Electron Acceleration Mechanism Research Articles

Stochastic electron acceleration in plasma waves driven by a high-power subpicosecond laser pulse

The mechanism of stochastic electron acceleration and heating by a picosecond laser pulse in underdense plasma is studied using particle-in-cell simulations and theoretical models. The formation of wide electron energy spectra in the simultaneously acting laser and plasma fields is analyzed. It is shown that electron scattering by turbulent plasma fluctuations excited through stimulated forward Raman scattering plays a governing role in the formation of high-energy tails in the electron distribution function.

A STATISTICAL STUDY OF THE SPECTRAL HARDENING OF CONTINUUM EMISSION IN SOLAR FLARES

The observed hard X-ray and {gamma}-ray continuum in solar flares is interpreted as Bremsstrahlung emission of accelerated non-thermal electrons. It has been noted for a long time that in many flares the energy spectra show hardening at energies around or above 300 keV. In this paper, we first conduct a survey of spectral hardening events that were previously studied in the literature. We then perform a systematic examination of 185 flares from the Solar Maximum Mission. We identify 23 electron-dominated events whose energy spectra show clear double power laws. A statistical study of these events shows that the spectral index below the break ({gamma}{sub 1}) anti-correlates with the break energy ({epsilon}{sub b}). Furthermore, {gamma}{sub 1} also anti-correlates with Fr, the fraction of photons above the break compared to the total photons. A hardening spectrum, as well as the correlations between ({gamma}{sub 1}, {epsilon}{sub b}) and ({gamma}{sub 1}, Fr), provide stringent constraints on the underlying electron acceleration mechanism. Our results support a recent proposal that electrons are being accelerated diffusively at a flare termination shock with a width of the order of an ion inertial length scale.

A statistical study of electron acceleration behind the dipolarization fronts in the magnetotail

AbstractWe investigate the electron acceleration behind dipolarization fronts (DFs) in the magnetotail from −25 RE to −10 RE through the examination of the energetic electron energy flux (>30 keV) with the observations from Time History of Events and Macroscale Interactions during Substorms (THEMIS). Statistical results of 133 DF events are presented based on the data set from January to April of the years 2008 and 2009. As the DFs propagate earthward, the acceleration of energetic electrons behind the DFs is found to take place over several RE along the tail. The increase in energetic electron energy flux can reach 2–4 orders of magnitude. The dominant acceleration mechanisms are different in the midtail (XGSM ≤ −15 RE) and the near‐Earth region (−15 < XGSM ≤ −10 RE). In the midtail, the majority of DF events show that the dominant electron acceleration mechanism is betatron acceleration. In the near‐Earth region, betatron acceleration is dominant in ~46% DF events while Fermi acceleration is dominant in ~39% DF events.

Dynamic variation and the fast acceleration of particles in Earth’s radiation belt

We have quantitatively investigated the radiation belt’s dynamic variations of 1.5–6.0 MeV electrons during 54 CME (coronal mass ejection)-driven storms from 1993 to 2003 and 26 CIR (corotating interaction region)-driven recurrent storms in 1995 by utilizing case and statistical studies based on the data from the SAMPEX satellite. It is found that the boundaries determined by fitting an exponential to the flux as a function of L shell obtained in this study agree with the observed outer and inner boundaries of the outer radiation belt. Furthermore, we have constructed the Radiation Belt Content (RBC) index by integrating the number density of electrons between those inner and outer boundaries. According to the ratio of the maximum RBC index during the recovery phase to the pre-storm average RBC index, we conclude that CME-driven storms produce more relativistic electrons than CIR-driven storms in the entire outer radiation belt, although the relativistic electron fluxes during CIR-related storms are much higher than those during CME-related storms at geosynchronous orbit. The physical radiation belt model STEERB is based on the three-dimensional Fokker-Planck equation and includes the physical processes of local wave-particle interactions, radial diffusion, and adiabatic transport. Due to the limitation of numerical schemes, formal radiation belt models do not include the cross diffusion term of local wave-particle interactions. The numerical experiments of STEERB have shown that the energetic electron fluxes can be overestimated by a factor of 5 or even several orders (depending on the pitch angle) if the cross diffusion term is ignored. This implies that the cross diffusion term is indispensable for the evaluation of radiation belt electron fluxes. Formal radiation belt models often adopt dipole magnetic field; the time varying Hilmer-Voigt geomagnetic field was adopted by the STEERB model, which self-consistently included the adiabatic transport process. The test simulations clearly indicate that the adiabatic process can significantly affect the evolution of radiation belt electrons. The interactions between interplanetary shocks and magnetosphere can excite ULF waves in the inner magnetosphere; the excited polodial mode ULF wave can cause the fast acceleration of “killer electrons”. The acceleration mechanism of energetic electrons by poloidal and toroidal mode ULF wave is different at different L shells. The acceleration of energetic electrons by the toroidal mode ULF waves becomes important in the region with a larger L shell (the outer magnetosphere); in smaller L shell regions (the inner magnetosphere), the poloidal mode ULF becomes responsible for the acceleration of energetic electrons.

Particle acceleration in dipolarization events

Using the electromagnetic fields of a recent MHD simulation of magnetotail reconnection, flow bursts and dipolarization, we investigate the acceleration of test particles (protons and electrons) to suprathermal energies, confirming and extending earlier results on acceleration mechanisms and sources. (Part of the new results have been reviewed recently in Birn et al., Space Science Reviews, 167, doi:10.1007/ s11214‐012‐9874‐4.) The test particle simulations reproduce major features of energetic particle events (injections) associated with substorms or other dipolarization events, particularly a rapid rise of energetic particle fluxes over limited ranges of energy. The major acceleration mechanisms for electrons are betatron acceleration and Fermi acceleration in the collapsing magnetic field. Ions, although non‐adiabatic, undergo similar acceleration. Two major entry mechanisms into the acceleration site are identified: cross‐tail drift from the inner tail plasma sheet and reconnection entry from field lines extending to the more distant plasma sheet. The former dominates early in an event and at higher energies (hundreds of keV) while the latter constitutes the main source later and at lower energies (tens of keV). Despite the fact that the injection front moves earthward in the tail, the peak of energetic particle fluxes moves to higher latitude when mapped from the near‐Earth boundary to Earth in a static magnetic field model.

YOUNG SUPERNOVAE AS EXPERIMENTAL SITES FOR STUDYING THE ELECTRON ACCELERATION MECHANISM

Radio emissions from young supernovae (~ 1 year after the explosion) show a peculiar feature in the relativistic electron population at a shock wave, where their energy distribution is steeper than typically found in supernova remnants (SNRs) and than the prediction from the standard diffusive shock acceleration (DSA) mechanism. This is especially established for a class of stripped envelope supernovae (SNe IIb/Ib/Ic) where a combination of high shock velocity and low circumstellar material (CSM) density makes it easier to derive the intrinsic energy distribution than in other classes of SNe. We suggest that this apparent discrepancy reflects the situation that the low energy electrons before accelerated by the DSA-like mechanism are responsible for the radio synchrotron emission from young SNe, and that studying young SNe sheds light on the still-unresolved electron injection problem in the acceleration theory of cosmic rays. We suggest that electron's energy distribution could be flattened toward the high energy, most likely around 100 MeV, which marks a transition from inefficient to efficient acceleration. Identifying this feature will be a major advance in understanding the electron acceleration mechanism. We suggest two further probes: (1) mm/sub-mm observations in the first year after the explosion, and (2) X-ray observations at about 1 year and thereafter. We show that these are reachable by ALMA and Chandra for nearby SNe.

Non-diffusive resonant acceleration of electrons in the radiation belts

We describe a mechanism of resonant electron acceleration by oblique high-amplitude whistler waves under conditions typical for the Earth radiation belts. We use statistics of spacecraft observations of whistlers in the Earth radiation belts to obtain the dependence of the angle θ between the wave-normal and the background magnetic field on magnetic latitude λ. According to this statistics, the angle θ already approaches the resonance cone at λ∼15° and remains close to it up to λ∼30°–40° on the dayside. The parallel component of the electrostatic field of whistler waves often increases around λ∼15° up to one hundred of mV/m. We show that due to this increase of the electric field, the whistler waves can trap electrons into the potential well via wave particle resonant interaction corresponding to Landau resonance. Trapped electrons then move with the wave to higher latitudes where they escape from the resonance. Strong acceleration is favored by adiabatic invariance along the increasing magnetic field, which continuously transfers the parallel energy gained to perpendicular energy, allowing resonance to be reached and maintained. The concomitant increase of the wave phase velocity allows for even stronger relative acceleration at low energy <50keV. Each trapping-escape event of electrons of ∼10keV to 100 keV results in an energy gain of up to 100 keV in the inhomogeneous magnetic field of the Earth dipole. For electrons with initial energy below 100 keV, such rapid acceleration should hasten their drop into the loss-cone and their precipitation into the atmosphere. We discuss the role of the considered mechanism in the eventual formation of a trapped distribution of relativistic electrons for initial energies larger than 100 keV and in microbursts precipitations of lower energy particles.

Quantifying radial diffusion coefficients of radiation belt electrons based on global MHD simulation and spacecraft measurements

Radial diffusion is one of the most important acceleration mechanisms for radiation belt electrons, which can be enhanced from drift‐resonant interactions with large‐scale fluctuations of the magnetosphere's magnetic and electric fields (Pc5 range of ULF waves). In order to physically quantify the radial diffusion coefficient,DLL, we run the global Lyon‐Fedder‐Mobarry (LFM) MHD simulations to obtain the mode structure and power spectrum of the ULF waves and validate the simulation results with available satellite measurements. The calculated diffusion coefficients, directly from the MHD fields over a Corotating Interaction Region (CIR) storm in March 2008, are generally higher when solar wind dynamic pressure is enhanced or AE index is high. In contrary to the conventional understanding, our results show that inside geosynchronous orbit the total diffusion coefficient from MHD fields is dominated by the contribution from electric field perturbations, rather than the magnetic field perturbations. The calculated diffusion coefficient has a physical dependence onμ (or electron energy) and L, which is missing in the empirical diffusion coefficient, DLLKp as a function of Kp index, and DLLKp are generally greater than our calculated DLLduring the storm event. Validation of the MHD ULF waves by spacecraft field data shows that for this event the LFM code reasonably well‐reproduces theBz wave power observed by GOES and THEMIS satellites, while the Eφ power observed by THEMIS probes are generally underestimated by LFM fields, on average by about a factor of ten.

SUZAKUOBSERVATIONS OF THE NON-THERMAL SUPERNOVA REMNANT HESS J1731–347

A detailed analysis of the nonthermal X-ray emission from the North-Western and Southern parts of the supernova remnant (SNR) HESS J1731$ - $347 with {\it Suzaku} is presented. The shell portions covered by the observations emit hard and line-less X-rays. The spectrum can be reproduced by a simple absorbed power-law model with a photon index $\Gamma$ of 1.8-2.7 and an absorption column density $N_{\rm H}$ of (1.0-2.1)$\times 10^{22}$ cm$^{-2}$. These quantities change significantly from region to region; the North-Western part of the SNR has the hardest and most absorbed spectrum. The Western part of the X-ray shell has a smaller curvature than North-Western and Southern shell segments. A comparison of the X-ray morphology to the Very High Energy (VHE) gamma-ray and radio images was performed. The efficiency of electron acceleration and emission mechanism in each portion of the shell are discussed. Thermal X-ray emission from the SNR was searched for but could not be detected at a significant level.

Mechanism of electron acceleration by chirped laser pulse

We studied the mechanism of electron acceleration by a chirped laser pulse. We found that, because of the chirp effect, a region exists where the laser wave phase experienced by the electron varies slowly, so that the electron can be accelerated for a long time. The mechanism of chirped laser acceleration is different to that of the capture and acceleration scenario, although both of them have a main acceleration stage in which the electrons are trapped for long periods.

High proton energies from cone targets: electron acceleration mechanisms

Recent experiments in the Trident laser facility (Los Alamos National Laboratory) have shown that hollow conical targets with a flat top at the tip can enhance the maximum energy of proton beams created during the interaction of an ultra-intense short laser pulse with the target (Gaillard S A et al 2011 Phys. Plasmas18 056710). The proton energies that have been seen in these experiments are the highest energies observed so far in laser-driven proton acceleration. This is attributed to a new acceleration mechanism, direct light pressure acceleration of electrons (DLLPA), which increases the number and energy of hot electrons that drive the proton acceleration. This acceleration process of protons due to a two-temperature sheath formed at the flat-top rear side is very robust and produces a large number of protons per shot, similar to what is regularly observed in target normal sheath acceleration (Hatchett S P et al 2000 Phys. Plasmas7 2076, Maksimchuk A et al 2000 Phys. Rev. Lett.84 4108, Snavely R A et al 2000 Phys. Rev. Lett.85 2945) with flat foils. In this paper, we investigate the electron kinetics during DLLPA, showing that they are governed by two mechanisms, both of which lead to continuous electron acceleration along the inner cone wall. Based on our model, we predict the scaling of the hot electron temperature and ion maximum energy with both laser and target geometrical parameters. The scaling of with the laser strength parameter a0 leads to an ion energy scaling that surpasses that of some recently proposed acceleration mechanisms such as radiation pressure acceleration (RPA), while in addition the maximum electron energy is found to scale linearly with the length of the cone neck. We find that when optimizing parameters, high proton energies suitable for applications can be reached using compact short-pulse laser systems with pulse durations of only a few tens to hundreds of laser periods.

Rapid acceleration of radiation belt energetic electrons by Z‐mode waves

We present the first simulation of the effect of Z‐mode waves on the outer radiation belt electron dynamics. We calculate bounce‐averaged diffusion rates in pitch angle and momentum and then use them as inputs to solve a 2‐D momentum‐pitch angle diffusion equation. Numerical results show that the phase space density (PSD) of 1 MeV electrons can enhance substantially and very rapidly (e.g., 30 minutes). In particular, the momentum diffusion rate exceeds the pitch angle and cross diffusion rates at 0.5 MeV and above, a behavior completely different from that for EMIC and chorus waves. Consequently, momentum (instead of pitch angle or cross) diffusion plays a dominant role in the dynamic evolution of energetic electrons. Moreover, the PSD evolution is found to be very dependent upon the assumed initial particle distributions. These results provide further insights on the interplay between acceleration mechanisms of outer radiation belt electrons.

Study of Particle Acceleration during Reconnection via TS-4 Particle Trajectory Simulations

Particle trajectory calculations were conducted based on TS-4 magnetic probe data in the R-Z plane assuming axisymmetry. An acceleration mechanism for electrons trapped in a merging Spheromak during the formation of a FRC that is causally connected to the out of plane Eφ field during reconnection is found. The energy profile resembles a stair step like motion as the electron is accelerated from the reconnection E field on multiple passes confined to constant magnetic field lines.

Mechanisms of electron acceleration in the excitation of nuclear reactions in solid-state laser plasmas

Investigation of nuclear reactions in a solid-state plasma generated by modern high-intensity sources of ultrashort-wavelength laser radiation is undoubtedly of interest for establishing nuclear-reaction yields versus the intensity of laser radiation and for efficiently exciting new nuclear and photonuclear reactions—in particular, in the resonance energy region. The present article is devoted to describing, for laser plasmas, various mechanisms of electron acceleration, which triggers the acceleration of atomic ions and the excitation of subsequent nuclear reactions.

Reanalysis of radiation belt electron phase space density using various boundary conditions and loss models

Data assimilation is becoming an increasingly important tool for understanding the near Earth hazardous radiation environments. Reanalysis of the radiation belts can be used to identify the electron acceleration mechanism and distinguish local acceleration from radial diffusion. However, for any practical applications we need to determine how reliable is reanalysis, and how significant is the dependence of the results on the assumptions of the code and choice of boundary conditions. We present the sensitivity of reanalysis of the radiation belt electron phase space density (PSD) to the assumed location of the outer boundary, using the VERB code and a Kalman filter. We analyze the sensitivity of reanalysis to changes in the electron-loss throughout the domain, and the sensitivity to the assumed boundary condition and its effect on the innovation vector. All the simulations presented in this study for all assumed loss models and boundary conditions, show that peaks in the phase space density of relativistic electrons build up between 4.5 and 6 R E during relativistic electron flux enhancements in the outer radiation belt. This clearly shows that peaks build up in the heart of the electron radiation belt independent of the assumptions in the model, and that local acceleration is operating there. The work here is also an important step toward performing reanalysis using observations from current and future missions.

SUPPRESSION OF REFLECTED ELECTRONS BY KINETIC ALFVÉN TURBULENCE IN A QUASI-PERPENDICULAR SHOCK: PARTICLE-IN-CELL SIMULATIONS

Shock drift acceleration is one of the important mechanisms for electron acceleration associated with magnetic mirror reflection along the magnetic field in a quasi-perpendicular collisionless shock. We study the influence of a rippled shock surface in the in-plane magnetic field on the magnetic mirror reflection of electrons. Simulation results show that the number of reflected electrons reduces after generation of the rippled shock surface. Electric and magnetic wavenumber spectra of the generated fluctuations in the shock transition region indicate the existence of kinetic Alfven turbulence. The kinetic Alfven turbulence decreases the electron pitch angle by parallel scattering, which reduces the magnetic mirror force acting on the electrons. These results suggest that the shock-generated kinetic Alfven turbulence suppresses the magnetic mirror reflection of electrons during the shock drift acceleration.

Space physics and space weather

CAS Key Laboratory of Basic Plasma Physics, School of Earth and Space Sciences, University of Science and Technology of China, Hefei 230026, China (qmlu@ustc.edu.cn) Space physics is a subject that has developed since the launch of the first artificial satellite in 1957. It has been promoted by space technology and is related closely with various adjacent disciplines. Space physics covers physical processes and phenomena that occur in the solar atmosphere, interplanetary environment and the Earth’s space environment (including the magnetosphere, ionosphere and upper atmosphere), and considers their relations and evolution. With the development of space and communication technology in the past 20–30 years, people’s daily lives and the efficient running of global economics have become heavily dependent on satellites operating in the space environment. However, hazardous weather events in space, such as coronal mass ejections, solar flares and substorms in the magnetosphere, lead to rapid changes in the space environment and the production of energetic particles. Such events, which are collectively referred to as space weather, damage satellites and space/ground-based technology systems and may even threaten astronauts and adversely affect human health or life on Earth. The study of space weather combines space physics and space/ground-based technology. It regards the solar atmosphere, interplanetary environment and Earth’s space as a complete system. Space weather research detects, studies and predicts the phenomena associated with solar eruptions and the related hazardous space weather events, as well as their effects on space/groundbased technology systems. Reducing the damage caused by space weather events and protecting human life is a further goal. Because of the high demand for advanced technology and national security, space weather is becoming a hot spot of international scientific activity. Since the United States proposed a national space weather program in 1995, more than 10 countries or agencies, such as the European Space Agency, Russia, Canada, Japan and Australia, have drawn up their own space weather programs and launched a series of satellites for research purposes. Additionally, many international organizations are promoting programs such as International Living with a Star (ILWS) and Climate and Weather of the Sun-Earth System (CAWSES). Research on space physics and space weather helps us learn more about hazardous space weather events in the space environment and thus allows us to predict them; this knowledge will serve the astronautics and communications industries. As a multidisciplinary research field, the development of space physics and space weather requires the participation of researchers from different fields. This special issue reviews several selected fronts in research on space physics and space weather: electron dynamics in collisionless magnetic reconnection, high-speed flowing plasmas in the Earth’s plasma sheet, energetic particles in the inner magnetosphere, and solar activity effects of the ionosphere. The main contents are as follows. Magnetic reconnection provides a physical mechanism for fast energy conversion from magnetic energy to plasma kinetic energy. It is closely associated with many explosive phenomena in space plasma. The first paper describes the importance of electron dynamics to the structures of magnetic reconnection, and the acceleration mechanisms of energetic electrons. High-speed flowing plasmas are frequently observed phenomena associated with dramatic changes in magnetic structures in the magnetosphere. The second paper discusses briefly the history of high-speed flows and the proposed mechanisms, the relations between high-speed flows and auroras and their interaction with background plasma. The relationships between high-speed flows and substorms are also summarized in the paper. Energetic particles in the radiation belt are the main space weather threat, and understanding their acceleration mechanisms is one of the major challenges in space physics. The third paper reviews recent progress on the fast acceleration of “killer” electrons and energetic ions by ultrafrequency waves excited in the inner magnetosphere by interplanetary shock. Solar radiation, which varies over multiple temporal scales, is the main cause of remarkable variation in the evolution of the ionosphere. The dependence of the ionosphere on solar activity is a fundamental issue in ionospheric physics, providing information essential to understanding variations in the ionosphere and its processes. Selected recent studies on solar activity effects of the ionosphere are briefly reviewed in the fourth paper. This special issue can be referred to by researchers in related fields.

Fast acceleration of “killer” electrons and energetic ions by interplanetary shock stimulated ULF waves in the inner magnetosphere

Energetic electrons and ions in the Van Allen radiation belt are the number one space weather threat. Understanding how these energetic particles are accelerated within the Van Allen radiation belt is one of the major challenges in space physics. This paper reviews the recent progress on the fast acceleration of “killer” electrons and energetic ions by ultralow frequency (ULF) waves stimulated by the interplanetary shock in the inner magnetosphere. Very low frequency (VLF) wave-particle interaction is considered to be one of the primary electron acceleration mechanisms because electron cyclotron resonances can easily occur in the VLF frequency range. Recently, using four Cluster spacecraft observations, we have found that, after interplanetary shocks impact the Earth’s magnetosphere, energetic electrons in the radiation belt are accelerated almost immediately and continue to accelerate for a few hours. The time scale (a few days) for traditional acceleration mechanisms, based on VLF wave-particle interactions to accelerate electrons to relativistic energies, is too long to explain our observations. Furthermore, we have found that interplanetary shocks or solar wind pressure pulses, with even small dynamic pressure changes, can play a non-negligible role in radiation belt dynamics. Interplanetary shocks interaction with the Earth’s magnetosphere manifests many fundamental space physics phenomena including energetic particle acceleration. The mechanism of fast acceleration of energetic electrons in the radiation belt responding to interplanetary shock impacts consists of three contributing parts: (1) the initial adiabatic acceleration due to strong shock-related magnetic field compression; (2) followed by the drift-resonant acceleration with poloidal ULF waves excited at different L-shells; and (3) particle acceleration due to the quickly damping electric fields associated with ULF waves. Particles end up with a net acceleration because they gain more energy in the first half of this cycle than they lose in the second. The results reported in this paper cast a new light on understanding the acceleration of energetic particles in the Earth’s Van Allen radiation belt. The results of this study can likewise be applied to interplanetary shock interaction with other planets such as Mercury, Jupiter, Saturn, Uranus and Neptune, and other astrophysical objects with magnetic fields.

HOW TO IDENTIFY AND SEPARATE BRIGHT GALAXY CLUSTERS FROM THE LOW-FREQUENCY RADIO SKY

In this work we simulate the $50-200$ MHz radio sky that is constrained in the field of view ($5^{\circ}$ radius) of the 21 Centimeter Array (21CMA), by carrying out Monte-Carlo simulations to model redshifted cosmological reionization signals and strong contaminating foregrounds, including emissions from our Galaxy, galaxy clusters, and extragalactic point sources. As an improvement of previous works, we consider in detail not only random variations of morphological and spectroscopic parameters within the ranges allowed by multi-band observations, but also evolution of radio halos in galaxy clusters, assuming that relativistic electrons are re-accelerated in the ICM in merger events and lose energy via both synchrotron emission and inverse Compton scattering with CMB photons. By introducing a new approach designed on the basis of independent component analysis (ICA) and wavelet detection algorithm, we prove that, with a cumulative observation of one month with the 21CMA array, about $80\%$ of galaxy clusters with central brightness temperatures of $> 10~{\rm K}$ at 65 MHz can be safely identified and separated from the overwhelmingly bright foreground. We find that the morphological and spectroscopic distortions are extremely small as compared to the input simulated clusters, and the reduced $\chi^2$ of brightness temperature profiles and spectra are controlled to be $\lesssim 0.5$ and $\lesssim 1.3$, respectively. These results robustly indicate that in the near future a sample of dozens of bright galaxy clusters will be disentangled from the foreground in 21CMA observations, the study of which will greatly improve our knowledge about cluster merger rates, electron acceleration mechanisms in cluster radio halos, and magnetic field in the ICM.

“Island surfing” mechanism of electron acceleration during magnetic reconnection

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 an explosive 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 from two‐dimensional particle‐in‐cell simulations that secondary islands generated in the reconnection region indeed produce energetic electrons. We found that when electrons are trapped inside the islands, they are energized continuously by the reconnection electric field prevalent in the reconnection diffusion region. Applications to observations in the Earth's magnetotail are briefly discussed.