Plasma dynamics in the diffusion regions of magnetic reconnection

Intermittent turbulence is key for understanding the stochastic nonlinear dynamics of space, astrophysical, and laboratory plasmas. We review the theory of deterministic and stochastic temporal chaos in plasmas and discuss its link to intermittent turbulence observed in space plasmas. First, we discuss the theory of chaos, intermittency, and complexity for nonlinear Alfvén waves, and parametric decay and modulational wave–wave interactions, in the absence/presence of noise. The transition from order to chaos is studied using the bifurcation diagram. The following two types of deterministic intermittent chaos in plasmas are considered: type-I Pomeau–Manneville intermittency and crisis-induced intermittency. The role of structures known as chaotic saddles in deterministic and stochastic chaos in plasmas is investigated. Alfvén complexity associated with noise-induced intermittency, in the presence of multistability, is studied. Next, we present evidence of magnetic reconnection and intermittent magnetic turbulence in coronal mass ejections in the solar corona and solar wind via remote and in situ observations. The signatures of turbulent magnetic reconnection, i.e., bifurcated current sheet, reconnecting jet, parallel/anti-parallel Alfvénic waves, and spiky dynamical pressure pulse, as well as fully developed turbulence, are detected at the leading edge of an interplanetary coronal mass ejection and the interface region of two merging interplanetary magnetic flux ropes. Methods for quantifying the degree of coherence, amplitude–phase synchronization, and multifractality of nonlinear multiscale fluctuations are discussed. The stochastic chaotic nature of Alfvénic intermittent structures driven by magnetic reconnection is determined by a complexity–entropy analysis. Finally, we discuss the relation of nonlinear dynamics and intermittent turbulence in space plasmas to similar phenomena observed in astrophysical and laboratory plasmas, e.g., coronal mass ejections and flares in the stellar-exoplanetary environment and Galactic Center, as well as chaos, magnetic reconnection, and intermittent turbulence in laser-plasma and nuclear fusion experiments.

In space plasma, various effects of magnetic reconnection and turbulence cause the electron motion to significantly deviate from their Larmor orbits. Collectively these orbits affect the electron velocity distribution function and lead to the appearance of the "non-gyrotropic" elements in the pressure tensor. Quantification of this effect has important applications in space and laboratory plasma, one of which is tracing the electron diffusion region (EDR) of magnetic reconnection in space observations. Three different measures of agyrotropy of pressure tensor have previously been proposed, namely, A∅ e , Dng and Q. The multitude of contradictory measures has caused confusion within the community. We revisit the problem by considering the basic properties an agyrotropy measure should have. We show that A∅ e , Dng and Q are all defined based on the sum of the principle minors (i.e. the rotation invariant I 2) of the pressure tensor. We discuss in detail the problems of I 2-based measures and explain why they may produce ambiguous and biased results. We introduce a new measure AG constructed based on the determinant of the pressure tensor (i.e. the rotation invariant I 3) which does not suffer from the problems of I 2-based measures. We compare AG with other measures in 2 and 3-dimension particle-in-cell magnetic reconnection simulations, and show that AG can effectively trace the EDR of reconnection in both Harris and force-free current sheets. On the other hand, A∅ e does not show prominent peaks in the EDR and part of the separatrix in the force-free reconnection simulations, demonstrating that A∅ e does not measure all the non-gyrotropic effects in this case, and is not suitable for studying magnetic reconnection in more general situations other than Harris sheet reconnection.

In strongly magnetized astrophysical plasma systems, magnetic reconnection is believed to be the primary process during which explosive energy release and particle acceleration occur, leading to significant high-energy emission. Past years have witnessed active development of kinetic modeling of relativistic magnetic reconnection, supporting this magnetically dominated scenario. A much less explored issue in studies of relativistic reconnection is the consequence of three-dimensional dynamics, where turbulent structures are naturally generated as various types of instabilities develop. This paper presents a series of three-dimensional, fully kinetic simulations of relativistic turbulent magnetic reconnection (RTMR) in positron–electron plasmas with system domains much larger than kinetic scales. Our simulations start from a force-free current sheet with several different modes of long-wavelength magnetic field perturbations, which drive additional turbulence in the reconnection region. Because of this, the current layer breaks up and the reconnection region quickly evolves into a turbulent layer filled with coherent structures such as flux ropes and current sheets. We find that plasma dynamics in RTMR is vastly different from its 2D counterpart in many aspects. The flux ropes evolve rapidly after their generation, and can be completely disrupted by the secondary kink instability. This turbulent evolution leads to superdiffusive behavior of magnetic field lines as seen in MHD studies of turbulent reconnection. Meanwhile, nonthermal particle acceleration and the timescale for energy release can be very fast and do not depend strongly on the turbulence amplitude. The main acceleration mechanism is a Fermi-like acceleration process supported by the motional electric field, whereas the nonideal electric field acceleration plays a subdominant role. We also discuss possible observational implications of three-dimensional RTMR in high-energy astrophysics.

Magnetic reconnection, a fundamental plasma process, explosively releases energy, generates particles with high energies and plays a crucial role in space weather. This process, which is very common in space plasmas, also occurs in Earth’s magnetotail, driving particle acceleration and affecting the plasma dynamics of the near-Earth space environment. To explore the connection between magnetic reconnection and particle acceleration, we present fully kinetic simulations of magnetic reconnection in Earth's magnetotail, including both ions and electrons. For this purpose, we employed the particle in cell (PIC) code ECsim and set up the simulation with parameters from a well-studied magnetic reconnection event observed by the Magnetospheric Multiscale (MMS) mission. This event, usually referred to as a “quiet magnetic reconnection” event, is characterized by less enhanced plasma heating and turbulence.Our study first compares the particle energization observed in the MMS data with the results from our simulation for this specific reconnection event. By examining the differences and similarities between the two, we aim to evaluate how well the simulation captures the key features of the observed event. Afterward, we vary the initial parameters to investigate how various reconnection scenarios affect particle acceleration. This approach allows us to analyze how different environmental conditions influence the acceleration of particles during magnetic reconnection.

Magnetic Relaxation and Self-Organization in Astrophysical and Laboratory Plasmas: Mean Field Dynamo Theory Origin, Structure and Stability of Astrophysical MHD Jets Turbulence and Turbulent Transport - The Agents of Relaxation and Structure Formation: A Tutorial on Basic Concepts in MHD Turbulence and Turbulent Transport Intermittency Like Phenomena in Plasma Turbulence Nonlinear Cascades and Spatial Structure of MHD Turbulence Scale Covariance and Scale-Ratio Covariance in Turbulent Front Propagation Transport Bifurcations and Relaxation: Transport Barrier Relaxations in Tokamak Edge Plasmas Dynamics of Edge Localized Modes On the Onset of Collapse Events in Toroidal Plasmas - Turbulence Trigger.

Magnetic reconnection is a key charged particle transport and energy conversion process in environments ranging from astrophysical systems to laboratory plasmas [Yamada et al., Rev. Mod. Phys. 82, 603–664 (2010)]. Magnetic reconnection facilitates plasma transport by establishing new connections of magnetic flux tubes, and it converts, often explosively, energy stored in the magnetic field to kinetic energy of charged particles [J. L. Burch and J. F. Drake, Am. Sci. 97, 392–299 (2009)]. The intensity of the magnetic reconnection process is measured by the reconnection electric field, which regulates the rate of flux tube connectivity changes. The change of magnetic connectivity occurs in the current layer of the diffusion zone, where the plasma transport is decoupled from the transport of magnetic flux. Here we report on computer simulations and analytic theory to provide a self-consistent understanding of the role of the reconnection electric field, which extends substantially beyond the simple change of magnetic connections. Rather, we find that the reconnection electric field is essential to maintain the current density in the diffusion region, which would otherwise be dissipated by a set of processes. Natural candidates for current dissipation are the average convection of current carriers away from the reconnection region by the outflow of accelerated particles, or the average rotation of the current density by the magnetic field reversal in the vicinity. Instead, we show here that the current dissipation is the result of thermal effects, underlying the statistical interaction of current-carrying particles with the adjacent magnetic field. We find that this interaction serves to redirect the directed acceleration of the reconnection electric field to thermal motion. This thermalization manifests itself in form of quasi-viscous terms in the thermal energy balance of the current layer. This collisionless viscosity, found in the pressure evolution equation, dominates near the x-line. These quasi-viscous terms act to increase the average thermal energy. Our predictions regarding current and thermal energy balance are readily amenable to exploration in the laboratory or by satellite missions, in particular, by NASA's Magnetospheric Multiscale mission.

Magnetic reconnection is a phenomenon of nature in which magnetic field lines change their topology and convert magnetic energy to plasma particles by acceleration and heating. The process can stretch out over time or occur quite suddenly. It is one of the most fundamental processes at work in laboratory and astrophysical plasmas. Magnetic reconnection occurs everywhere: In solar flares; coronal mass ejections; the earth’s magnetosphere; in the star forming galaxies; and in plasma fusion devices. This paper reviews the most recent progress in the research of magnetic reconnection.

This paper describes the attitude ground system (AGS) design to be used for support of the Magnetospheric MultiScale (MMS) mission. The AGS exists as one component of the mission operations control center. It has responsibility for validating the onboard attitude and accelerometer bias estimates, calibrating the attitude sensors and the spacecraft inertia tensor, and generating a definitive attitude history for use by the science teams. NASA's Goddard Space Flight Center (GSFC) in Greenbelt, Maryland is responsible for developing the MMS spacecraft, for the overall management of the MMS mission, and for mission operations. MMS is scheduled for launch in 2014 for a planned two-year mission. The MMS mission consists of four identical spacecraft flying in a tetrahedral formation in an eccentric Earth orbit. The relatively tight formation, ranging from 10 to 400 km, will provide coordinated observations giving insight into small-scale magnetic field reconnection processes. By varying the size of the tetrahedron and the orbital semi-major axis and eccentricity, and making use of the changing solar phase, this geometry allows for the study of both bow shock and magnetotail plasma physics, including acceleration, reconnection, and turbulence. The mission divides into two phases for science; these phases will have orbit dimensions of 1.2 x 12 Earth radii in the first phase and 1.2x25 Earth radii in the second in order to study the dayside magnetopause and the nightside magnetotail, respectively. The orbital periods are roughly one day and three days for the two mission phases. Each of the four MMS spacecraft will be spin stabilized at 3 revolutions per minute (rpm), with the spin axis oriented near the ecliptic north pole but tipped approximately 2.5 deg towards the Sun line. The main body of each spacecraft will be an eight-sided platform with diameter of 3.4 m and height of 1.2 m. Several booms are attached to this central core: two axial booms of 14.9 m length, two radial magnetometer booms of 5 m length, and four radial wire booms of 60 m length. Attitude and orbit control will use a set of axial and radial thrusters. A four-head star tracker and a slit-type digital Sun sensor (DSS) provide input for attitude determination. In addition, an accelerometer will be used for closed-loop orbit maneuver control. The primary AGS product will be a daily definitive attitude history. Due to power limitations, the star tracker and accelerometer data will not be available at all times. However, tracker data from at least 10 percent of each orbit and continuous DSS data will be provided. An extended Kalman filter (EKF) will be used to estimate the three-axis attitude (i.e., spin axis orientation and spin phase) and rotation rate for all times when the tracker data is valid. For other times, the attitude is generated by assuming a constant angular momentum vector in the inertial frame. The DSS sun pulse will provide a timing signal to maintain an accurate spin phase. There will be times when the Sun is occulted and DSS data is not available. If this occurs at the start or end of a definitive attitude product, then the spin phase will be extrapolated using the mean rate determined by the EKF.

The "International Topical Conference on Plasma Physics: New Frontiers in Nonlinear Sciences" was held at the University of Algarve (UA), Faro (Portugal), during the period 6–10 September 1999. The conference was organized by P K Shukla, R Bingham, J T Mendonça and L Stenflo with the help of an international advisory board and a program committee that included scientists from all over the world. The conference enters into a series of previous biennial activities that we have held at the Abdus Salam International Centre for Theoretical Physics, Trieste, since 1989.The purpose of the Faro meeting was to provide an informal forum for scientists who have dealt with various aspects ofnonlinear processes in space, astrophysical and laboratory plasmas, as well as in fluids and nonlinear optics. The selectedtopics, which were interdisciplinary, are expected to have a great deal of impact on the development of nonlinear sciencesin the coming millennium.The response of the conference was almost overwhelming. It was attended by approximately 120 delegates from Europe,USA, Japan, and developing countries. Many participants were young researchers from both the industrial and developingcountries, as the organizers tried to keep a good balance in inviting senior and younger generations of nonlinear scientiststo our Faro conference.The scientific program included five review talks (45 minutes) and thirty-five invited topical lectures (30 minutes). Inaddition, there were about eighty poster papers in three sessions. The latter gave opportunities to younger physicistsfor displaying the results of their recent work and to obtain comments from the other participants. During the five daysat the UA, we focused on fundamental aspects of: (i) the nonlinear physics in various branches of sciences (plasmas, fluids,and optics), (ii) nonlinearities in space and astrophysics, (iii) coherent processes in non-ideal systems (colloidal and dusty as well as pure electron plasmas), (iv) nonlinear charged particle beams and laser/neutrino-plasma interactions, and(v) nonlinearities in controlled laboratory devices. The focus was on nonlinear phenomena involving wave–wave and wave–particle interactions in ideal and non-ideal complex plasmas, intense short laser pulse interactions with plasmas and atomic clusters, the Kerr nonlinearity in optics, generation of harmonics as well as modulated wave packets in fluids, anomalous transport processes and complexities, etc. The nonlinear Schrödinger-like models for the propagation of particle and laser beams and optical pulses are still common in nonlinear dispersive media. The formation of coherent nonlinear structures (voids, envelope solitons, shocks, various types of solitary vortices, and vortex crystals) was exclusively demonstrated in data from low-temperature laboratory and space plasmas. For example, observations from the auroral ionosphere and microgravity dusty plasma experiments reveal the simultaneous presence of solitary vortex structures of various scale sizes as well as large scale density holes (voids). During the Faro meeting, some talks also concerned the role of self-organized criticality in nature as well as techniques for controlling chaos. Computer modeling of numerous kinetic instabilities and phase space vortex structures revived renewed interest at the conference. Furthermore, charged particle acceleration involving collective processes in ionospheric, astrophysical, and laboratory plasmas remained frontiers of the nonlinear sciences. Novel fields identified during the conference were dusty and neutrino plasma physics, which take advantage of knowledge from condensed matter and particle physics, making plasma physics truly cross-disciplinaryand very fascinating with wide ranging applications. Most of the contributions from the Faro meeting appear in this TopicalIssue of Physica Scripta, which will be distributed to all the participants. It is expected that the papers of the present proceedings, which systematically describe the advancement of a particular subject matter, shall be useful for understanding the many complex nonlinear phenomena that are occurring in science and technology.The organizers are grateful to Professor Adriano Pimpão, the President of the UA, for his generous support and warm hospitality in Faro. The excellent work of the scientific secretary Dr Rui Guerra is also acknowledged. The Editors want to express sincere gratitude to their colleagues and co-organizers Profs Tito Mendonça and Bob Bingham for their constant and wholehearted support in our endeavours. Thanks are also due to the Universidade do Algarve for providing the venue, and for administrative support, the Universidade Técnica de Lisbon for secretarial and other support, and theFCT-Fundação para a Ciência e a Tecnologia for a limited financial support to our conference at the UA, Faro.Finally, the organizers cordial thanks are extended to the speakers and the attendees for their contributions which resulted in the success of the Faro conference. Specifically, we appreciate the speakers for delivering excellent talks, supplying well prepared manuscripts for publication, and enhancing the nonlinear science activity at the UA, where we hope to create a new center of excellence for carrying out high quality research and for training young researchers in the fascinating new areas of nonlinear sciences which may have a tremendous impact on the development of new technologies andnew materials in the twenty-first century.

In the last few years it has been demonstrated, both by data analysis and by numerical simulations, that the transport of energetic particles in the presence of magnetic turbulence can be superdiffusive rather than normal diffusive (Gaussian). The term ‘superdiffusive’ refers to the mean square displacement of particle positions growing superlinearly with time, as compared to the normal linear growth. The so-called anomalous transport, which in general comprises both subdiffusion and superdiffusion, has gained growing attention during the last two decades in many fields including laboratory plasma physics, and recently in astrophysics and space physics. Here we show a number of examples, both from laboratory and from astrophysical plasmas, where superdiffusive transport has been identified, with a focus on what could be the main influence of superdiffusion on fundamental processes like diffusive shock acceleration and heliospheric energetic particle propagation. For laboratory plasmas, superdiffusion appears to be due to the presence of electrostatic turbulence which creates long-range correlations and convoluted structures in perpendicular transport: this corresponds to a similar phenomenon in the propagation of solar energetic particles (SEPs) which leads to SEP dropouts. For the propagation of energetic particles accelerated at interplanetary shocks in the solar wind, parallel superdiffusion seems to be prevailing; this is based on a pitch-angle scattering process different from that envisaged by quasi-linear theory, and this emphasizes the importance of nonlinear interactions and trapping effects. In the case of supernova remnant shocks, parallel superdiffusion is possible at quasi-parallel shocks, as occurring in the interplanetary space, and perpendicular superdiffusion is possible at quasi-perpendicular shocks, as corresponding to Richardson diffusion: therefore, cosmic ray acceleration at supernova remnant shocks should be formulated in terms of superdiffusion. The possible relations among anomalous transport in laboratory, heliospheric, and astrophysical plasmas will be indicated.

Magnetic reconnection is a fundamental process that can take place in astrophysical or laboratory plasmas. It occurs within regions of large magnetic gradient where the magnetic field is no longer frozen to the plasma but instead diffuses through it, releasing magnetic energy and causing a change in the connectivity of the field lines. In particular, on the Sun, magnetic reconnection is believed to play an important role in coronal heating, X ray bright points, solar flares and canceling magnetic features. Here, an exact time‐dependent solution of the MHD equations for magnetic annihilation in response to a time‐varying stagnation point flow is presented. The main assumptions in this model are that the magnetic field lines are straight (so that there is no magnetic tension acting on the plasma) and the flow that carries the field lines together is of stagnation point type. This is a reasonable model for the resistive MHD behaviour near the X point of a reconnecting field, especially when the central diffusion region is long, as in the flux pile up regime (Priest and Forbes 1986). The general solution is used to conduct a series of numerical experiments, namely, the evolution of different initial magnetic profiles in a steady flow; the effect of a sudden change in magnetic diffusivity on an initially steady state; the effects of a velocity that either increases linearly in time or ramps up from one steady value to another. The results exhibit the effects of subtle imbalances in diffusion and advection but have the following general features: (1) a diffusion layer is created, the thickness of which is determined by the nature of the plasma flow; (2) the magnetic field outside the diffusion region is determined by advection and will either exponentially increase, exponentially decay or remain in a steady state, depending on whether the initial magnetic profile B (y) ∼ y−n has n < 1, n > 1, or n = 1, respectively; and (3) the magnetic field within the diffusion layer tends to respond to the advected magnetic field at its edge.

Magnetic reconnection is a crucial process responsible for energy conversion and particle acceleration in space, astrophysical, and laboratory plasmas. Turbulence and magnetic reconnection can be mutually driven, but the underlying nature of energy dissipation, intrinsic turbulence waves, and magnetic field topologies in turbulent magnetic reconnection is still poorly understood. Here, using advanced multi-spacecraft mission and innovative methods, we provide a few new perspectives to investigate the properties of the turbulence and topology in a turbulent magnetic reconnection in the magnetotail. Our results reveal that in turbulent magnetic reconnection: (1) cyclotron resonance, an important mechanism of energy dissipation, is more effective in the core region of the reconnection than in the outflow regions; (2) energy is deposited in the form of kinetic Alfvén waves (KAWs) and fast/slow waves, with KAWs corresponding to low-frequency (ion cyclotron scale) and fast/slow waves corresponding to high-frequency (low-hybrid scale); and (3) the number of spiral nulls (O-lines) were about 3.6 times more than radial ones (X-lines), and three-dimensional structures were about 8 times more prevalent than two-dimensional ones. These findings should help us better unravel the dynamics of turbulent magnetic reconnection.

Electron-only magnetic reconnection, a novel form of magnetic reconnection recently discovered in plasma turbulence, exhibits distinct features from the well-studied standard magnetic reconnection with ion coupling. Our study investigates its energy partition features by utilizing in situ measurements from the Magnetospheric Multiscale mission. Electron enthalpy flux exhibits a strong linear relationship with electron velocity. The spatial distributions of electron kinetic energy and enthalpy fluxes are influenced by the asymmetric effects and guide fields in a similar manner to how the spatial distributions of electron velocity are affected. The guide field enhances Poynting flux to a magnitude that rivals, or even surpasses, electron enthalpy flux, while also deflects it toward the outflow direction. These findings impact the understanding of energy partition in magnetic reconnection.

The terrestrial magnetosphere is a natural laboratory where many important plasma processes can be studied in detail by using high-quality spacecraft measurements of electromagnetic fields and particle distribution functions over a broad range of spatial and temporal scales. One such important process is magnetic reconnection. We discuss recent results on the detailed structure of reconnection sites, on suprathermal electron energization within reconnection regions and on reconnection within turbulent plasma. Particularly we demonstrate the importance of understanding in detail processes occurring at the characteristic ion and electron scales. Our results are based on multi-spacecraft observations by the Cluster spacecraft. We also briefly discuss the need for future multi-spacecraft missions, such as MMS and Cross-Scale, to further advance the understanding of magnetic reconnection. The results obtained by using spacecraft measurements can find direct applications to laboratory plasmas as well as to plasma environments around other planets, in the solar atmosphere and solar wind and in distant astrophysical objects.

Magnetic reconnection, which occurs in high conducting plasmas, changes the topology of magnetic field lines and converts magnetic energy into the kinetic and thermal energy of plasma and also accelerates charged particles. This phenomenon plays an important role in changing the dynamic of laboratory and space plasmas such as fusion tokamaks and sun’s corona. The electric and magnetic fields generated by magnetic reconnection result in acceleration and drift motion of charged particles. Therefore, charged particles, depending on their injection position and initial kinetic energy, can be accelerated and escape or can be trapped in magnetic fields. In this study by considering different injection positions and initial kinetic energies, we investigate how a particle (proton) is accelerated or trapped. Our numerical analyses show that the spine structure for three-dimensional magnetic reconnection can be considered as a potential mechanism for particle acceleration. In this model, a proton can be accelerated up to a few MeV within a few milliseconds. The particle’s trajectory and final kinetic energy strongly depend on its injection position.