Asymptotic Magnetic Field Research Articles

Determining the Orientation of a Magnetic Reconnection X Line and Implications for a 2D Coordinate System

AbstractAn LMN coordinate system for magnetic reconnection events is sometimes determined by defining N as the direction of the gradient across the current sheet and L as the direction of maximum variance of the magnetic field. The third direction, M, is often assumed to be the direction of zero gradient, and thus the orientation of the X line. But when there is a guide field, the X line direction may have a significant component in the L direction defined in this way. For a 2D description, a coordinate system describing such an event would preferably be defined using a different coordinate direction M′ oriented along the X line. Here we use a 3D particle‐in‐cell simulation to show that the X line is oriented approximately along the direction bisecting the asymptotic magnetic field directions on the two sides of the current sheet. We describe two possible ways to determine the orientation of the X line from spacecraft data, one using the minimum gradient direction from Minimum Directional Derivative analysis at distances of the order of the current sheet thickness from the X line, and another using the bisection direction based on the asymptotic magnetic fields outside the current sheet. We discuss conditions for validity of these estimates, and we illustrate these conditions using several Magnetospheric Multiscale (MMS) events. We also show that intersection of a flux rope due to secondary reconnection with the primary X line can destroy invariance along the X line and negate the validity of a two‐dimensional description.

On a plasma sheath with a small normal magnetic field separating regions of oppositely directed magnetic field

The Harris-sheet model provides an elegant solution to the kinetic plasma equation for a steady state 1D current sheet geometry separating regions with oppositely directed magnetic field. However, adding just a small normal magnetic field to the Harris configuration yields thermal streaming of particles into and out of the current sheet, fundamentally changing the form of its kinetic description. The action variable, Jz, associated with the oscillatory orbit motion perpendicular to the current sheet is well conserved and can be applied for solving the kinetic equation in the 1D sheet geometry that includes a small normal magnetic field. Revisiting this problem, we develop a new formalism that permits numerical solutions to be readily obtained for general upstream/asymptotic electron and ion distributions. In particular, we consider the case of isotropic ion pressure and anisotropic bi-Maxwellian electrons. The current sheets are then supported by electron pressure anisotropy. Furthermore, the total current across a particular sheet is set by the fire-hose condition based on the electron pressures normalized by the asymptotic magnetic field pressure. Analytical approximations are obtained for the numerical solutions expressed in terms of the asymptotic electron temperature anisotropy and the ion temperature. We discuss a preliminary application of the framework to the electron diffusion region of anti-parallel magnetic reconnection.

The Role of a Strong Out‐Of‐Plane Magnetic Field at the X‐Line in Antiparallel Magnetic Reconnection as a Guide Field

AbstractThe magnetic reconnection process substantially changes the configuration of the magnetic field in plasma and explosively releases magnetic energy. The asymptotic magnetic field lines during magnetic reconnection events can be strictly antiparallel or only have one antiparallel component, and the magnetic reconnection features are distinct under different asymptotic magnetic fields. Here, we provide the first observational evidence demonstrating the existence of a strong out‐of‐plane magnetic field at the X‐line in antiparallel reconnection. The analyses described herein show that this strong out‐of‐plane magnetic field significantly changes the structure of the diffusion region, thereby altering the reconnection features in terms of particle dynamics and energy dissipation by way of a guide field. A new pattern of the normal electric field near the X‐line is responsible for producing this out‐of‐plane magnetic field. Our findings suggest that, in addition to asymptotic conditions, local processes inside the diffusion region can also determine whether magnetic reconnection events develop as antiparallel reconnection or component reconnection.

Chaos in a Magnetized Modified Gravity Schwarzschild Spacetime

Based on the scalar–tensor–vector modified gravitational theory, a modified gravity Schwarzschild black hole solution has been given in the existing literature. Such a black hole spacetime is obtained through the inclusion of a modified gravity coupling parameter, which corresponds to the modified gravitational constant and the black hole charge. In this sense, the modified gravity parameter acts as not only an enhanced gravitational effect but also a gravitational repulsive force contribution to a test particle moving around the black hole. Because the modified Schwarzschild spacetime is static spherical symmetric, it is integrable. However, the spherical symmetry and the integrability are destroyed when the black hole is immersed in an external asymptotic uniform magnetic field and the particle is charged. Although the magnetized modified Schwarzschild spacetime is nonintegrable and inseparable, it allows for the application of explicit symplectic integrators when its Hamiltonian is split into five explicitly integrable parts. Taking one of the proposed explicit symplectic integrators and the techniques of Poincaré sections and fast Lyapunov indicators as numerical tools, we show that the charged particle can have chaotic motions under some circumstances. Chaos is strengthened with an increase of the modified gravity parameter from the global phase space structures. There are similar results when the magnetic field parameter and the particle energy increase. However, an increase of the particle angular momentum weakens the strength of chaos.

Formation of the Electron Inflow Along the Separatrices During Collisionless Magnetic Reconnection

AbstractIn this paper, by performing two‐dimensional (2‐D) particle‐in‐cell simulations of collisionless magnetic reconnection in a Harris current sheet, we analyze the formation of electron inflow along the separatrices toward the X‐line from the perspective of fluid. The results show that both the parallel electric field and mirror force can drive the electron inflow to stream toward the X‐line. The speed of the electron inflow can reach about 4VA(where VA is the Alfvén speed based on the upstream asymptotic magnetic field magnitude and peak density in the current sheet). Although the contribution of the parallel electric field is much larger than that of the mirror force, the mirror force cannot be ignored. When the electron inflow streams toward the X‐line, it is heated in the parallel direction. The resulted gradient of the parallel electron pressure leads to the attenuation of the electron inflow. We also investigate the effects of the density and temperature of the background plasma on the formation of the electron inflow. With the decrease of the background plasma density, the contribution of the parallel electric field becomes larger while that of the mirror force almost remains unchanged. With the decrease of the background plasma temperature, the contribution of the parallel electric field becomes larger while that of the mirror force becomes smaller.

Numerical studies on electron magnetohydrodynamics tearing mode instability

The 2D electron-magnetohydrodynamics (EMHD) dominant tearing mode in an electron-skin-depth-scale current sheet (ECS) is further studied. The resistive diffusion is proved to be insignificant at the scale. Electron inertia leads to the expansion of the “inner region” as well as a wider saturation island and the invalidity of the boundary layer approximation. The unstable tearing mode index Δ′ thus decreases dramatically from that in classical asymptotic theory. As for nonlinear evaluation, the inverse spectral cascade and the flattening of the m = 0 anti-parallel asymptotic magnetic field will result in an m = 1 final island after nonlinear coupling in a long ECS. A rapid normal saturation transition is observed and only expected for a larger wave number due to the growth rate dependence on the wave number being a single humped function. A linear analysis of the EMHD tearing mode is also presented for the force-free equilibrium. With a strong guide field, it shows that the tearing mode can be suppressed by the shear flow. Nonlinear simulation results with specific parameters then showed that the dynamic structures in the current sheet are consistent with the observation in the Earth’s turbulent magnetosheath.

Electromagnetic emission from a binary black hole merger remnant in plasma: Field alignment and plasma temperature

Comparable-mass black-hole mergers generically result in moderate to highly spinning holes, whose spacetime curvature will significantly affect nearby matter in observable ways. We investigate how the moderate spin of a post-merger Kerr black hole immersed in a plasma with initially uniform density and uniform magnetic field affects potentially observable accretion rates and energy fluxes. Varying the initial specific internal energy of the plasma over two decades, we find very little change in steady-state mass accretion rate or Poynting luminosity, except at the lowest internal energies, where fluxes do not exhibit steady-state behavior during the simulation timescale. Fixing the internal energy and varying the initial fixed magnetic-field amplitude and orientation, we find that the steady-state Poynting luminosity depends strongly on the initial field angle with respect to the black hole spin axis, while the matter accretion rate is more stable until the field angle exceeds $\sim 45\degree$. The proto-jet formed along the black hole spin-axis conforms to a thin, elongated cylinder near the hole, while aligning with the asymptotic magnetic field at large distances.

Particle-in-cell Simulations of Secondary Magnetic Islands: Ion-scale Flux Ropes and Plasmoids

Abstract Ion-scale flux ropes and plasmoids are secondary magnetic islands produced during magnetic reconnection in various heliospheric plasma environments. Here we study the structure of secondary islands and the particle dynamics within them using particle-in-cell simulations. Ion-scale flux ropes (secondary islands with a strong core field) are formed in a strong guide field regime, whereas ion-scale plasmoids (secondary islands with a weak core field) are formed in a weak guide field regime. Currents in both types of secondary islands are carried primarily by electrons. Both types of secondary islands have a magnetic tension force pointing radially inward toward their center. In the flux rope type, this inward tension force is balanced by an outward magnetic pressure gradient of the strong core field; in the plasmoid type, it is countered by an outward thermal pressure gradient caused by electron and ion energizations. The transition between these two types occurs when B g /B 0 = 0.1–0.2 (B g is the guide field, and B 0 is the asymptotic magnetic field).

Influence of the vacuum polarization effect on the motion of charged particles in the magnetic field around a Schwarzschild black hole

The consequences of the vacuum polarization effect in magnetic fields around a Schwarzschild Black Hole on the motion of charged particles are investigated in this work. Using the weak electromagnetic field approximation, we discuss the non-minimal coupling between magnetic fields and gravity caused by the vacuum polarization and study the equations of motion for the case of a magnetic field configuration which asymptotically approaches a dipole magnetic field. It is shown that the presence of non-minimal coupling can significantly influence the motion of charged particles around Black Holes. In particular, the vacuum polarization effect, leading to strong amplification or suppression of the magnetic field strength around the event horizon (depending on the sign of the coupling parameter), can affect the scattering angle and minimal distance for the electrons moving in the gravitational field of the Black Hole as well as the dependence of these parameters on the asymptotic magnetic field strength, initial distance and the Black Hole mass. It is further demonstrated that the non-minimal coupling between gravity and astrophysical magnetic fields, caused by the vacuum polarization, can cause significant changes of the parameter space corresponding to bound trajectories around the Black Hole. In certain cases, the bounded or unbounded character of a trajectory is determined solely by the presence of non-minimal coupling and its strength. These effects could in principle be used as observational signatures of the vacuum polarization effect and also to constrain the value of the coupling parameter.

Astrophysical jets from boosted compact objects

We perform full 3D numerical simulations of compact objects, such as black holes or neutron stars, boosted through an ambient force-free plasma that posses a uniform magnetization. We study jet formation and energy extraction from the resulting stationary late time solutions.The implementation of appropriate boundary conditions has allowed us to explore a wide range of boost velocities, finding the jet power scales as $\gamma v^2$ (being $\gamma$ the Lorentz factor). We also explore other parameters of the problem like the orientation of the motion respect to the asymptotic magnetic field or the inclusion of black hole spin. Additionally, by comparing a black hole with a perfectly conducting sphere in flat spacetime, we manage to disentangle curvature effects from those produced by the perfect conducting surface. It is shown that when the stellar compactness is increased these two effects act in combination, further enhancing the luminosity produced by the neutron star.

On the charge density and asymptotic tail of a monopole

We propose a new definition for the abelian magnetic charge density of a non-abelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose expansion in powers of 1/r agrees with that of the conventional asymptotic magnetic field to all orders. We also show that the asymptotic field can be easily calculated from the spectral curve. Explicit examples are given for known monopole solutions.

Kinetic simulations of plasmoid chain dynamics

The dynamics of a plasmoid chain is studied with three dimensional Particle-in-Cell simulations. The evolution of the system with and without a uniform guide field, whose strength is 1/3 the asymptotic magnetic field, is investigated. The plasmoid chain forms by spontaneous magnetic reconnection: the tearing instability rapidly disrupts the initial current sheet generating several small-scale plasmoids that rapidly grow in size coalescing and kinking. The plasmoid kink is mainly driven by the coalescence process. It is found that the presence of guide field strongly influences the evolution of the plasmoid chain. Without a guide field, a main reconnection site dominates and smaller reconnection regions are included in larger ones, leading to an hierarchical structure of the plasmoid-dominated current sheet. On the contrary in presence of a guide field, plasmoids have approximately the same size and the hierarchical structure does not emerge, a strong core magnetic field develops in the center of the plasmoid in the direction of the existing guide field, and bump-on-tail instability, leading to the formation of electron holes, is detected in proximity of the plasmoids.

Electric field structure inside the secondary island in the reconnection diffusion region

Secondary islands have recently been intensively studied because of their essential role in dissipating energy during reconnection. Secondary islands generally form by tearing instability in a stretched current sheet, with or without guide field. In this article, we study the electric field structure inside a secondary island in the diffusion region using large-scale two-and-half dimensional particle-in-cell (PIC) simulation. Intense in-plane electric fields, which point toward the center of the island, form inside the secondary island. The magnitudes of the in-plane electric fields Ex and Ez inside the island are much larger than those outside the island in the surrounding diffusion region. The maximum magnitudes of the fields are about three times the B0VA, where B0 is the asymptotic magnetic field strength and VA is the Alfvén speed based on B0 and the initial current sheet density. Our results could explain the intense electric field (~100 mV/m) inside the secondary island observed in the Earth’s magnetosphere. The electric field Ex inside the secondary island is primarily balanced by the Hall term (j × B)/ne, while Ez is balanced by a combination of (j × B)/ne, −(vi × B), and the divergence of electron pressure tensor, with (j × B)/ne term being dominant. This large Hall electric field is due to the large out-of-plane current density jy inside the island, which consists mainly of accelerated electrons forming a strong bulk flow in the –y direction. The electric field Ey shows a bipolar structure across the island, with negative Ey corresponding to negative Bz and positive Ey corresponding to positive Bz. It is balanced by (j × B)/ne and the convective electric field. There are significant parallel electric fields, forming a quadrupolar structure inside the island, with maximum amplitude of about 0.3B0VA.

The structure of the magnetic reconnection exhaust boundary

The structure of shocks that form at the exhaust boundaries during collisionless reconnection of anti-parallel fields is studied using particle-in-cell (PIC) simulations and modeling based on the anisotropic magnetohydrodynamic equations. Large-scale PIC simulations of reconnection and companion Riemann simulations of shock development demonstrate that the pressure anisotropy produced by counterstreaming ions within the exhaust prevents the development of classical Petschek switch-off-slow shocks (SSS). The shock structure that does develop is controlled by the firehose stability parameter ɛ=1-μ0(P‖-P⊥)/B2 through its influence on the speed order of the intermediate and slow waves. Here, P‖ and P⊥ are the pressure parallel and perpendicular to the local magnetic field. The exhaust boundary is made up of a series of two shocks and a rotational wave. The first shock takes ɛ from unity upstream to a plateau of 0.25 downstream. The condition ɛ=0.25 is special because at this value, the speeds of nonlinear slow and intermediate waves are degenerate. The second slow shock leaves ɛ=0.25 unchanged but further reduces the amplitude of the reconnecting magnetic field. Finally, in the core of the exhaust, ɛ drops further and the transition is completed by a rotation of the reconnecting field into the out-of-plane direction. The acceleration of the exhaust takes place across the two slow shocks but not during the final rotation. The result is that the outflow speed falls below that expected from the Walén condition based on the asymptotic magnetic field. A simple analytic expression is given for the critical value of ɛ within the exhaust below which SSSs no longer bound the reconnection outflow.

Investigation of tearing instability using GeFi particle simulation model

The gyrokinetic (GK) electron and fully kinetic ion (GeFi) simulation model of Lin et al. [Plasmas Phys. Controlled Fusion 53, 054013 (2011)] has been thoroughly benchmarked and validated for a two-dimensional (2D) Harris current sheet with a finite guide field. First, a gyrokinetic eigenmode theory for the collisionless tearing mode in the small Larmor radius limit is presented. The linear eigenmode structure and growth rate of the tearing mode obtained from the GeFi simulation are benchmarked against those from the GK eigenmode analysis in the limit of L≫ρi>ρe, where L is the current sheet half-width, ρi is ion Larmor radius, and ρe is electron Larmor radius. Second, to valid the GeFi model, both the linear and nonlinear tearing instabilities obtained from the GeFi simulations are compared with the Darwin particle-in-cell (PIC) simulation. The validation of the GeFi model for laboratory and space plasmas is also discussed. Meanwhile, the GeFi simulation is carried out to investigate both the linear and nonlinear tearing instabilities for cases with a broad range of L and guide magnetic field BG. It is found that in a wide current sheet with L > 4.5ρeK, the nonlinear saturation level of the island half-width is ws ≃ 3ρeK, where ρeK = ρeB0/Bx0, B0 is the strength of the asymptotic magnetic field, and Bx0 is the antiparallel field. On the other hand, in a thin current sheet with L < 2.5ρeK, ws ≃ 2.2 L. In addition, a high frequency electrostatic drift mode is found to coexist with the tearing mode.

Magnetospheres of black hole systems in force-free plasma

The interaction of black holes with ambient magnetic fields is important for a variety of highly energetic astrophysical phenomena. We study this interaction within the force-free approximation in which a tenuous plasma is assumed to have zero inertia. Blandford and Znajek used this approach to demonstrate the conversion of some of the black hole's energy into electromagnetic Poynting flux in stationary and axisymmetric single black hole systems. We adopt this approach and extend it to examine asymmetric and, most importantly, dynamical systems by implementing the fully nonlinear field equations of general relativity coupled to Maxwell's equations. For single black holes, we study, in particular, the dependence of the Poynting flux and show that, even for misalignments between the black hole spin and the direction of the asymptotic magnetic field, a Poynting flux is generated with a luminosity dependent on such misalignment. For binary black hole systems, we show both in the head-on and orbiting cases that the moving black holes generate a Poynting flux.

Three-dimensional evolution of magnetic and velocity shear driven instabilities in a compressible magnetized jet

The problem of three-dimensional combined magnetic and velocity shear driven instabilities of a compressible magnetized jet modeled as a plane neutral/current double vortex sheet in the framework of the resistive magnetohydrodynamics is addressed. The resulting dynamics given by the stream+current sheet interaction is analyzed and the effects of a variable geometry of the basic fields are considered. Depending on the basic asymptotic magnetic field configuration, a selection rule of the linear instability modes can be obtained. Hence, the system follows a two-stage path developing either through a fully three-dimensional dynamics with a rapid evolution of kink modes leading to a final turbulent state, or rather through a driving two-dimensional instability pattern that develops on parallel planes on which a reconnection+coalescence process takes place.

Collisionless instability of thin current sheets in the presence of sheared parallel flows

The first results of an ongoing investigation of the influence of sheared parallel flows on the onset of collisionless magnetic reconnection in thin current sheets are reported. In particular, an exact kinetic equilibrium that incorporates flow with a symmetric profile into the well-known Harris model is proposed and its linear stability is described. The complete linearized Vlasov–Maxwell system is solved using a numerical approach that introduces no approximations regarding the shape of the particle orbits or relative magnitude of the different components of the electromagnetic potentials. Thus accurate results are obtained in a difficult, but practically important limit where the characteristic length scales for the variation of the equilibrium magnetic field and flow are comparable to the ion kinetic length scales. In particular, the dispersion relation for an instability that produces magnetic reconnection is traced as a function of the flow speed V0 at the center of the sheet, starting with the collisionless tearing mode at V0=0. The effects of the sheared flow are shown to qualitatively depend on the thickness of the current sheet. In relatively thick sheets the characteristic features of the dispersion relation depend mostly on the value of the flow shear. In this regime there exist regions of the parameter space where the flow is destabilizing. However, the growth rate of the instability never significantly exceeds that of the collisionless tearing mode and the mode is always stabilized at high enough values of V0. When the sheet is thinner than the ion gyroradius in the asymptotic magnetic field, the flow shear introduces strong non-Maxwellian features into the equilibrium distribution function. In this regime, the flow is purely stabilizing for the equilibrium considered. The instability produces magnetic reconnection in all the parameter regimes considered. Finally, the results of the linear analysis are verified using large-scale particle-in-cell simulations.

Physics of saturation of collisionless tearing mode as a function of guide field

The tearing instability has been the subject of much study in space and laboratory plasmas and is thought to play a role as an onset mechanism for reconnection at the magnetotail and at the magnetopause. However, the nonlinear evolution is not completely understood. Here we employ a combination of theory and full particle simulations, including one for realistic mass ratio, to address the saturation of a single, linearly unstable tearing mode as a function of guide field. For the parameter regime considered, we find no agreement with any of the previous theories of tearing mode saturation. There are marked differences in the electron behavior and the associated saturation mechanism in the antiparallel (zero guide field) and finite guide field cases. Electrons become nongyrotropic and also develop temperature anisotropies in the antiparallel case, whereas they remain isotropic in the presence of a guide field. In the antiparallel limit there are two competing saturation mechanisms. One is due to preferential parallel heating of electrons which leads to a saturation amplitude of ws ∼ 2.9 ρe, where ρe is the electron gyroradius in the asymptotic magnetic field and ws is the half‐width of the magnetic island. The other saturation mechanism is electron trapping in the magnetic island which leads to a saturation amplitude comparable to the singular layer thickness (ΔNS). Electron parallel heating is usually the dominant saturation mechanism. However, in the presence of sufficiently fast electron pitch angle scattering, caused either by current‐aligned Weibel instability or turbulence, the second saturation mechanism due to trapping becomes dominant. In the presence of a guide field, the only saturation mechanism is electron trapping which leads to a saturation amplitude of ws ∼ 1.8 ρeG in the strong guide field and ws ∼ (2ρeGΔNS)1/2 in the intermediate regime. Here ρeG is the electron gyroradius in the guide field. The predicted saturation amplitudes for all cases, including the antiparallel regime, are much smaller than the thickness of the magnetopause current layer. Thus a single tearing mode saturates at too small of an amplitude to be of relevance to reconnection in the magnetosphere.

Long Range Scattering and Modified Wave Operators for the Maxwell-Schr�dinger System I. The Case of Vanishing Asymptotic Magnetic Field

We study the theory of scattering for the Maxwell-Schr"odinger system in space dimension 3,in the Coulomb gauge.In the special case of vanishing asymptotic magnetic field,we prove the existence of modified wave operators for that system with no size restriction on the Schr"odinger data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators.The method consists in partially solving the Maxwell equations for the potentials,substituting the result into the Schr"odinger equation,which then becomes both nonlinear and nonlocal in time,and treating the latter by the method previously used for the Hartree equation and for the Wave-Schr"odinger system.