Self-consistent Magnetic Field Research Articles

The RAM-SCB model and its applications to advance space weather forecasting

Energetic particle fluxes that are part of the Earth’s ring current and radiation belts can intensify significantly during space weather events like geomagnetic storms and could cause severe damage to satellite-based technologies. Understanding the physical processes that control their dynamics and improving our capability for their prediction is thus extremely important. In the context of space weather applications and user needs, this paper provides a brief description of our kinetic ring current-atmosphere interactions model with self-consistent magnetic field (RAM-SCB) and its further extension to implement a self-consistent electric (E) field. Specific examples that demonstrate RAM-SCB capabilities and limitations to reproduce the near-Earth space weather environment are given. The current status of RAM-SCB is assessed and plans for its further improvement are discussed.

Physics of Thermonuclear Explosions: Magnetic Field Effects on Deflagration Fronts and Observable Consequences

Abstract We present a study of the influence of magnetic field strength and morphology in Type Ia supernovae and their late-time light curves and spectra. In order to both capture self-consistent magnetic field topologies and evolve our models to late times, a two-stage approach is taken. We study the early deflagration phase (∼1 s) using a variety of magnetic field strengths and find that the topology of the field is set by the burning, independent of the initial strength. We study late-time (∼1000 days) light curves and spectra with a variety of magnetic field topologies and infer magnetic field strengths from observed supernovae. Lower limits are found to be 106 G. This is determined by the escape, or lack thereof, of positrons that are tied to the magnetic field. The first stage employs 3D MHD and a local burning approximation and uses the code Enzo. The second stage employs a hybrid approach, with 3D radiation and positron transport and spherical hydrodynamics. The second stage uses the code HYDRA. In our models, magnetic field amplification remains small during the early deflagration phase. Late-time spectra bear the imprint of both magnetic field strength and morphology. Implications for alternative explosion scenarios are discussed.

Simulating the effects of warm O[formula omitted] ions on the growth of electromagnetic ion cyclotron (EMIC) waves

Electromagnetic ion cyclotron (EMIC) waves are believed to play a crucial role in the dynamics of the Earth’s magnetosphere. It has been widely accepted that plasma compositions can influence the growth rate of EMIC waves in the inner magnetosphere, but how warm O+ ions change the wave growth rate is not well known. In this study, we investigate the impact of ring current O+ concentration on the EMIC growth rate during a specific storm when the O+ ion flux significantly increases. We calculate the growth rate of EMIC waves by using physics-based ion distributions output from the Ring current–Atmosphere interactions Model with Self-Consistent magnetic (B) and Electric (E) fields (RAM-SCBE) model. The percentage of warm O+ is parametrically varied to examine how the maximum EMIC growth rate changes over time and how the global distribution of the maximum EMIC growth rate is affected. We found that the maximum growth rate of H-band appears in the dusk-to-midnight sector near the plasmapause, while O-band is excited at a slightly outer region. The maximum growth rate of He-band is closely related to the cold plasma density. With the increase of warm O+ density, the maximum growth rate of H-band and He-band EMIC wave is reduced, while that of O-band EMIC wave is increased, and the region with this wave excitation is widened. Such variation in the maximum EMIC growth rate implies a potential impact on the associated wave–particle interactions and change of the decay rate in the ring current.

Magnetized discs and photon rings around Yukawa-like black holes

We present stationary solutions of geometrically thick discs (or tori) endowed with a self-consistent toroidal magnetic field distribution surrounding a non-rotating black hole in an analytical, static, spherically-symmetric $f(R)$-gravity background. These $f(R)$-gravity models introduce a Yukawa-like modification to the Newtonian potential, encoded in a single parameter $\delta$ which controls the strength of the modified potential and whose specific values affect the disc configurations when compared to the general relativistic case. Our models span different magnetic field strengths, from purely hydrodynamical discs to highly magnetized tori. The characteristics of the solutions are identified by analyzing the central density, mass, geometrical size, angular size, and the black hole metric deviations from the Schwarzschild space-time. In the general relativistic limit ($\delta=0$) our models reproduce previous results for a Schwarzschild black hole. For small values of the $\delta$ parameter, corresponding to $\sim 10\%$ deviations from general relativity, we find variations of $\sim 2 \%$ in the event horizon size, a $\sim 5\%$ shift in the location of the inner edge and center of the disc, while the outer edge increases by $\sim 10\%$. Our analysis for $|\delta|>0.1$, however, reveals notable changes in the black hole space-time solution which have a major impact in the morphological and thermodynamical properties of the discs. The comparison with general relativity is further investigated by computing the size of the photon ring produced by a source located at infinity. This allows us to place constraints on the parameters of the $f(R)$-gravity model based on the Event Horizon Telescope observations of the size of the light ring in M87 and SgrA$^*$.

Average field approximation for almost bosonic anyons in a magnetic field

We study the ground state of a large number N of 2D extended anyons in an external magnetic field. We consider a scaling limit where the statistics parameter α is proportional to N−1 when N → ∞, which allows the statistics to be seen as a “perturbation around the bosonic end.” Our model is that of bosons in a magnetic field interacting through long-range magnetic potential generated by magnetic charges carried by each particle, smeared over discs of radius R. Our method allows us to take R → 0 not too fast at the same time as N → ∞ : R = N−1/4+ɛ. We use the information theoretic version of the de Finetti theorem of Brandão and Harrow to justify the so-called “average field approximation”: the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.

Particle simulation of plasmons

Abstract Particle simulation has been widely used in studying plasmas. The technique follows the motion of a large assembly of charged particles in their self-consistent electric and magnetic fields. Plasmons, collective oscillations of the free electrons in conducting media such as metals, are connected to plasmas by very similar physics, in particular, the notion of collective charge oscillations. In many cases of interest, plasmons are theoretically characterized by solving the classical Maxwell’s equations, where the electromagnetic responses can be described by bulk permittivity. That approach pays more attention to fields rather than motion of electrons. In this work, however, we apply the particle simulation method to model the kinetics of plasmons, by updating both particle position and momentum (Newton–Lorentz equation) and electromagnetic fields (Ampere and Faraday laws) that are connected by current. Particle simulation of plasmons can offer insights and information that supplement those gained by traditional experimental and theoretical approaches. Specifically, we present two case studies to show its capabilities of modeling single-electron excitation of plasmons, tracing instantaneous movements of electrons to elucidate the physical dynamics of plasmons, and revealing electron spill-out effects of ultrasmall nanoparticles approaching the quantum limit. These preliminary demonstrations open the door to realistic particle simulations of plasmons.

Interpretation of suprathermal emission at deuteron cyclotron harmonics from deuterium plasmas heated by neutral beam injection in the KSTAR tokamak

Intense bursts of suprathermal radiation, with spectral peaks at frequencies corresponding to the deuteron cyclotron frequency in the outer midplane edge region, are often detected from deuterium plasmas in the KSTAR tokamak that are heated by tangential neutral beam injection (NBI) of deuterons at 100 keV. Identifying the physical process by which this deuterium ion cyclotron emission (ICE) is generated, typically during the crash of edge localised modes, assists the understanding of collective energetic ion behaviour in tokamak plasmas. In the context of KSTAR deuterium plasmas, it is also important to distinguish deuterium ICE from the ICE at cyclotron harmonics of fusion-born protons examined by Chapman et al (2017 Nucl. Fusion 57 124004; 2018 Nucl. Fusion 58 096027). We use particle orbit studies in KSTAR-relevant magnetic field geometry, combined with a linear analytical treatment of the magnetoacoustic cyclotron instability (MCI), to identify the sub-population of freshly ionised NBI deuterons that is likely to excite deuterium ICE. These deuterons are then represented as an energetic minority, together with the majority thermal deuteron population and electrons, in first principles kinetic particle-in-cell (PIC) computational studies. By solving the Maxwell–Lorentz equations directly for hundreds of millions of interacting particles with resolved gyro-orbits, together with the self-consistent electric and magnetic fields, the PIC approach enables us to study the collective relaxation of the energetic deuterons through the linear phase and deep into the saturated regime. The Fourier transform of the excited fields displays strong spectral peaks at multiple successive deuteron cyclotron harmonics, mapping well to the observed KSTAR deuterium ICE spectra. This outcome, combined with the time-evolution of the energy densities of the different particle populations and electric and magnetic field components seen in the PIC computations, supports our identification of the driving sub-population of NBI deuterons, and the hypothesis that its relaxation through the MCI generates the observed deuterium ICE signal. We conclude that the physical origin of this signal in KSTAR is indeed distinct from that of KSTAR proton ICE, and is in the same category as the NBI-driven ICE seen notably in the TFTR tokamak and LHD heliotron–stellarator plasmas. ICE has been proposed as a potential passive diagnostic of energetic particle populations in ITER plasmas; this is assisted by clarifying and extending the physics basis of ICE in contemporary magnetically confined plasmas.

Biermann-Battery-Mediated Magnetic Reconnection in 3D Colliding Plasmas.

Recent experiments have demonstrated magnetic reconnection between colliding plasma plumes, where the reconnecting magnetic fields were self-generated in the plasma by the Biermann-battery effect. Using fully kinetic 3D simulations, we show the full evolution of the magnetic fields and plasma in these experiments, including self-consistent magnetic field generation about the expanding plume. The collision of the two plasmas drives the formation of a current sheet, where reconnection occurs in a strongly time- and space-dependent manner, demonstrating a new 3D reconnection mechanism. Specifically, we observe a fast, vertically localized Biermann-mediated reconnection, an inherently 3D process where the temperature profile in the current sheet coupled with the out-of-plane ablation density profile conspires to break inflowing field lines, reconnecting the field downstream. Fast reconnection is sustained by both the Biermann effect and the traceless electron pressure tensor, where the development of plasmoids appears to modulate the contribution of the latter. We present a simple and general formulation to consider the relevance of Biermann-mediated reconnection in general astrophysical scenarios.

Enhancement of pressure perturbations in ablation due to kinetic magnetized transport effects under direct-drive inertial confinement fusion relevant conditions.

We present kinetic two-dimensional Vlasov-Fokker-Planck simulations, including both self-consistent magnetic fields and ablating ion outflow, of a planar ablating foil subject to nonuniform laser irradiation. Even for small Hall parameters (ωτ_{ei}≲0.05) self-generated magnetic fields are sufficient to invert and enhance pressure perturbations. The mode inversion is caused by a combination of the Nernst advection of the magnetic field and the Righi-Leduc heat flux. Nonlocal effects modify these processes. The mechanism is robust under plasma conditions tested; it is amplitude independent and occurs for a broad spectrum of perturbation wavelengths, λ_{p}=10-100μm. The ablating plasma response to a dynamically evolving speckle pattern perturbation, analogous to an optically smoothed beam, is also simulated. Similar to the single-mode case, self-generated magnetic fields increase the degree of nonuniformity at the ablation surface by up to an order of magnitude and are found to preferentially enhance lower modes due to the resistive damping of high mode number magnetic fields.

Integration of RAM-SCB into the Space Weather Modeling Framework

Numerical simulations of the ring current are a challenging endeavor. They require a large set of inputs, including electric and magnetic fields and plasma sheet fluxes. Because the ring current broadly affects the magnetosphere-ionosphere system, the input set is dependent on the ring current region itself. This makes obtaining a set of inputs that are self-consistent with the ring current difficult. To overcome this challenge, researchers have begun coupling ring current models to global models of the magnetosphere-ionosphere system. This paper describes the coupling between the Ring current Atmosphere interaction Model with Self-Consistent Magnetic field (RAM-SCB) to the models within the Space Weather Modeling Framework. Full details on both previously introduced and new coupling mechanisms are defined. The impact of self-consistently including the ring current on the magnetosphere-ionosphere system is illustrated via a set of example simulations.

Local density approximation for the almost-bosonic anyon gas

We study the minimizers of an energy functional with a self-consistent magnetic field, which describes a quantum gas of almost-bosonic anyons in the average-field approximation. For the homogeneous gas we prove the existence of the thermodynamic limit of the energy at fixed effective statistics parameter, and the independence of such a limit from the shape of the domain. This result is then used in a local density approximation to derive an effective Thomas--Fermi-like model for the trapped anyon gas in the limit of a large effective statistics parameter (i.e., "less-bosonic" anyons).

Dynamics of a Self-Consistent Magnetic Field and Diffusive Scattering of Ions in a Plasma with Strong Thermal Anisotropy

Dynamics of a Self-Consistent Magnetic Field and Diffusive Scattering of Ions in a Plasma with Strong Thermal Anisotropy

On the Vlasov--Maxwell System with a Strong Magnetic Field

This paper establishes the long time asymptotic limit of the $2d\times 3d$ Vlasov--Maxwell system with a strong external magnetic field. Hence, a guiding-center approximation is obtained in the two-dimensional case with a self-consistent electromagnetic field given by Poisson type equations. Then, we perform several numerical experiments with high order approximation of the asymptotic model, which provide a solid validation of the method and illustrate the effect of the self-consistent magnetic field on the current density.

RAM-SCB simulations of electron transport and plasma wave scattering during the October 2012 "double-dip" storm.

Mechanisms for electron injection, trapping, and loss in the near‐Earth space environment are investigated during the October 2012 “double‐dip” storm using our ring current‐atmosphere interactions model with self‐consistent magnetic field (RAM‐SCB). Pitch angle and energy scattering are included for the first time in RAM‐SCB using L and magnetic local time (MLT)‐dependent event‐specific chorus wave models inferred from NOAA Polar‐orbiting Operational Environmental Satellites (POES) and Van Allen Probes Electric and Magnetic Field Instrument Suite and Integrated Science observations. The dynamics of the source (approximately tens of keV) and seed (approximately hundreds of keV) populations of the radiation belts simulated with RAM‐SCB is compared with Van Allen Probes Magnetic Electron Ion Spectrometer observations in the morning sector and with measurements from NOAA 15 satellite in the predawn and afternoon MLT sectors. We find that although the low‐energy (E< 100 keV) electron fluxes are in good agreement with observations, increasing significantly by magnetospheric convection during both SYM‐H dips while decreasing during the intermediate recovery phase, the injection of high‐energy electrons is underestimated by this mechanism throughout the storm. Local acceleration by chorus waves intensifies the electron fluxes at E≥50 keV considerably, and RAM‐SCB simulations overestimate the observed trapped fluxes by more than an order of magnitude; the precipitating fluxes simulated with RAM‐SCB are weaker, and their temporal and spatial evolutions agree well with POES/Medium Energy Proton and Electron Detectors data.

POLARIZATION SIGNATURES OF RELATIVISTIC MAGNETOHYDRODYNAMIC SHOCKS IN THE BLAZAR EMISSION REGION. I. FORCE-FREE HELICAL MAGNETIC FIELDS

ABSTRACT The optical radiation and polarization signatures in blazars are known to be highly variable during flaring activities. It is frequently argued that shocks are the main driver of the flaring events. However, the spectral variability modelings generally lack detailed considerations of the self-consistent magnetic field evolution modeling; thus, so far the associated optical polarization signatures are poorly understood. We present the first simultaneous modeling of the optical radiation and polarization signatures based on 3D magnetohydrodynamic simulations of relativistic shocks in the blazar emission environment, with the simplest physical assumptions. By comparing the results with observations, we find that shocks in a weakly magnetized environment will largely lead to significant changes in the optical polarization signatures, which are seldom seen in observations. Hence an emission region with relatively strong magnetization is preferred. In such an environment, slow shocks may produce minor flares with either erratic polarization fluctuations or considerable polarization variations, depending on the parameters; fast shocks can produce major flares with smooth polarization angle rotations. In addition, the magnetic fields in both cases are observed to actively revert to the original topology after the shocks. All these features are consistent with observations. Future observations of the radiation and polarization signatures will further constrain the flaring mechanism and the blazar emission environment.

The Average Field Approximation for Almost Bosonic Extended Anyons

Anyons are 2D or 1D quantum particles with intermediate statistics, interpolating between bosons and fermions. We study the ground state of a large number N of 2D anyons, in a scaling limit where the statistics parameter $$\alpha $$ is proportional to $$N ^{-1}$$ when $$N\rightarrow \infty $$ . This means that the statistics is seen as a “perturbation from the bosonic end”. We model this situation in the magnetic gauge picture by bosons interacting through long-range magnetic potentials. We assume that these effective statistical gauge potentials are generated by magnetic charges carried by each particle, smeared over discs of radius R (extended anyons). Our method allows to take $$R\rightarrow 0$$ not too fast at the same time as $$N\rightarrow \infty $$ . In this limit we rigorously justify the so-called “average field approximation”: the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.

AN EXACT ANALYTICAL SOLUTION FOR THE INTERSTELLAR MAGNETIC FIELD IN THE VICINITY OF THE HELIOSPHERE

An analytical representation of the interstellar magnetic field in the vicinity of the heliosphere is derived. The three-dimensional field structure close to the heliopause is calculated as a solution of the induction equation under the assumption that it is frozen into a prescribed plasma flow resembling the characteristic interaction of the solar wind with the local interstellar medium. The usefulness of this analytical solution as an approximation to self-consistent magnetic field configurations obtained numerically from the full MHD equations is illustrated by quantitative comparisons.

ION PRE-ACCELERATION IN FULLY SELF-CONSISTENT PARTICLE-IN-CELL SIMULATIONS OF SUPERCRITICAL PERPENDICULAR REFORMING SHOCKS IN MULTIPLE ION SPECIES PLASMAS

Supernova remnant and heliopause termination shock plasmas may contain significant populations of minority heavy ions, with relative number densities n α/ni up to 50%. Preliminary kinetic simulations of collisionless shocks in these environments showed that the reformation cycle and acceleration mechanisms at quasi-perpendicular shocks can depend on the value of n α/ni . Shock reformation unfolds on ion spatio-temporal scales, requiring fully kinetic simulations of particle dynamics, together with the self-consistent electric and magnetic fields. This paper presents the first set of particle-in-cell simulations for two ion species, protons (np ) and α-particles (n α), with differing mass and charge-to-mass ratios, that spans the entire range of n α/ni from 0% to 100%. The interplay between the differing gyro length scales and timescales of the ion species is crucial to the time-evolving phenomenology of the shocks, the downstream turbulence, and the particle acceleration at different n α/ni . We show how the overall energization changes with n α/ni , and relate this to the processes individual ions undergo in the shock region and in the downstream turbulence, and to the power spectra of magnetic field fluctuations. The crossover between shocks dominated by the respective ion species happens when n α/ni = 25%, and minority ion energization is strongest in this regime. Energization of the majority ion species scales with injection energy. The power spectrum of the downstream turbulence includes peaks at sequential ion cyclotron harmonics, suggestive of ion ring-beam collective instability.

Vlasov multi-dimensional model dispersion relation

A hybrid model of the Vlasov equation in multiple spatial dimension D &amp;gt; 1 [H. A. Rose and W. Daughton, Phys. Plasmas 18, 122109 (2011)], the Vlasov multi dimensional model (VMD), consists of standard Vlasov dynamics along a preferred direction, the z direction, and N flows. At each z, these flows are in the plane perpendicular to the z axis. They satisfy Eulerian-type hydrodynamics with coupling by self-consistent electric and magnetic fields. Every solution of the VMD is an exact solution of the original Vlasov equation. We show approximate convergence of the VMD Langmuir wave dispersion relation in thermal plasma to that of Vlasov-Landau as N increases. Departure from strict rotational invariance about the z axis for small perpendicular wavenumber Langmuir fluctuations in 3D goes to zero like θN, where θ is the polar angle and flows are arranged uniformly over the azimuthal angle.

A unified radiative magnetohydrodynamics code for lightning-like discharge simulations

A two-dimensional Eulerian finite difference code is developed for solving the non-ideal magnetohydrodynamic (MHD) equations including the effects of self-consistent magnetic field, thermal conduction, resistivity, gravity, and radiation transfer, which when combined with specified pulse current models and plasma equations of state, can be used as a unified lightning return stroke solver. The differential equations are written in the covariant form in the cylindrical geometry and kept in the conservative form which enables some high-accuracy shock capturing schemes to be equipped in the lightning channel configuration naturally. In this code, the 5-order weighted essentially non-oscillatory scheme combined with Lax-Friedrichs flux splitting method is introduced for computing the convection terms of the MHD equations. The 3-order total variation diminishing Runge-Kutta integral operator is also equipped to keep the time-space accuracy of consistency. The numerical algorithms for non-ideal terms, e.g., artificial viscosity, resistivity, and thermal conduction, are introduced in the code via operator splitting method. This code assumes the radiation is in local thermodynamic equilibrium with plasma components and the flux limited diffusion algorithm with grey opacities is implemented for computing the radiation transfer. The transport coefficients and equation of state in this code are obtained from detailed particle population distribution calculation, which makes the numerical model is self-consistent. This code is systematically validated via the Sedov blast solutions and then used for lightning return stroke simulations with the peak current being 20 kA, 30 kA, and 40 kA, respectively. The results show that this numerical model consistent with observations and previous numerical results. The population distribution evolution and energy conservation problems are also discussed.