In solar flares and other astrophysical systems, a major challenge for solving particle acceleration problem associated with magnetic reconnection is the enormous scale separation between kinetic scales and observed reconnection scale. Because of this, it has been difficult to draw any definite conclusions by just using kinetic simulations. Particle acceleration model that solves energetic particle transport equation can capture the main acceleration physics found in kinetic simulations, and thus provide a practical way to make observable predictions and directly compare model results with observations. Here we study compression particle acceleration in magnetic reconnection by solving Parker (diffusion-advection) transport equation using velocity and magnetic fields from two-dimensional high-Lundquist-number magnetohydrodynamics (MHD) simulations of a low-$β$ reconnection layer. We show that the compressible reconnection layer can give significant particle acceleration, leading to the formation of power-law particle energy distributions. We analyze the acceleration rate and find that the acceleration in the reconnection layer is a mixture of first order and second order Fermi processes. When including a guide field, we find the spectrum becomes steeper and both the power-law cutoff energy and maximum particle energy decrease as plasma becomes less compressible. This model produces 2D particle distribution that one can use to generate radiation map and directly compare with solar flare observations. This provides a framework to explain particle acceleration at large-scale astrophysical reconnection sites, such as solar flares.
Particle acceleration in space and astrophysical reconnection sites is an important unsolved problem in studies of magnetic reconnection. Earlier kinetic simulations have identified several acceleration mechanisms that are associated with particle drift motions. Here, we show that, for sufficient large systems, the energization processes due to particle drift motions can be described as fluid compression and shear, and that the shear energization is proportional to the pressure anisotropy of energetic particles. By analyzing results from fully kinetic simulations, we show that the compression …
By means of fully kinetic simulations, we investigate electron acceleration during magnetic reconnection in a nonrelativistic proton--electron plasma with conditions similar to solar corona and flares. We demonstrate that reconnection leads to a nonthermally dominated electron acceleration with a power-law energy distribution in the nonrelativistic low-$β$ regime but not in the high-$β$ regime, where $β$ is the ratio of the plasma thermal pressure and the magnetic pressure. The accelerated electrons contain most of the dissipated magnetic energy in the low-$β$ regime. A guiding-center current …
Magnetic reconnection in strongly magnetized astrophysical plasma environments is believed to be the primary process for fast energy release and particle energization. Currently there is strong interest in relativistic magnetic reconnection, in that it may provide a new explanation for high-energy particle acceleration and radiation in strongly magnetized astrophysical systems. We review recent advances in particle acceleration and reconnection physics in the magnetically-dominated regime. More discussion is focused on the physics of particle acceleration, power-law formation as well as the re…
While a growing body of research indicates that relativistic magnetic reconnection is a prodigious source of particle acceleration in high-energy astrophysical systems, the dominant acceleration mechanism remains controversial. Using a combination of fully kinetic simulations and theoretical analysis, we demonstrate that Fermi-type acceleration within the large-scale motional electric fields dominates over direct acceleration from non-ideal electric fields within small-scale diffusion regions. This result has profound implications for modeling particle acceleration in large-scale astrophysical…
Particle acceleration during magnetic reconnection is a long-standing topic in space, solar and astrophysical plasmas. Recent 3D particle-in-cell simulations of magnetic reconnection show that particles can leave flux ropes due to 3D field-line chaos, allowing particles to access additional acceleration sites, gain more energy through Fermi acceleration, and develop a power-law energy distribution. This 3D effect does not exist in traditional 2D simulations, where particles are artificially confined to magnetic islands due to their restricted motions across field lines. Full 3D simulations, ho…
We propose the particle acceleration model coupled with multiple plasmoid ejections in a solar flare. Unsteady reconnection produces plasmoids in a current sheet and ejects them out to the fast shocks, where particles in a plasmoid are reflected upstream the shock front by magnetic mirror effect. As the plasmoid passes through the shock front, the reflection distance becomes shorter and shorter driving Fermi acceleration, until it becomes proton Larmor radius. The fractal distribution of plasmoids may also have a role in naturally explaining the power-law spectrum in nonthermal emissions.
The nonthermal particle acceleration during magnetic reconnection remains a fundamental topic in several astrophysical phenomena, such as solar flares, pulsar wind, magnetars, etc, for more than half a century, and one of the unresolved questions is its efficiency. Recently, nonthermal particle acceleration mechanisms during reconnection have been extensively studied by particle-in-cell simulations, yet it is an intriguing enigma as to how the magnetic field energy is divided into thermally heated plasmas and nonthermal particles. Here we study both non-relativistic and relativistic magnetic r…
Magnetic reconnection is a primary driver of particle acceleration processes in space and astrophysical plasmas. Understanding how particles are accelerated and the resulting particle energy spectra is among the central topics in reconnection studies. We review recent advances in addressing this problem in nonrelativistic reconnection that is relevant to space and solar plasmas and beyond. We focus on particle acceleration mechanisms, particle transport due to 3D reconnection physics, and their roles in forming power-law particle energy spectra. We conclude by pointing out the challenges in st…
It has been proposed that particles bouncing between magnetized flows converging in a reconnection region can be accelerated by the first order Fermi mechanism. Analytical considerations of this mechanism have shown that the spectral index of accelerated particles is related to the total plasma compression within the reconnection region similarly to the case of diffusive shock acceleration mechanism. As a first step to investigate the efficiency of Fermi acceleration in reconnection regions in producing hard energy spectra of particles in the solar corona, we explore the degree of plasma compr…
The basic physics and recent progresses in theoretical and particle-in-cell (PIC) simulation studies of particle acceleration in multi-island magnetic reconnection are briefly reviewed. Particle acceleration in multi-island magnetic reconnection is considered a plausible mechanism for the acceleration of energetic particles in solar flares and the solar wind. Theoretical studies have demonstrated that such a mechanism can produce the observed power-law energy distribution of energetic particles if the particle motion is sufficiently randomized in the reconnection event. However, PIC simulation…
Magnetic reconnection is thought to be the driver for many explosive phenomena in the universe. The energy release and particle acceleration during reconnection have been proposed as a mechanism for producing high-energy emissions and cosmic rays. We carry out two- and three-dimensional kinetic simulations to investigate relativistic magnetic reconnection and the associated particle acceleration. The simulations focus on electron-positron plasmas starting with a magnetically dominated, force-free current sheet ($σ\equiv B^2/(4πn_e m_e c^2) \gg 1$). For this limit, we demonstrate that relativis…
The acceleration of solar flare ions during magnetic reconnection is explored via particle-in-cell simulations that self-consistently follow the motions of both protons and $α$ particles. We demonstrate that the dominant ion heating during reconnection with a guide field (a magnetic component perpendicular to the reconnection plane) results from pickup behavior during the entry into reconnection exhausts. In contrast with anti-parallel reconnection, the temperature increment is dominantly transverse, rather than parallel, to the local magnetic field. The comparison of protons and alphas reveal…
Magnetic reconnection is a ubiquitous astrophysical process that rapidly converts magnetic energy into some combination of plasma flow energy, thermal energy, and non-thermal energetic particles, including energetic electrons. Various reconnection acceleration mechanisms in different low-$β$ (plasma-to-magnetic pressure ratio) and collisionless environments have been proposed theoretically and studied numerically, including first- and second-order Fermi acceleration, betatron acceleration, parallel electric field acceleration along magnetic fields, and direct acceleration by the reconnection e…
We report a newly found two-stage mechanism of electron acceleration near X-lines of 3D collisionless guide-field magnetic reconnection in the non-relativistic regime typical, e.g., for stellar coronae. We found that after electrons are first pre-accelerated during the linear growth of reconnection, they become additionally accelerated in the course of the nonlinear stage of 3D guide-field magnetic reconnection. This additional acceleration is due to the filamentation of electric and magnetic fields caused by streaming instabilities. In addition to enhanced parallel electric fields, the filame…
Turbulence is ubiquitous in astrophysics. It radically changes many astrophysical phenomena, in particular, the propagation and acceleration of cosmic rays. We present the modern understanding of compressible magnetohydrodynamic (MHD) turbulence, in particular its decomposition into Alfvén, slow and fast modes, discuss the density structure of turbulent subsonic and supersonic media, as well as other relevant regimes of astrophysical turbulence. All this information is essential for understanding the energetic particle acceleration that we discuss further in the review. For instance, we show h…
The important role played by magnetic reconnection in the early acceleration of coronal mass ejections (CMEs) has been widely discussed. However, as CMEs may have expansion speeds comparable to their propagation speeds in the corona, it is not clear whether and how reconnection contributes to the true acceleration and expansion separately. To address this question, we analyze the dynamics of a moderately fast CME on 2013 February 27, associated with a continuous acceleration of its front into the high corona, even though its speed had reached $\sim$700~km~s$^{-1}$ and larger than the solar win…
Plasma energization through magnetic reconnection in the magnetically-dominated regime featured by low plasma beta ($β= 8 πnkT_0/B^2 \ll 1$) and/or high magnetization ($σ= B^2/(4 πnmc^2) \gg 1$) is important in a series of astrophysical systems such as solar flares, pulsar wind nebula, and relativistic jets from black holes, etc. In this paper, we review the recent progress on kinetic simulations of this process and further discuss plasma dynamics and particle acceleration in a low-$β$ reconnection layer that consists of electron-positron pairs. We also examine the effect of different initial …
Astrophysical reconnection takes place in a turbulent medium. The turbulence in most cases is pre-existing, not caused by the reconnection itself. The model of magnetic reconnection in Lazarian & Vishniac (1999) predicts that in the presence of turbulence the reconnection becomes fast, i.e. it is independent of resistivity, but dependent on the level of turbulence. Magnetic reconnection injects energy into plasmas through a turbulent outflow from the reconnection region and this outflow can enhance the level of turbulence creating bursts of reconnection. Magnetic reconnection in the presence o…
The linear and nonlinear evolution of magnetic reconnection in collisionless high-temperature plasmas with a strong guide field is analyzed on the basis of a two-dimensional gyrofluid model. The linear growth rate of the reconnecting instability is compared to analytical calculations over the whole spectrum of linearly unstable wave numbers. In the strongly unstable regime (large Δ'), the nonlinear evolution of the reconnecting instability is found to undergo two distinctive acceleration phases separated by a stall phase in which the instantaneous growth rate decreases. The first acceleration …
While observations have suggested that power-law electron energy spectra are a common outcome of strong energy release during magnetic reconnection, e.g., in solar flares, kinetic simulations have not been able to provide definite evidence of power-laws in energy spectra of non-relativistic reconnection. By means of 3D large-scale fully kinetic simulations, we study the formation of power-law electron energy spectra in non-relativistic low-$β$ reconnection. We find that both the global spectrum integrated over the entire domain and local spectra within individual regions of the reconnection la…
Where particle acceleration and plasma heating take place in relation to magnetic reconnection is a fundamental question for solar flares. We report analysis of an M7.7 flare on 2012 July 19 observed by SDO/AIA and RHESSI. Bi-directional outflows in forms of plasmoid ejections and contracting cusp-shaped loops originate between an erupting flux rope and underlying flare loops at speeds of typically 200-300 km/s up to 1050 km/s. These outflows are associated with spatially separated double coronal X-ray sources with centroid separation decreasing with energy. The highest temperature is located …
By means of fully kinetic particle-in-cell simulations, we study whether the proton-to-electron mass ratio $m_i/m_e$ influences the energy spectrum and underlying acceleration mechanism during magnetic reconnection. While kinetic simulations are essential for studying particle acceleration during magnetic reconnection, a reduced $m_i/m_e$ is often used to alleviate the demanding computing resources, which leads to artificial scale separation between electron and proton scales. Recent kinetic simulations with high-mass-ratio have suggested new regimes of reconnection, as electron pressure aniso…
Processes driven by unsteady reconnection can efficiently accelerate particles in many astrophysical plasmas. An example are the reconnection jet fronts in an outflow region. We present evidence of suprathermal ion acceleration between two consecutive reconnection jet fronts observed by the Magnetospheric Multiscale mission in the terrestrial magnetotail. An earthward propagating jet is approached by a second faster jet. Between the jets, the thermal ions are mostly perpendicular to magnetic field, are trapped and are gradually accelerated in the parallel direction up to 150 keV. Observations …
In strongly magnetized astrophysical plasma systems, magnetic reconnection is believed to be a 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 is the consequence of 3D dynamics, where turbulent structures are naturally generated as various types of instabilities develop. This paper presents a series of 3D, fully-kinetic simulations of…
Magnetic reconnection is an important driver of energetic particles in many astrophysical phenomena. Using kinetic particle-in-cell (PIC) simulations, we explore the impact of three-dimensional reconnection dynamics on the efficiency of particle acceleration. In two-dimensional systems, Alfvénic outflows expel energetic electrons into flux ropes where they become trapped and disconnected from acceleration regions. However, in three-dimensional systems these flux ropes develop axial structure that enables particles to leak out and return to acceleration regions. This requires a finite guide fie…
A new computational model is presented suitable for exploring the self-consistent production of energetic electrons during magnetic reconnection in macroscale systems. The equations are based on the recent discovery that parallel electric fields are ineffective drivers of energetic particles during reconnection so that the kinetic scales which control the development of such fields can be ordered out of the equations. The resulting equations consist of a magnetohydrodynamic (MHD) backbone with the energetic component represented by macro-particles described by the guiding center equations. Cru…
The acceleration of charged particles in magnetized plasmas is considered during turbulent multi-island magnetic reconnection. The particle acceleration model is constructed for an ensemble of islands which produce adiabatic compression of the particles. The model takes into account the statistical fluctuations in the compression rate experienced by the particles during their transport in the acceleration region. The evolution of the particle distribution function is described as a simultaneous first and second-order Fermi acceleration process. While the efficiency of the first-order process i…
Here is reported in situ observation of energetic electrons (~100-500 keV) associated with magnetic reconnection in the solar wind by the ACE and Wind spacecraft. The properties of this magnetic cloud driving reconnection and the associated energetic electron acceleration problem are discussed. Further analyses indicate that the electric field acceleration and Fermi type mechanism are two fundamental elements in the electron acceleration processes and the trapping effect of the specific magnetic field configuration maintains the acceleration status that increases the totally gained energy.
Properties of plasmoid-dominated turbulent reconnection in a low-$β$ background plasma are investigated by resistive magnetohydrodynamic (MHD) simulations. In the $β_{\rm in} < 1$ regime, where $β_{\rm in}$ is plasma $β$ in the inflow region, the reconnection site is dominated by shocks and shock-related structures and plasma compression is significant. The effective reconnection rate increases from $0.01$ to $0.02$ as $β_{\rm in}$ decreases. We hypothesize that plasma compression allows faster reconnection rate, and then we estimate a speed-up factor, based on a compressible MHD theory. We va…
Astrophysical media are turbulent and therefore reconnection should be treated in the presence of pre-existing turbulence. We consider the model of fast magnetic reconnection in Lazarian & Vishniac (1999) which predicts that the rate of reconnection is controlled by the intensity and the injection scale of turbulent motions. We provide new evidence of successful testing of the model and argue that the model presents a generic set up for astrophysical reconnection events. We study particle acceleration that takes place in volumes of driven turbulence as well turbulent volumes in the presence of…
While the exact acceleration mechanism of energetic particles during solar flares is (as yet) unknown, magnetic reconnection plays a key role both in the release of stored magnetic energy of the solar corona and the magnetic restructuring during a flare. Recent work has shown that special field lines, called separators, are common sites of reconnection in 3D numerical experiments. To date, 3D separator reconnection sites have received little attention as particle accelerators. We investigate the effectiveness of separator reconnection as a particle acceleration mechanism for electrons and prot…
Turbulence, magnetic reconnection, and shocks can be present in explosively unstable plasmas, forming a new electromagnetic environment, which we call here turbulent reconnection, and where spontaneous formation of current sheets takes place. We will show that the heating and the acceleration of particles is the result of the synergy of stochastic (second order Fermi) and systematic (first order Fermi) acceleration inside fully developed turbulence. The solar atmosphere is magnetically coupled to a turbulent driver (the convection zone), therefore the appearance of turbulent reconnection in th…
The relaxation of field-line tension during magnetic reconnection gives rise to a universal Fermi acceleration process involving the curvature drift of particles. However, the efficiency of this mechanism is limited by the trapping of energetic particles within flux-ropes. Using 3D fully kinetic simulations, we demonstrate that the flux-rope kink instability leads to strong field-line chaos in weak-guide-field regimes where the Fermi mechanism is most efficient, thus allowing particles to transport out of flux-ropes and undergo further acceleration. As a consequence, both ions and electrons de…
Understanding how the release of stored magnetic energy contributes to the generation of non-thermal high energy particles during solar flares is an important open problem in solar physics. Magnetic reconnection plays a fundamental role in the energy release and conversion processes taking place during flares. A common approach for investigating particle acceleration is to use test particles in fields derived from magnetohydrodynamic (MHD) simulations of reconnection. These MHD simulations use anomalous resistivities that are much larger than the Spitzer resistivity based on Coulomb collisions…
Electron acceleration by turbulent reconnection in solar flares
School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）；Key Laboratory for Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education（教育部现代天文学和天体物理学重点实验室（南京大学））；Institute of Science and Technology for Deep Space Exploration, Suzhou Campus, Nanjing University（南京大学苏州校区深空探测科学与技术研究院）；State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology（澳门科技大学月球与行星科学国家重点实验室）
The possibility of studying non-thermal electron energization in laser-driven plasma experiments of magnetic reconnection is studied using two- and three-dimensional particle-in-cell simulations. It is demonstrated that non-thermal electrons with energies more than an order of magnitude larger than the initial thermal energy can be produced in plasma conditions currently accessible in the laboratory. Electrons are accelerated by the reconnection electric field, being injected at varied distances from the X-points, and in some cases trapped in plasmoids, before escaping the finite-sized system.…
Theoretically, CME kinematics are related to magnetic reconnection processes in the solar corona. However, the current quantitative understanding of this relationship is based on the analysis of only a handful of events. Here we report a statistical study of 60 CME-flare events from August 2010 to December 2013. We investigate kinematic properties of CMEs and magnetic reconnection in the low corona during the early phase of the eruptions, by combining limb observations from STEREO with simultaneous on-disk views from SDO. For a subset of 42 events with reconnection rate evaluated by the magnet…
One of the key unresolved problems in the study of space plasmas is to explain the production of energetic electrons as magnetic field lines `reconnect' and release energy in a exposive manner. Recent observations suggest possible roles played by small scale magnetic islands in the reconnection region, but their precise roles and the exact mechanism of electron energization have remained unclear. Here we show that secondary islands generated in the reconnection region are indeed efficient electron accelerators. We found that, when electrons are trapped inside the islands, they are energized co…
The effect of a parallel velocity shear on the explosive phase of a double current sheet system is investigated within the 2D resistive magnetohydrodynamic (MHD) framework. We further explore the effect of this shear on acceleration of test particles. The general evolution pattern of the double current sheets is similar for all sub-Alfvénic shears with respect to the initial transient phase, the onset of the plasmoid instability and the final relaxation phase. We find that the theoretical scaling of the reconnection rate with shear holds if the rate is measured when the islands have a similar …
Energetic electrons of up to tens of MeV are created during explosive phenomena in the solar corona. While many theoretical models consider magnetic reconnection as a possible way of generating energetic electrons, the precise roles of magnetic reconnection during acceleration and heating of electrons still remain unclear. Here we show from 2D particle-in-cell simulations that coalescence of magnetic islands that naturally form as a consequence of tearing mode instability and associated magnetic reconnection leads to efficient energization of electrons. The key process is the secondary magneti…
Aims: We investigate the electron acceleration in convective electric fields of cascading magnetic reconnection in a flaring solar corona and show the resulting hard X-ray (HXR) radiation spectra caused by Bremsstrahlung for the coronal source. Methods: We perform test particle calculation of electron motions in the framework of a guiding center approximation. The electromagnetic fields and their derivatives along electron trajectories are obtained by linearly interpolating the results of high-resolution adaptive mesh refinement (AMR) MHD simulations of cascading magnetic reconnection. Hard X-…
Particle acceleration is one of the most significant features that are ubiquitous among space and cosmic plasmas. It is most prominent during flares in the case of the Sun, with which huge amount of electromagnetic radiation and high-energy particles are expelled into the interplanetary space through acceleration of plasma particles in the corona. Though it has been well understood that energies of flares are supplied by the mechanism called magnetic reconnection based on the observations in X-rays and EUV with space telescopes, where and how in the flaring magnetic field plasmas are accelerat…
The conversion of magnetic energy into other forms during solar flares is one of the outstanding open problems in solar physics. It is generally accepted that magnetic reconnection plays a crucial role in these conversion processes. To achieve the rapid energy release required in solar flares, an anomalous resistivity, orders of magnitude higher than the Spitzer resistivity, is often used in MHD simulations of reconnection. Spitzer resistivity is based on Coulomb scattering, which becomes negligible at the high energies achieved by accelerated particles. As a result, simulations of particle ac…
Compression and Reconnection Investigations of the MagnetoPause (CRIMP): A Mission Concept to Uncover the Impact of Mesoscale Reconnection and Plasma Outflow Processes at the Dayside Magnetopause
Space Science Center, University of New Hampshire（新罕布什尔大学空间科学中心）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Center for Astrophysics | Harvard & Smithsonian（哈佛与史密森尼天体物理中心）；Massachusetts Institute of Technology（麻省理工学院）；Dartmouth College（达特茅斯学院）；NASA Goddard Space Flight Center（美国宇航局戈达德太空飞行中心）；Georgia State University（佐治亚州立大学）；The Catholic University of America（美利坚天主教大学）；Instituto Tecnológico de Aeronáutica（巴西航空技术研究所）；The Aerospace Corporation（航空航天公司）；Arizona State University（亚利桑那州立大学）；Remcom Inc.（Remcom公司）；NASA Jet Propulsion Laboratory, California Institute of Technology（美国宇航局喷气推进实验室，加州理工学院）；Space Sciences Laboratory, University of California, Berkeley（加州大学伯克利分校空间科学实验室）；University of California, Los Angeles（加州大学洛杉矶分校）；Southwest Research Institute（西南研究院）
The primary focus of this paper is on the particle acceleration mechanism in solar coronal three-dimensional reconnection null-point regions. Starting from a potential field extrapolation of a Solar and Heliospheric Observatory (SOHO) magnetogram taken on 2002 November 16, we first performed magnetohydrodynamics (MHD) simulations with horizontal motions observed by SOHO applied to the photospheric boundary of the computational box. After a build-up of electric current in the fan-plane of the null-point, a sub-section of the evolved MHD data was used as initial and boundary conditions for a kin…
We reexamine the relationship between energy spectral indices and element abundance enhancements in solar energetic particle (SEP) events at energies of a few MeV/amu. We find a correlated behavior only in the largest gradual SEP4 events when all ions are accelerated from the ambient coronal plasma by shock waves driven by fast, wide coronal mass ejections (CMEs). This correlated abundance behavior can track complex time variations in the spectral indices during an event. In other (SEP3) events, CME-driven shock waves, days apart, sample seed particles from a single pool of suprathermal impuls…
Solar flares and coronal mass ejections (CMEs) are closely coupled through magnetic reconnection. CMEs are usually accelerated impulsively within the low solar corona, synchronized with the impulsive flare energy release. We investigate the dynamic evolution of a fast CME and its associated X2.8 flare occurring on 2013 May 13. The CME experiences two distinct phases of enhanced acceleration, an impulsive one with a peak value of ~5 km s$^{-2}$ followed by an extended phase with accelerations up to 0.7 km s$^{-2}$. The two-phase CME dynamics is associated with a two-episode flare energy release…
Magnetic B-stars often exhibit circularly polarized radio emission thought to arise from gyrosynchrotron emission by energetic electrons trapped in the circumstellar magnetosphere. Recent empirical analyses show that the onset and strength of the observed radio emission scale with both the magnetic field strength and the stellar rotation rate. This challenges the existing paradigm that the energetic electrons are accelerated in the current sheet between opposite-polarity field lines in the outer regions of magnetised stellar winds, which includes no role for stellar rotation. Building on recen…
Recent years have been marked by substantial changes in our understanding of magnetic turbulence and magnetic reconnection, which, in its turn induced better understanding of cosmic ray diffusion and acceleration. Current models of magnetized turbulence are no more ad hoc constructions, but numerically tested theories. In this very short review we summarize topics presented in two talks given at the conference and provide a brief sketch of the vast and rapidly developing field. We discuss how turbulence decreases the efficient mean free path of the particles in the collisionless plasmas in gal…
