical theory, the dimensionless coefficients depend on the collisionality quantified by a Knudsen number, the ratio of the collision length to the angular wavelength. The key difference comes from the proper treatment of the viscosity and friction terms in the momentum balance equation, accurately reflecting the free streaming and collision terms in the kinetic equation. For an arbitrary fluctuation, the transport relations may be expressed by a Fourier series or transform. Finally, for low collisionality, the electric resistivity can be significantly larger than that of classical theory and may predict the correct timescale for fast magnetic reconnection.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

Nonlinear saturation of kinetic ballooning modes by zonal fields in toroidal plasmas

Kinetic ballooning modes (KBMs) are widely believed to play a critical role in disruptive dynamics as well as turbulent transport in magnetic fusion and space plasmas. While the nonlinear evolution of the ballooning modes has been proposed as a mechanism for “detonation” in various scenarios such as the edge localized modes in tokamaks, the role of the kinetic effects in such nonlinear dynamics remains largely unexplored. In this study, global gyrokinetic simulation results of KBM nonlinear behavior are presented. Instead of the finite-time singularity predicted by ideal magnetohydrodynamic theory, the kinetic instability is shown to develop into an intermediate nonlinear regime of exponential growth, followed by a nonlinear saturation regulated by spontaneously generated zonal fields. In the intermediate nonlinear regime, rapid growth of localized current sheets, which can induce magnetic reconnection, is observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

Acceleration of charged particles to extremely large energies by a sub-Dreicer electric field

Acceleration of a fraction of initially low-energy electrons in a cold, collisional plasma to energies orders of magnitude larger than thermal is shown to be possible with a sub-Dreicer electric field. Because such an electric field does not satisfy the runaway condition, any acceleration will be statistical. Random scattering collisions are probabilistic such that there is 63% chance that a particle collides after traveling one mean free path and a 37% chance of not colliding. If one considers only the electrons that do not collide on traversing a mean free path and also considers that the collisional mean free path scales quadratically with particle kinetic energy, one realizes that there will be a small fraction of electrons that never collide and are accelerated to increasingly high energy. Because the mean free path scales quadratically with kinetic energy, after each successfully traveled mean free path, continued acceleration becomes more likely. This model is applied to an MHD-driven plasma jet experiment at Caltech and it is shown that electrons are accelerated by an electric field associated with a fast magnetic reconnection event occurring as the jet breaks apart. This statistical acceleration model indicates that a fraction ~1.3 × 10 -7 of electrons with initial energy distributed according to a Maxwellian with T = 2 eV will be accelerated to 6 keV in the Caltech experiment and then collide to produce the observed X-ray signal. It is demonstrated that the statistical acceleration model provides a credible explanation for the production of solar energetic electrons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

A new explanation of the sawtooth phenomena in tokamaks

The ubiquitous sawtooth phenomena in tokamaks are so named because the central temperature rises slowly and falls rapidly, similar to the blades of a saw. First discovered in 1974, it has so far eluded a theoretical explanation that is widely accepted and consistent with experimental observations. We propose here a new theory for the sawtooth phenomena in auxiliary heated tokamaks, which is motivated by our recent understanding of “magnetic flux pumping.” In this theory, the role of the (m, n) = (1, 1) mode is to generate a dynamo voltage, which keeps the central safety factor, q 0 , just above 1.0 with low central magnetic shear. When central heating is present, the temperature on axis will increase until at some point, and the configuration abruptly becomes unstable to ideal MHD interchange modes with equal poloidal and toroidal mode numbers, m = n > 1. It is these higher order modes and the localized magnetic stochasticity they produce that cause the sudden crash of the temperature profile, not magnetic reconnection. In conclusion, long time 3D MHD simulations demonstrate these phenomena, which appear to be consistent with many experimental observations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Analytical model for quasi-linear flow response to resonant magnetic perturbation in resistive-inertial and viscous-resistive regimes

In this work, a quasi-linear model for plasma flow response to the resonant magnetic perturbation (RMP) in a tokamak has been rigorously developed in the resistive-inertial (RI) and viscousresistive (VR) regimes purely from the two-field reduced MHD model. Models for plasma response to RMP are commonly composed of equations for the resonant magnetic field response (i.e. the magnetic island) and the torque balance of plasma flow. However, in previous plasma response models, the magnetic island and the torque balance equations are often derived separately from reduced MHD and full MHD equations, respectively. By contrast, in this work we derive both the magnetic island response and the torque balance equations in a quasi-linear model for plasma flow response entirely from a set of two-field reduced MHD equations. Such a quasi-linear model can recover previous plasma flow response models within certain limits and approximations. Furthermore, the physical origins of quasi-linear forces and moments in the flow response equation are also accurately calculated and clarified self-consistently.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Collective optical Thomson scattering in pulsed-power driven high energy density physics experiments (invited)

Optical collective Thomson scattering is used to diagnose magnetized high energy density physics experiments at the Magpie pulsed-power generator at Imperial College London. The system uses an amplified pulse from the 2nd harmonic of a Nd:YAG laser (3 J, 8 ns, 532 nm) to probe a wide diversity of hightemperature plasma objects; with densities in the range of 10 17 -10 19 cm -3 and temperatures between 10 eV and a few keV. The scattered light is collected from 100 μm-scale volumes within the plasmas, which are imaged onto optical fiber arrays. Multiple collection systems observe these volumes from different directions, providing simultaneous probing with different scattering K-vectors (and different associated α-parameters, typically in the range 0.5 – 3) allowing independent measurements of separate velocity components of the bulk plasma flow. The fiber arrays are coupled to an imaging spectrometer with a gated ICCD. The spectrometer is configured to view the ion-acoustic waves (IAWs) of the collective Thomson scattered spectrum. Fits to the spectra with the theoretical spectral density function S(K,ω) yield measurements of the local plasma temperatures and velocities. Fitting is constrained by independent measurements of the electron density from laser interferometry, and the corresponding spectra for different scattering vectors. Furthermore, this TS diagnostic has been successfully implemented on a wide range of experiments, revealing temperature and flow velocity transitions across magnetized shocks, inside rotating plasma jets and imploding wire arrays, as well as providing direct measurements of drift velocities inside a magnetic reconnection current sheet.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Laboratory study of the failed torus mechanism in arched, line-tied, magnetic flux ropes

Coronal mass ejections (CMEs) are some of the most energetic and violent events in our solar system. The prediction and understanding of CMEs are of particular importance due to the impact that they can have on Earth-based satellite systems and, in extreme cases, ground-based electronics. CMEs often occur when long-lived magnetic flux ropes (MFRs) anchored to the solar surface destabilize and erupt away from the Sun. One potential cause for these eruptions is an ideal magnetohydrodynamic (MHD) instability, such as the kink or torus instability. Previous experiments on the magnetic reconnection experiment revealed a class of MFRs that were torus-unstable but kink-stable, which failed to erupt. These “failed-tori” went through a process similar to Taylor relaxation, where the toroidal current was redistributed before the eruption ultimately failed. Herein we have investigated this behavior through additional diagnostics that measure the current distribution at the foot points and the energy distribution before and after an event. These measurements indicate that ideal MHD effects are sufficient to explain the energy distribution changes during failed torus events. This excludes Taylor relaxation as a possible mechanism of current redistribution during an event. A new model that only requires non-ideal effects in a thin layer above the electrodes is presented to explain the observed phenomena. This work broadens our understanding of the stability of MFRs and the mechanism behind the failed torus through the improved prediction of the torus instability and through new diagnostics to measure the energy inventory and current profile at the foot points.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Investigation of tearing mode stability near ideal stability boundaries via asymptotic matching techniques

A number of improvements to the TJ toroidal tearing mode code [Fitzpatrick, Phys. Plasmas 31, 102507 (2024)] are documented. The TJ code is also successfully benchmarked against the STRIDE toroidal tearing mode code [Glasser and Koleman, Phys. Plasmas 25, 082502 (2018)]. Finally, the new capabilities of the TJ code are used to investigate the stability of tearing modes in tokamak plasmas as an ideal stability boundary, associated with either an external-kink or an internal-kink mode, is approached. All elements of the tearing stability matrix are found to tend to infinity as an ideal stability boundary is approached. Furthermore, as the stability boundary is approached, the eigenfunctions of the various tearing modes in the plasma, which are decoupled by sheared plasma rotation, are all found to morph into that of the marginally stable ideal mode. However, the growth-rates and real frequencies of the various “ideal-tearing-modes” are different from one another. Moreover, the growth-rate of the ideal-tearing-mode that reconnects magnetic flux at the rational surface that lies closest to the edge of the plasma is the one that tends to a very large value as the stability boundary is approached. A relatively simple test for ideal stability that is capable of detecting stability boundaries for external-kink and internal-kink modes, even in the presence of a very close-fitting ideal wall, is described and verified.

FOS: Physical sciences↗

DOE OSTI2018

Detection of an electron beam in a high density plasma via an electrostatic probe

Here, an electron beam is detected by a 1D floating potential probe array in a relatively high density (10 12 –10 13 cm -3 ) and low temperature (~5 eV) plasma of the Magnetic Reconnection Experiment. Clear perturbations in the floating potential profile by the electron beam are observed. Based on the floating potential profile and a current balance equation to the probe array tips, the effective width of the electron beam is determined, from which we determine the radial and toroidal beam current density profiles. After the profile of the electron beam is specified from the measured beam current, we demonstrate the consistency of the current balance equation and the location of the perturbation is also in agreement with field line mapping. No significant broadening of the electron beam is observed after the beam propagates for tens of centimeters through the high density plasma. These results prove that the field line mapping is, in principle, possible in high density plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Model for current drive induced crash cycles in W7-X

In the Wendelstein 7-X (W7-X) stellarator, the vacuum rotational transform, ι, has a flat radial profile and does not cross any major rational resonance. Nevertheless, during plasma operation the ι–profile can be strongly modified by electron cyclotron current drive in such a way that the resulting ι-profile passes through low-order rational values, and this can trigger magnetohydrodynamic (MHD) events. Indeed, W7-X plasmas are sometimes subject to repetitive collapses of core confinement, which can be observed regardless of the direction in which the EC current is driven. Even though the origin of these MHD instabilities is under investigation, the crashes may be connected to the formation of magnetic islands and magnetic reconnection. In the present work, we try to shed light on the dynamics of different events happening during the course of sawtooth cycles in W7-X by proposing a model that combines a slow current diffusion with a recipe for fast relaxation that conserves the corresponding helical flux (Kadomtsev 1975 Fiz. Plazmy 1 710–15). We also propose a simple model based on Taylor relaxation (Taylor 1974 Phys. Rev. Lett. 33 1139), (Taylor 1986 Rev. Mod. Phys. 58 741) to predict the nonlinear redistribution of plasma current caused by the largest of the observed events.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Effect of parallel flow on resonant layer responses in high beta plasmas

Abstract Resonant layers in a tokamak respond to non-axisymmetric magnetic perturbations by amplifying the mode amplitude and balancing the plasma rotation through magnetic reconnection and force balance, respectively. This resonant response can be characterized by local layer parameters and especially by a single quantity in the linear regime, the so-called inner-layer Δ. The computation of Δ under two-fluid drift-MHD formalism has been progressed by reducing the order of the system in the phase space, where the shielding current is approximated as being only carried by electrons, a posteriori . In this study, we relax the approximation and compute Δ accounted for by the parallel flow associated with the ion shielding current. The posteriori is numerically verified in great agreement with the original SLAYER developed in a previous paper (J.-K. Park 2022 Phys. Plasmas 29 072506). Extending the resonant layer response theory to high β plasmas, our research findings answer two important questions: how the parallel flow influences the resonant layer response and why the parallel flow effect appears in high β plasmas. The complicated plasma compression in high β regime allows the parallel flow response to give rise to the ion shielding current, which not only shifts the zero-crossing condition of the ExB flow but also enhances the field penetration threshold. Technically, the Riccati matrix transformation method is adapted to handle the numerical stiffness due to the increased order of the system. The high fidelity of this numerical method makes use of further extension of the model to higher-order systems to take other physical phenomena into account. This work is envisaged to predict the resonant layer response under high β fusion reactor conditions.

Lee, Yeongsun (ORCID:000000034474416X)↗

DOE OSTI2017

Dissipation and particle energization in moderate to low beta turbulent plasma via PIC simulations

Here, we simulate decaying turbulence in electron-positron pair plasmas using a fully-kinetic particle-in-cell (PIC) code. We run two simulations with moderate-to-low plasma β (the ratio of thermal pressure to magnetic pressure). The energy decay rate is found to be similar in both cases. The perpendicular wave-number spectrum of magnetic energy shows a slope between ${k}_{\perp }^{-1.3}$ and ${k}_{\perp }^{-1.1}$, where the perpendicular (⊥) and parallel (∥) directions are defined with respect to the magnetic field. The particle kinetic energy distribution function shows the formation of a non-thermal feature in the case of lower plasma β, with a slope close to E-1. The correlation between thin turbulent current sheets and Ohmic heating by the dot product of electric field (E) and current density (J) is investigated. By heating the parallel E∥ centerdot J∥ term dominates the perpendicular E⊥ centerdot J⊥ term. Regions of strong E∥ centerdot J∥ are spatially well-correlated with regions of intense current sheets, which also appear correlated with regions of strong E∥ in the low β simulation, suggesting an important role of magnetic reconnection in the dissipation of low β plasma turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Relativistic turbulence with strong synchrotron and synchrotron self-Compton cooling

Many relativistic plasma environments in high-energy astrophysics, including pulsar wind nebulae (PWN), hot accretion flows on to black holes, relativistic jets in active galactic nuclei and gamma-ray bursts, and giant radio lobes, are naturally turbulent. The plasma in these environments is often so hot that synchrotron and inverse-Compton (IC) radiative cooling becomes important. In this paper, we investigate the general thermodynamic and radiative properties (and hence the observational appearance) of an optically thin relativistically hot plasma stirred by driven magnetohydrodynamic (MHD) turbulence and cooled by radiation. We find that if the system reaches a statistical equilibrium where turbulent heating is balanced by radiative cooling, the effective electron temperature tends to attain a universal value θ=kT e /m e c 2 ~ 1/√τ T , where τT = n e σT L « 1 is the system's Thomson optical depth, essentially independent of the strength of turbulent driving and hence of the magnetic field. This is because both MHD turbulent dissipation and synchrotron cooling are proportional to the magnetic energy density. We also find that synchrotron self-Compton (SSC) cooling and perhaps a few higher order IC components are automatically comparable to synchrotron in this regime. The overall broad-band radiation spectrum then consists of several distinct components (synchrotron, SSC, etc.), well separated in photon energy (by a factor ~τ T -1 ) and roughly equal in power. The number of IC peaks is checked by Klein–Nishina effects and depends logarithmically on τT and the magnetic field. We also examine the limitations due to synchrotron self-absorption, explore applications to Crab PWN and blazar jets, and discuss links to radiative magnetic reconnection.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

GRB and blazar jets shining through their stripes

Black hole-driven relativistic astrophysical jets, such as blazars and gamma-ray bursts (GRBs), are powerful sources of electromagnetic radiation. Their emission is powered by some energy dissipation and particle acceleration mechanism operating in situ at large distances from the black hole. We propose that the formation of the dissipative structures in the jet is controlled by the time variability of the accretion disc. We argue that the open magnetic field lines through the black hole, which drive a strongly magnetized jet, may have their polarity reversing over time-scales related to the growth of the magnetorotational dynamo in the disc. Consequently, the jet is characterized by an alternating toroidal field polarity along its propagation axis, i.e. it is a ‘striped jet’. Magnetic reconnection in the current sheets that form between the stripes dissipates the alternating field energy and thus powers further jet acceleration. Here, we consider a jet with a broad distribution of stripe widths l > l min , above a dominant scale l min . We find that the bulk acceleration of the jet, driven by the annihilation of the stripes, is very gradual. The dissipation rate peaks at a distance $z_{\rm peak}\sim 10^6 R_\mathrm{ g}\, (\Gamma _\infty /30)^2\, (l_{\rm min}/1000R_\mathrm{ g})$| , where R g is the black hole’s gravitational radius and Γ ∞ the jet’s asymptotic Lorentz factor, and exhibits a very broad plateau extending by ~4–5 orders of magnitude in distance. The prolonged energy dissipation accounts for the flat-to-inverted long-wavelength spectra commonly observed in jets. The model can also account for the broad range of flaring time-scales of blazars and the fact that their bulk acceleration appears to continue out to ~100 pc scales. In GRB jets, the model predicts comparable power for the photopsheric and Thomson-thin emission components.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Observations of heteroclinic bifurcations in resistive magnetohydrodynamic simulations of the plasma response to resonant magnetic perturbations

A class of topological magnetic island bifurcations that has not previously been observed in toroidal plasmas is described. Increasing an externally applied three-dimensional magnetic field in resistive magnetohydrodynamic simulations results in the asymmetric elongation of resonant island flux surfaces followed by a sequence of heteroclinic bifurcations. Here, these bifurcations produce new sets of hyperbolic-elliptic fixed points as predicted by the Poincaré-Birkoff fixed point theorem. Field line calculations verify that the new fixed points do not connect to those of the prebifurcated islands as required for heteroclinic bifurcations on a torus with winding numbers composed of common integer factors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Role of Ion Kinetic Physics in the Interaction of Magnetic Flux Ropes

To explain many natural magnetized plasma phenomena, it is crucial to understand how rates of collisionless magnetic reconnection scale in large magnetohydrodynamic (MHD) scale systems. Simulations of isolated current sheets conclude such rates are independent of system size and can be reproduced by the Hall-MHD model, but neglect sheet formation and coupling to MHD scales. Here in this study, it is shown for the problem of flux-rope merging, which includes this formation and coupling, that the Hall-MHD model fails to reproduce the kinetic results. The minimum sufficient model must retain ion kinetic effects, which set the ion diffusion region geometry and give time-averaged rates that reduce significantly with system size, leading to different global evolution in large systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Quantifying Energy Conversion in Higher-Order Phase Space Density Moments in Plasmas

Weakly collisional and collisionless plasmas are typically far from local thermodynamic equilibrium (LTE), and understanding energy conversion in such systems is a forefront research problem. The standard approach is to investigate changes in internal (thermal) energy and density, but this omits energy conversion that changes any higher-order moments of the phase space density. In this Letter, we calculate from first principles the energy conversion associated with all higher moments of the phase space density for systems not in LTE. Particle-in-cell simulations of collisionless magnetic reconnection reveal that energy conversion associated with higher-order moments can be locally significant. Furthermore, the results may be useful in numerous plasma settings, such as reconnection, turbulence, shocks, and wave-particle interactions in heliospheric, planetary, and astrophysical plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗