Electron Inertial Length Research Articles

Interplay between the Weibel instability and the Biermann battery in realistic laser-solid interactions

A novel setup allows the Weibel instability and its interplay with the Biermann battery to be probed in laser-driven collisionless plasmas. Ab initio particle-in-cell (PIC) simulations of the interaction of short ($ \le ps$) intense $(a_0 \ge 1)$ laser-pulses with overdense plasma targets show observable Weibel generated magnetic fields. This field strength surpasses that of the Biermann battery, usually dominant in experiments, as long as the gradient scale length is much larger than the local electron inertial length; this is achievable by carefully setting the appropriate gradients in the front of the target e.g. by tuning the delay between the main laser pulse and the pre-pulse.

Reconnection from a turbulence perspective

The spectral properties associated with laminar, anti-parallel reconnection are examined using a 2.5D kinetic particle in cell simulation. Both the reconnection rate and the energy spectrum exhibit three distinct phases: an initiation phase where the reconnection rate grows, a quasi-steady phase, and a declining phase where both the reconnection rate and the energy spectrum decrease. During the steady phase, the energy spectrum exhibits approximately a double power law behavior, with a slope near −5/3 at wave numbers smaller than the inverse ion inertial length and a slope steeper than −8/3 for larger wave numbers up to the inverse electron inertial length. This behavior is consistent with a Kolmogorov energy cascade and implies that laminar reconnection may fundamentally be an energy cascade process. Consistent with this idea is the fact that the reconnection rate exhibits a rough correlation with the energy spectrum at wave numbers near the inverse ion inertial length. The 2D spectrum is strongly anisotropic with most energy associated with the wave vector direction normal to the current sheet. Reconnection acts to isotropize the energy spectrum, reducing the Shebalin angle from an initial value of 70° to about 48° (nearly isotropic) by the end of the simulation. The distribution of energy over length scales is further analyzed by dividing the domain into spatial subregions and employing structure functions.

Spontaneous Onset of Collisionless Magnetic Reconnection on an Electron Scale

Abstract Using particle-in-cell simulations, we investigate the onset of magnetic reconnection from a quiescent Harris current sheet in collisionless plasmas. After the current sheet is destabilized by the collisionless tearing mode instability, it proceeds to onset of reconnection, which manifests spontaneous thinning of current sheet and pileup of upstream magnetic flux. Once the current sheet thins to a critical thickness, about two electron inertial lengths, reconnection begins to grow explosively in this electron current sheet. This study shows that the spontaneous onset of collisionless magnetic reconnection is controlled by electron kinetics.

Relativistic HPIC-LBM and its application in large temporal-spatial turbulent magnetic reconnection. Part I. model development and validation

Magnetic energy release conversion, plasma heating and charged particle energization-acceleration in the magnetic fluctuation-induced self-generating-organization region and the plasma turbulence-induced self-feeding-sustaining region are key issues for large temporal-spatial scale turbulent magnetic reconnection (LTSTMR; observed current sheet thickness to characteristic electron length, electron Larmor radius for low-β and electron inertial length for high-β, ratios on the order of 1010∼1011; observed evolution time to electron cyclotron time ratios on the order of 1010∼1011) that ranges from Earth’s magnetosphere to solar eruptions and other astrophysical phenomena. As the first part of a two-paper series, this paper introduces a relativistic hybrid particle-in-cell and lattice Boltzmann (RHPIC-LBM) model that describes the continuous kinetic-dynamic-hydro fully coupled LTSTMR evolution process. First, based on the governing equations of resistive relativistic magnetohydrodynamics (MHD), the relativistic discrete distribution functions for a magnetic field (D3Q7), electric field (D3Q13), electromagnetic field (D3Q13), charged particle (D3Q19) and neutral particle (D3Q27) of different plasma species are obtained for the RHPIC-LBM lattice grid. Then, the numerical process, algorithm, pseudocode, flowchart and GPU-CPU heterogenous framework of the RHPIC-LBM are described. Finally, this model is tested and validated on Tianhe-2 from the National Supercomputer Center in Guang Zhou (NSCC-GZ) with 10,000 ∼ 100,000 CPU cores and 50∼120 hours per case. We investigate the solar atmosphere LTSTMR activities, including the picoscale (10−2 m ∼105 m), nanoscale (105 m ∼106 m), microscale (106 m ∼107 m), macroscale (107 m ∼108 m) and large hydroscale (108 m ∼109 m). All the simulation results are consistent with observations and theories. The validated model is applied to explore the turbulence evolution of the interactions of the magnetic helical structures in the 3D LTSTMR self-generating-organization magnetic field region and self-feeding-sustaining plasma region in Part II.

Inner and outer electron diffusion region of antiparallel collisionless reconnection: Density dependence

We study inflow density dependence of substructures within electron diffusion region (EDR) of collisionless symmetric magnetic reconnection. We perform a set of 2.5D particle-in-cell simulations which start from a Harris current layer with a uniform background density nb. A scan of nb ranging from 0.02 n0 to 2 n0 of the peak current layer density (n0) is studied keeping other plasma parameters the same. Various quantities measuring reconnection rate, EDR spatial scales, and characteristic velocities are introduced. We analyze EDR properties during quasisteady stage when the EDR length measures saturate. Consistent with past kinetic simulations, electrons are heated parallel to the B field in the inflow region. The presence of the strong parallel anisotropy acts twofold: (1) electron pressure anisotropy drift gets important at the EDR upstream edge in addition to the E×B drift speed and (2) the pressure anisotropy term −∇·P(e)/(ne) modifies the force balance there. We find that the width of the EDR demagnetization region and EDR current are proportional to the electron inertial length ∼de and ∼denb0.22, respectively. Magnetic reconnection is fast with a rate of ∼0.1 but depends weakly on density as ∼nb−1/8. Such reconnection rate proxies as EDR geometrical aspect or the inflow-to-outflow electron velocity ratio are shown to have different density trends, making electric field the only reliable measure of the reconnection rate.

Resonant Mode Conversion of Alfvén Waves to Kinetic Alfvén Waves in an Inhomogeneous Plasma

Abstract Kinetic Alfvén waves (KAWs) are dispersive Alfvén waves (AWs) with a perpendicular wavelength comparable to the ion (ion–acoustic) gyroradius or the electron inertial length and can play an important role in wave energy dissipation and particle energization. In this paper, we investigate the resonant mode conversion of AWs into KAWs for the case of an arbitrary angle α between the density gradient of the ambient plasma and the ambient magnetic field in an inhomogeneous two-temperature magnetoplasma. The results show that the mode conversion sensitively depends on the angle α, the density inhomogeneous gradient , and the parallel wavenumber , as well as the ion to electron temperature ratio . In particular, the excited KAWs are stronger when α is closer to 90° and are hardly excited for . Moreover, the maximal strength of the excited KAW increases with the increase of , but decreases with the increase of . Also, the maximal strength of the excited KAW has a larger value at larger for . These results are helpful for our comprehensive understanding of the resonant mode conversion of AWs into KAWs in solar magnetic atmospheres when AWs originating from the photosphere propagate along solar magnetic fields into the corona.

MMS Measurements of the Vlasov Equation: Probing the Electron Pressure Divergence Within Thin Current Sheets

AbstractWe investigate the kinetic structure of electron‐scale current sheets found in the vicinity of the magnetopause and embedded in the magnetosheath within the reconnection exhaust. A new technique for computing terms of the Vlasov equation using Magnetospheric Multiscale (MMS) measurements is presented and applied to study phase space density gradients and the kinetic origins of the electron pressure divergence found within these current sheets. Crescent‐shaped structures in ∇⊥2fe give rise to bipolar and quadrupolar signatures in v·∇fe measured near the maximum ∇·Pe inside the current layers. The current density perpendicular to the magnetic field is strong (J⊥∼2 μA/m2), and the thickness of the current layers ranges from 3 to 5 electron inertial lengths. The electron flows supporting the current layers mainly result from the combination of E×B and diamagnetic drifts. We find nonzero J·E′ within the current sheets even though they are observed apart from typical diffusion region signatures.

In situ spacecraft observations of a structured electron diffusion region during magnetopause reconnection.

The electron diffusion region (EDR) is the region where magnetic reconnection is initiated and electrons are energized. Because of experimental difficulties, the structure of the EDR is still poorly understood. A key question is whether the EDR has a homogeneous or patchy structure. Here we report Magnetospheric Multiscale (MMS) spacecraft observations providing evidence of inhomogeneous current densities and energy conversion over a few electron inertial lengths within an EDR at the terrestrial magnetopause, suggesting that the EDR can be rather structured. These inhomogenenities are revealed through multipoint measurements because the spacecraft separation is comparable to a few electron inertial lengths, allowing the entire MMS tetrahedron to be within the EDR most of the time. These observations are consistent with recent high-resolution and low-noise kinetic simulations.

Localized Structures and Turbulent Spectra in the Magnetopause

AbstractKinetic Alfvén wave (KAW) and whistler wave play a key role in the framework of turbulence and reconnection. There are lot of observations of these wave in the magnetopause region. The present paper deals with the nonlinear evolution of KAW and a weak whistler wave through the preexisting magnetic reconnection site. For this study the dynamical evolution equations are derived by taking into account the ponderomotive force driven density modification and magnetic field fluctuations due to shear field modeled by the Harris sheet. Furthermore, these equations have been solved numerically as well as semianalytically. For numerical integrations we have used the pseudospectral method and finite difference method and for semianalytically Runge Kutta method. Simulated results have shown the evolution of coherent structures or current sheets, which are capable to energy transfer efficiently. These structures have scale size around ion gyroradius as well as electron inertial length as calculated analytically. At a later time the chaotic structures arise in this reconnection site. This gives the signature of turbulence generation. Therefore, the magnetic power spectrum with scaling is also presented in this manuscript and their relevance with the observed spectrum (calculated from the Cluster data (Chaston, 2008, https://doi.org/10.1029/2008GL033601)) is also pointed out.

Electron Inertial Effects on Linearly Polarized Electromagnetic Ion Cyclotron Waves at Earth's Magnetosphere

AbstractWe discuss a role of the electron inertial effect on linearly polarized electromagnetic ion cyclotron (EMIC) waves at Earth. The linearly polarized EMIC waves have been previously suggested to be generated via mode conversion from the fast compressional wave at the ion‐ion hybrid (IIH) resonance. When the electron inertial effects are neglected, the wave normal angle of the mode‐converted IIH waves is 90° because the wave vector perpendicular to the magnetic field becomes infinite at the IIH resonance. When the electron inertial effect is considered, the mode‐converted IIH waves can propagate across the magnetic field lines, and the wavelength perpendicular to the magnetic field approaches the electron inertial length scale near the Buchsbaum resonance. These waves are referred to as electron inertial waves. Due to the electron inertial effect, the perpendicular wave number to the ambient magnetic field near the IIH resonance remains finite, and the wave normal angle is less than 90°. The wave normal angle where the maximum absorption occurs in a dipole magnetic field is 30–80°, which is consistent with the observed values near the magnetic equator. Therefore, the numerical results suggest that the linearly polarized EMIC wave generated via mode conversion near the IIH resonance can be detected in between the Buchsbaum and the IIH resonance frequencies, and these waves can have normal angle less than 90°.

Electron-scale Vertical Current Sheets in a Bursty Bulk Flow in the Terrestrial Magnetotail

Abstract We report Magnetospheric Multiscale observations of multiple vertical current sheets (CSs) in a bursty bulk flow in the near-Earth magnetotail. Two of the CSs were fine structures of a dipolarization front (DF) at the leading edge of the flow. The other CSs were a few Earth radii tailward of the DF; that is, in the wake of the DF. Some of these vertical CSs were a few electron inertial lengths thick and were converting energy from magnetic field to plasma. The currents of the CSs in the DF wake were carried by electrons that formed flow shear layers. These electron-scale CSs were probably formed during the turbulent evolution of the bursty bulk flow and are important for energy conversion associated with fast flows.

Evidence of Magnetic Nulls in Electron Diffusion Region

AbstractTheoretically, magnetic reconnection—the process responsible for solar flares and magnetospheric substorms—occurs at the X‐line or radial null in the electron diffusion region (EDR). However, whether this theory is correct is unknown, because the radial null (X‐line) has never been observed inside the EDR due to the lack of efficient techniques and the scarcity of EDR measurements. Here we report such evidence, using data from the recent MMS mission and the newly developed First‐Order Taylor Expansion (FOTE) Expansion technique. We investigate 12 EDR candidates at the Earth's magnetopause and find radial nulls (X‐lines) in all of them. In some events, spacecraft are only 3 km (one electron inertial length) away from the null. We reconstruct the magnetic topology of these nulls and find it agrees well with theoretical models. These nulls, as reconstructed for the first time inside the EDR by the FOTE technique, indicate that the EDR is active and the reconnection process is ongoing.

Reconstruction of the Electron Diffusion Region of Magnetotail Reconnection Seen by the MMS Spacecraft on 11 July 2017

AbstractWe present results from the reconstruction of the electron diffusion region of magnetotail reconnection observed by the Magnetospheric Multiscale (MMS) spacecraft on 11 July 2017. In the event, the conditions were suited for the reconstruction technique, developed by Sonnerup et al. (2016, https://doi.org/10.1002/2016JA022430), that produces magnetic field and electron streamline maps based on a two‐dimensional, time‐independent, inertialess form of electron magnetohydrodynamic equation, assuming an approximately symmetric current sheet and negligible guide magnetic field. For such a two‐dimensional and steady structure, the X line orientation can be estimated from a method based on Ampère's law using single‐spacecraft measurements of the magnetic field and electric current density. Our reconstruction results indicate that although the X point was not captured inside its tetrahedron, MMS approached the X point as close as one electron inertial length ~27 km. The opening angle of the recovered separatrix field line, combined with theory, suggests that the dimensionless reconnection rate was 0.17, which is consistent with the measured reconnection electric field 2–4 mV/m. The stagnation point of the reconstructed electron flow is shifted earthward of the X point by ~90 km, one possible interpretation of which is discussed. The energy conversion rate j · E′ in the electron frame tends to be higher near the stagnation point, consistent with earlier observations and simulations, and is not correlated with the amplitude of broadband electrostatic waves observed in the upper‐hybrid frequency range. The latter suggests that the waves did not contribute to energy dissipation in this particular electron diffusion region.

Observations of an Electron Diffusion Region in Symmetric Reconnection with Weak Guide Field

Abstract The Magnetospheric Multiscale spacecraft encountered an electron diffusion region (EDR) in a symmetric reconnection in the Earth’s magnetotail. The EDR contained a guide field of about 2 nT, which was 13% of the magnetic field in the inflow region, and its thickness was about 2 local electron inertial lengths. Intense energy dissipation, a super-Alfvénic electron jet, electron nongyrotropy, and crescent-shaped electron velocity distributions were observed in association with this EDR. These features are similar to those of the EDRs in asymmetric reconnection at the dayside magnetopause. Electrons gained about 50% of their energy from the immediate upstream to the EDR. Crescent electron distributions were seen at the boundary of the EDR, while highly curved magnetic field lines inside the EDR may have gyrotropized the electrons. The EDR was characterized by a parallel current that was carried by antiparallel drifting electrons that were probably accelerated by a parallel electric field along the guide field. These results reveal the essential electron physics of the EDR and provide a significant example of an EDR in symmetric reconnection with a weak guide field.

Electron acceleration in interaction of magnetic islands in large temporal-spatial turbulent magnetic reconnection

A new combined Fermi, betatron, and turbulent electron acceleration mechanism is proposed in interaction of magnetic islands during turbulent magnetic reconnection evolution in explosive astrophysical phenomena at large temporal-spatial scale (LTSTMR), the ratio of observed current sheets thickness to electron characteristic length, electron Larmor radius for low-β and electron inertial length for high-β, is on the order of 1010–1011; the ratio of observed evolution time to electron gyroperiod is on the order of 107–109). The original combined acceleration model is known to be one of greatest importance in the interaction of magnetic islands; it assumes that the continuous kinetic-dynamic temporal-spatial scale evolution occurs as two separate independent processes. In this paper, we reconsider the combined acceleration mechanism by introducing a kinetic-dynamic-hydro full-coupled model instead of the original micro-kinetic or macro-dynamic model. We investigate different acceleration mechanisms in the vicinity of neutral points in magnetic islands evolution, from the stage of shrink and breakup into smaller islands (kinetic scale), to the stage of coalescence and growth into larger islands (dynamic scale), to the stages of constant and quasi-constant (contracting-expanding) islands (hydro scale). As a result, we give for the first time the acceleration efficiencies of different types of acceleration mechanisms in magnetic islands’ interactions in solar atmosphere LTSTMR activities (pico-, 10–2–105 m; nano-, 105–106 m; micro-, 106–107 m; macro-, 107–108 m; large-, 108–109 m).

Wave‐Particle Interaction of Alfvén Waves in Jupiter's Magnetosphere: Auroral and Magnetospheric Particle Acceleration

AbstractWe investigate spatial and temporal scales at which wave‐particle interaction of Alfvén waves occurs in Jupiter's magnetosphere. We consider electrons, protons, and oxygen ions and study the regions along magnetic flux tubes where the plasma is the densest, that is, the equatorial plasma sheet, and where the plasma is the most dilute, that is, above the ionosphere, where auroral particle acceleration is expected to occur. We find that within a dipole L‐shell of roughly 30, the electron inertial length scale in the auroral region is the dominating scale, suggesting that electron Landau damping of kinetic Alfvén waves can play an important role in converting field energy into auroral particle acceleration. This mechanism is consistent with the broadband bidirectional electron distributions frequently observed by Juno. Due to interchange‐driven mass transport in Jupiter's magnetosphere, its magnetosphere‐ionosphere coupling is expected to be mostly not in local force balance. This might be a key reason for the dominant role of Alfvénically driven stochastic acceleration compared to the less frequently occurring, locally forced‐balanced, and thus static mono‐energetic unidirectional acceleration. Outside of approximately L = 30, the ion gyroperiod is the dominating scale suggesting that ion cyclotron damping of heavy ions plays a major role in heating magnetospheric plasma. We also present properties of the dispersion relationship and the polarization relationships of kinetic Alfvén waves including the important effects from the relativistic correction due to the displacement current in Ampère's law.

Two- and Three-dimensional Nonlinear Instabilities of Whistler Waves

Abstract Recently, two-dimensional (2D) nonlinear instabilities of whistler waves from resonant wave–wave interaction have gained much attention in numerical simulations as well as observations in space plasmas. In this paper, both 2D and three-dimensional (3D) nonlinear instabilities of whistler waves are investigated using electron magnetohydrodynamics (EMHD). It is found that decay instabilities can excite waves with a broadband wavenumber spectrum, including highly oblique propagating whistler waves. Whistler waves with λ e k = 1 would excite counter-propagating whistler waves, and the wave with can produce both co- and counter-propagating whistler waves, where λ e is the electron inertial length and k is the wavenumber. Moreover, it is shown that 3D instabilities have similar nonlinear growth rate distributions as in 2D decay for the azimuthal wavelength much larger than λ e . These results suggest that nonlinear wave–wave interaction can play an important role in the scattering of whistler waves in the solar wind and the Earth’s magnetosphere, and are also helpful for understanding nonlinear wave–wave interaction in the formation and development of EMHD turbulence.

Interaction of magnetoacoustic solitons in plasmas with dispersion effects through electron inertia

The head‐on collision between two magnetoacoustic solitons is investigated in a magnetized plasma containing inertial cold ions and warm electrons. A two‐fluid magnetohydrodynamic (MHD) model is used to study the magnetoacoustic solitons interaction in plasmas. The magnetoacoustic wave dispersion effects appearing through electron inertial length (skin depth) are also included in the model. By using the extended Poincaré–Lighthill–Kuo (PLK) method, the Korteweg–de Vries (KdV) equations are derived for the low amplitude left and right moving magnetoacoustic solitons, their trajectories, and corresponding phase shifts after their elastic collisions are obtained analytically and examined numerically as well. It is found that only positive polarity (compressive) soliton structures of magnetoacoustic waves are formed. The profiles of head‐on collision and the time evolution of two compressive interacting magnetoacoustic solitons are also presented for illustration. The effect of plasma beta, which depends on plasma density, electron temperature, and magnetic field intensity, on the phase shift of the interacting magnetoacoustic solitons is also examined.

An Electron‐Scale Current Sheet Without Bursty Reconnection Signatures Observed in the Near‐Earth Tail

AbstractObservations of a current sheet as thin as the electron scale are extremely rare in the near‐Earth magnetotail. By measurement from the novel Magnetospheric Multiscale mission in the near‐Earth magnetotail, we identified such an electron‐scale current sheet and determined its detailed properties. The electron current sheet was bifurcated, with a half‐thickness of nine electron inertial lengths, and was sandwiched between the Hall field. Because of the strong Hall electric field, the super‐Alfvénic electron bulk flows were created mainly by the electric field drift, leading to the generation of the strong electron current. Inevitably, a bifurcated current sheet was formed since the Hall electric field was close to zero at the center of the current sheet. Inside the electron current sheet, the electrons were significantly heated while the ion temperature showed no change. The ions kept moving at a low speed, which was not affected by this electron current sheet. The energy dissipation was negligible inside the current sheet. The observations indicate that a thin current sheet, even as thin as electron scale, is not the sufficient condition for triggering bursty reconnection.

A generalized quasi-neutral fluid-particle hybrid plasma model and its application to energetic-particle-magnetohydrodynamics hybrid simulation

A generalized fluid-particle hybrid model for collisionless plasmas under the assumption of quasi-neutrality is presented. The system consists of fluid ions and electrons as well as arbitrary numbers of species whose dynamics is governed by the Vlasov equation. The proposed model is thus a generalized version of the well-known standard hybrid plasma simulation model, in which the ions are fully kinetic whereas the electrons are assumed to be a fluid. Since the proposed model employs the exact form of the generalized Ohm's law, the mass and energy densities, as well as the charge-to-mass ratio of the kinetic species, are taken to be arbitrary. In the absence of the kinetic species, it reduces to the quasi-neutral two-fluid model [1]. In the opposite situation where the mass and energy densities of the kinetic species are much larger than the fluid ions, it is nothing more than the standard hybrid model with finite electron inertia effect. If the kinetic species is an energetic particle (EP) population having negligible mass density but substantial energy density and the scale size is much larger than the ion and electron inertial lengths, it describes the self-consistent coupling between the magnetohydrodynamics (MHD) and the EP dynamics. The energetic-particle-magnetohydrodynamics (EP-MHD) hybrid model is thus a special case of the more general model described in this paper. Advantages of this approach over the existing models are discussed. A three-dimensional simulation code solving the proposed set of equations is described. The code combines the Particle-in-Cell scheme for solving the kinetic species and a Riemann-solver-based code for the two-fluid equations. Several benchmark simulation results are shown to confirm that the code successfully captures the dynamics of the EP population interacting self-consistently with the MHD fluid.