Turbulent Electromagnetic Fields Research Articles

Global gyrokinetic simulations of electromagnetic turbulence in stellarator plasmas

Global electromagnetic turbulence is simulated in stellarator geometry using the gyrokinetic particle-in-cell code EUTERPE. The evolution of the turbulent electromagnetic field and the plasma profiles is considered at different values of the plasma beta and for different magnetic configurations. It is found that turbulence is linearly driven at relatively high toroidal mode numbers. In the nonlinear regime, lower toroidal mode numbers, including zonal flows, are excited resulting in a quench of the linear instability drive. The turbulent heat flux is outward and leads to the nonlinear relaxation of the plasma temperature profile. The particle flux is inward for the parameters considered. The effect of the parallel perturbation of the magnetic field on the stellarator turbulence is addressed.

Electron Heating in Magnetosheath Turbulence: Dominant Role of the Parallel Electric Field Within Coherent Structures

AbstractHow particles are being energized by turbulent electromagnetic fields is an outstanding question in plasma physics and astrophysics. This paper investigates the electron acceleration mechanism in strong turbulence (δB/B0 ∼ 1) in the Earth's magnetosheath based on the novel observations of the Magnetospheric Multiscale mission. We find that electrons are magnetized in turbulent fields for the majority of the time. By directly calculating the electron acceleration rate from Fermi, betatron mechanism, and parallel electric field, it is found that electrons are primarily accelerated by the parallel electric field within coherent structures. Moreover, the acceleration rate by parallel electric fields increases as the spatial scale reduces, with the most intense acceleration occurring over about one ion inertial length. This study is an important step toward fully understanding the turbulent energy dissipation in weakly collisional plasmas.

Simulation of a Multifractal Turbulent Electromagnetic Field in Cosmic Plasma

A two-dimensional model of a multifractal turbulent electromagnetic field is proposed that allows flexibly varying the width of the multifractal spectrum and the level of intermittency. The electromagnetic field is modeled using a superposition of wavelets that are distributed uniformly throughout the computational domain. By means of a special distribution of amplitudes, we ensure that the resulting field is multifractal and intermittent. This model was used to study the effect of multifractality and intermittency on the acceleration of charged particles in a turbulent field in the Earth’s magnetotail. It was shown that, in the case of a multifractal field, individual particles are able to achieve higher energy values in comparison with monofractal turbulence.

Effect of the electronic pressure on the energy and magnetic moment of charged test particles in turbulent electromagnetic fields

In this work, we perform direct numerical simulations of three-dimensional magnetohydrodynamics with a background magnetic field, representing solar wind plasma, and introduce test particles to explore how a turbulent electromagnetic environment affects them. Our focus is on the terms of the electric field present in the generalized Ohm's law that is usually dismissed as unimportant. These are the Hall and the electronic pressure (EP) terms, but we concentrate primarily on the latter. We discover that the EP term generates an acceleration of the particles, which represent protons, in the direction parallel to the background magnetic field, in contrast to the known preferential perpendicular energization. By studying the electric field itself, we are able to detect the type of structures of the EP field that produce such parallel acceleration. These are thin and elongated structures placed on top of a monotonic and near-zero background. A statistical study to understand the real significance of the electronic pressure term is also performed.

Acceleration of Charged Particles in Astrophysical Plasmas

The origin of high-energy particles in the Universe is one of the key issues of high-energy solar physics, space science, astrophysics, and particle astrophysics. Charged particles in astrophysical plasmas can be accelerated to very high energies by electric fields. Based on the characteristics of interactions between charged particles and electric fields carried by the background plasma, the mechanisms of charged particle acceleration can be divided into several groups: resonant interactions between plasma waves and particles, acceleration by electric fields parallel to magnetic fields, and acceleration caused by drift of the guiding center of particle gyro-motion around magnetic fields in magnetic field in-homogeneity-related curvature and gradient, etc. According to macroscopic energy conversion mechanisms leading to acceleration of particles, several theories of particle acceleration have been developed: stochastic particle acceleration by turbulent electromagnetic fields, diffusive shock acceleration of particles, and particle acceleration during magnetic re-connections. These theories have their own assumptions and characteristics and find applications in different astrophysical contexts. With advances in high-energy astrophysical observations and in combination with analyses of characteristics of high-energy particle acceleration and radiation, we can better understand the underlying physical processes in dramatically evolving astrophysical environments.

Electron Landau damping of kinetic Alfvén waves in simulated magnetosheath turbulence

Turbulence is thought to play a role in the heating of the solar wind plasma, though many questions remain to be solved regarding the exact nature of the mechanisms driving this process in the heliosphere. In particular, the physics of the collisionless interactions between particles and turbulent electromagnetic fields in the kinetic dissipation range of the turbulent cascade remains incompletely understood. A recent analysis of an interval of Magnetospheric Multiscale (MMS) observations has used the field–particle correlation technique to demonstrate that electron Landau damping is involved in the dissipation of turbulence in the Earth's magnetosheath. Motivated by this discovery, we perform a high-resolution gyrokinetic numerical simulation of the turbulence in the MMS interval to investigate the role of electron Landau damping in the dissipation of turbulent energy. We employ the field–particle correlation technique on our simulation data, compare our results to the known velocity–space signatures of Landau damping outside the dissipation range, and evaluate the net electron energization. We find qualitative agreement between the numerical and observational results for some key aspects of the energization and speculate on the nature of disagreements in light of experimental factors, such as differences in resolution, and of developing insights into the nature of field–particle interactions in the presence of dispersive kinetic Alfvén waves.

Evidence for electron Landau damping in space plasma turbulence

How turbulent energy is dissipated in weakly collisional space and astrophysical plasmas is a major open question. Here, we present the application of a field-particle correlation technique to directly measure the transfer of energy between the turbulent electromagnetic field and electrons in the Earth’s magnetosheath, the region of solar wind downstream of the Earth’s bow shock. The measurement of the secular energy transfer from the parallel electric field as a function of electron velocity shows a signature consistent with Landau damping. This signature is coherent over time, close to the predicted resonant velocity, similar to that seen in kinetic Alfven turbulence simulations, and disappears under phase randomisation. This suggests that electron Landau damping could play a significant role in turbulent plasma heating, and that the technique is a valuable tool for determining the particle energisation processes operating in space and astrophysical plasmas

Turbulent electromagnetic fields at sub-proton scales: Two-fluid and full-kinetic plasma simulations

Plasma dynamics is a multi-scale problem that involves many spatial and temporal scales. Turbulence connects the disparate scales in this system through a cascade that is established by nonlinear interactions. Most astrophysical plasma systems are weakly collisional, making a fully kinetic Vlasov description of the system essential. The use of reduced models to study such systems is computationally desirable, but careful benchmarking of physics in different models is needed. We perform one such comparison here between the fully kinetic Particle-In-Cell model and a two-fluid model that includes Hall physics and electron inertia, with a particular focus on the sub-proton scale electric field. We show that in general, the two fluid model captures large scale dynamics reasonably well. At smaller scales, the Hall physics is also captured reasonably well by the fluid code, but electron features show departures from the fully kinetic model. Implications for the use of such fluid models are discussed.

A multiphysics model of the electroslag rapid remelting (ESRR) process

This paper presents a numerical model (3D) incorporating multiphysics for an electroslag rapid remelting (ESRR) process of industrial scale. The electromagnetic field is calculated in the whole system including the electrode, molten slag, ingot, graphite ring, and mold; the interaction between the turbulent flow and electromagnetic field is calculated for all fluid domains (molten slag and melt pool); the thermal field is calculated in the molten slag, ingot and mold. The solidification of the billet ingot and the formation of solid slag skin layer along the T-mold are considered as well. The formation of the skin layer adjacent to the T-mold can remarkably impact the electric current path in the whole system. The modeling result indicates that no skin layer would form on the graphite ring, as the local electric current density is very high. In contrast, a thick slag skin layer forms along the inclined part of the T-mold, blocks the electric current path there. Those modeling results are verified by experiments. A typical non-axis symmetry flow/thermal field in the slag region, which has been observed in-situ from the slag surface during operation, is predicted. Detailed analyses of the quasi-steady state results of flow/thermal fields are presented. A symmetric melt pool (profile of the solidifying mushy zone) of the ingot is predicted, which agrees with the experiments.

Conservation laws for collisional and turbulent transport processes in toroidal plasmas with large mean flows

A novel gyrokinetic formulation is presented by including collisional effects into the Lagrangian variational principle to yield the governing equations for background and turbulent electromagnetic fields and gyrocenter distribution functions, which can simultaneously describe classical, neoclassical, and turbulent transport processes in toroidal plasmas with large toroidal flows on the order of the ion thermal velocity. Noether's theorem modified for collisional systems and the collision operator given in terms of Poisson brackets are applied to derivation of the particle, energy, and toroidal momentum balance equations in the conservative forms, which are desirable properties for long-time global transport simulation.

On the compressibility effect in test particle acceleration by magnetohydrodynamic turbulence

The effect of compressibility in a charged particle energization by magnetohydrodynamic (MHD) fields is studied in the context of test particle simulations. This problem is relevant to the solar wind and the solar corona due to the compressible nature of the flow in those astrophysical scenarios. We consider turbulent electromagnetic fields obtained from direct numerical simulations of the MHD equations with a strong background magnetic field. In order to explore the flow compressibility effect over the particle dynamics, we performed different numerical experiments: an incompressible case and two weak compressible cases with Mach number M = 0.1 and M = 0.25. We analyze the behavior of protons and electrons in those turbulent fields, which are well known to form aligned current sheets in the direction of the guide magnetic field. What we call protons and electrons are test particles with scales comparable to (for protons) and much smaller than (for electrons) the dissipative scale of MHD turbulence, maintaining the correct mass ratio me/mi. For these test particles, we show that compressibility enhances the efficiency of proton acceleration, and that the energization is caused by perpendicular electric fields generated between currents sheets. On the other hand, electrons remain magnetized and display an almost adiabatic motion, with no effect of compressibility observed. Another set of numerical experiments takes into account two fluid modifications, namely, electric field due to Hall effect and electron pressure gradient. We show that the electron pressure has an important contribution to electron acceleration allowing highly parallel energization. In contrast, no significant effect of these additional terms is observed for the protons.

Transient melting of an ESR electrode

Melting parameters of ESR process such as melt rate and immersion depth of electrode are of great importance. In this paper, a dynamic mesh based simulation framework is proposed to model melt rate and shape of electrode during the ESR process. Coupling interactions between turbulent flow, temperature, and electromagnetic fields are fully considered. The model is computationally efficient, and enables us to directly calculate melting parameters. Furthermore, dynamic change of electrode shape by melting can be captured. It is necessary to control the feeding velocity of electrode due to melting instabilities in the ESR process. As such, a numerical control is implemented based on the immersion depth of electrode to achieve the steady state in the simulation. Furthermore, the modeling result is evaluated against an experiment.

Cosmic ray transport in astrophysical plasmas

Since the development of satellite space technology about 50 years ago the solar heliosphere is explored almost routinely by several spacecrafts carrying detectors for measuring the properties of the interplanetary medium including energetic charged particles (cosmic rays), solar wind particle densities, and electromagnetic fields. In 2012, the Voyager 1 spacecraft has even left what could be described as the heliospheric modulation region, as indicated by the sudden disappearance of low energy heliospheric cosmic ray particles. With the available in-situ measurements of interplanetary turbulent electromagnetic fields and of the momentum spectra of different cosmic ray species in different interplanetary environments, the heliosphere is the best cosmic laboratory to test our understanding of the transport and acceleration of cosmic rays in space plasmas. I review both the historical development and the current state of various cosmic ray transport equations. Similarities and differences to transport theories for terrestrial fusion plasmas are highlighted. Any progress in cosmic ray transport requires a detailed understanding of the electromagnetic turbulence that is responsible for the scattering and acceleration of these particles.

Cosmic-ray acceleration at collisionless astrophysical shocks using Monte-Carlo simulations

Context. The di usive shock acceleration mechanism has been widely accepted as the acceleration mechanism for galactic cosmic rays. While self-consistent hybrid simulations have shown how power-law spectra are produced, detailed information on the interplay of di usive particle motion and the turbulent electromagnetic fields responsible for repeated shock crossings are still elusive. Aims. The framework of test-particle theory is applied to investigate the e ect of di usive shock acceleration by inspecting the obtained cosmic-ray energy spectra. The resulting energy spectra can be obtained this way from the particle motion and, depending on the prescribed turbulence model, the influence of stochastic acceleration through plasma waves can be studied. Methods. A numerical Monte-Carlo simulation code is extended to include collisionless shock waves. This allows one to trace the trajectories of test particle while they are being accelerated. In addition, the di usion coe cients can be obtained directly from the particle motion, which allows for a detailed understanding of the acceleration process. Results. The classic result of an energy spectrum with E 2 is only reproduced for parallel shocks, while, for all other cases, the energy spectral index is reduced depending on the shock obliqueness. Qualitatively, this can be explained in terms of the di usion coe cients in the directions that are parallel and perpendicular to the shock front.

The role of electron heating in electromagnetic collisionless shock formation

The role of electron dynamics in the process of a collisionless shock formation is analyzed with particle-in-cell simulations, the test-particles method, and quasilinear theory. The model of electron stochastic heating in turbulent electromagnetic fields corresponding to the nonlinear stage of two-stream and Weibel instabilities is developed. The analysis of electron and field heating rates shows that the ion motion provides the energy supply for a significant continuous heating of electrons. Such a heating thus plays a role of a friction force for ions, leading to their deceleration and a shock formation.

Cosmic wave‐particle interactions: Astrophysical magnetic turbulence and high‐energy particles

AbstractUnderstanding the origin and the properties of energetic charged particles has been an important problems of both plasma astro‐physics and astroparticle physics. Here, an introduction is given about the complicated interaction processes between cosmic rays and turbulent electromagnetic fields. First, the formation of turbulent electromagnetic fields due to plasma instabilities is discussed. Second, the microphysics of particle scattering due to such turbulent fields is explained and a comparison with measurements in the Solar wind is shown. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Extended gyrokinetic field theory for time-dependent magnetic confinement fields

A gyrokinetic system of equations for turbulent toroidal plasmas in time-dependent axisymmetric background magnetic fields is derived from the variational principle. Besides governing equations for gyrocenter distribution functions and turbulent electromagnetic fields, the conditions which self-consistently determine the background magnetic fields varying on a transport time scale are obtained by using the Lagrangian, which includes the constraint on the background fields. Conservation laws for energy and toroidal angular momentum of the whole system in the time-dependent background magnetic fields are naturally derived by applying Noether's theorem. It is shown that the ensemble-averaged transport equations of particles, energy, and toroidal momentum given in the present work agree with the results from the conventional recursive formulation with the WKB representation except that collisional effects are disregarded here.

Modification of cosmic-ray energy spectra by stochastic acceleration

Context. Typical space plasmas contain spatially and temporally variable turbulent electromagnetic fields. Understanding the transport of energetic particles and the acceleration mechanisms for charged particles is an important goal of today’s astroparticle physics.

Laboratory Astrophysics with Lasers: Turbulent Electromagnetic Field Associated with Collisionless Shocks

Laboratory Astrophysics with Lasers: Turbulent Electromagnetic Field Associated with Collisionless Shocks

Velocity space diffusion of charged particles in weak magnetostatic fields: Nonlinear effects, model constraints, and implications for simulations

The velocity space diffusion of charged test particles in random magnetostatic fields is re-investigated from a semi-dynamical point of view. The dynamics of charged particles in resonance with parallel propagating electromagnetic waves is investigated numerically and compared with analytical results for the trapping width in velocity space, Δv∥, and the bounce frequency, ωb. It is demonstrated how an understanding of the basic resonance phenomenon can lead to a better understanding of the validity regions of the quasi-linear theory and their implications for numerical simulations. It is shown, using established analytical expressions for Δv∥ and ωb, that the quasi-linear diffusion coefficient can be written in a new physically illuminating form. The concept of an effective trapping width in velocity space for the turbulence modified resonance structure is introduced. It is shown how this effective resonance width implies a condition on the density of wave modes in Fourier space, in the vicinity of the resonant wave number. The implications of this condition for simulations utilizing discrete fields are discussed in detail and examples of simulations violating this condition are presented. Other issues pertinent to the simulation of velocity diffusion in turbulent electromagnetic fields are discussed, paying attention to the discretization of the fields and the temporal discretization of the dynamical equations.