[Show abstract][Hide abstract] ABSTRACT: (abridged) Magnetic reconnection is the topological reconfiguration of the
magnetic field in a plasma, accompanied by the violent release of energy and
particle acceleration. Reconnection is as ubiquitous as plasmas themselves,
with solar flares perhaps the most popular example. Over the last few years,
the theoretical understanding of magnetic reconnection in large-scale fluid
systems has undergone a major paradigm shift. The steady-state model of
reconnection described by the famous Sweet-Parker (SP) theory, which dominated
the field for ~50 years, has been replaced with an essentially time-dependent,
bursty picture of the reconnection layer, dominated by the continuous formation
and ejection of multiple secondary islands (plasmoids). Whereas in the SP model
reconnection was predicted to be slow, a major implication of this new paradigm
is that reconnection in fluid systems is fast (i.e., independent of the
Lundquist number), provided that the system is large enough. This conceptual
shift hinges on the realization that SP-like current layers are violently
unstable to the plasmoid instability - implying, therefore, that such current
sheets are super-critically unstable and thus can never form in the first
place. This suggests that the formation of a current sheet and the subsequent
reconnection process cannot be decoupled, as is commonly assumed. This paper
provides an introductory-level overview of the recent developments in
reconnection theory and simulations that led to this essentially new framework.
We briefly discuss the role played by the plasmoid instability in selected
applications, and describe some of the outstanding challenges that remain at
the frontier of this subject. Amongst these are the analytical and numerical
extension of the plasmoid instability to (i) 3D and (ii) non-MHD regimes. New
results are reported in both cases.
[Show abstract][Hide abstract] ABSTRACT: We investigate the distribution of particle acceleration sites during
plasmoid-dominated, relativistic collisionless magnetic reconnection by
analyzing the results of a particle-in-cell numerical simulation. The
simulation is initiated with Harris-type current layers in pair plasma with no
guide magnetic field, negligible radiative losses, no initial perturbation, and
using periodic boundary conditions. We find that the plasmoids develop a robust
internal structure, with colder dense cores and hotter outer shells, that is
recovered after each plasmoid merger on a dynamical time scale. We use
spacetime diagrams of the reconnection layers to probe the evolution of
plasmoids, and in this context we investigate the individual particle histories
for a representative sample of energetic electrons. We distinguish three
classes of particle acceleration sites associated with (1) magnetic X-points,
(2) regions between merging plasmoids, and (3) the trailing edges of
accelerating plasmoids. We evaluate the contribution of each class of
acceleration sites to the final energy distribution of energetic electrons --
magnetic X-points dominate at moderate energies, and the regions between
merging plasmoids dominate at higher energies. We also identify the dominant
acceleration scenarios, in order of decreasing importance -- (1) single
acceleration between merging plasmoids, (2) single acceleration at a magnetic
X-point, and (3) acceleration at a magnetic X-point followed by acceleration in
a plasmoid. Particle acceleration is absent only in the vicinity of stationary
plasmoids, and it can hardly be associated with magnetic mirrors due to the
absence of plasmoid contraction after the initial stage of the simulation.
[Show abstract][Hide abstract] ABSTRACT: Energy dissipation is highly intermittent in turbulent plasmas, being
localized in coherent structures such as current sheets. The statistical
analysis of spatial dissipative structures is an effective approach to studying
turbulence. In this paper, we generalize this methodology to investigate
four-dimensional spatiotemporal structures, i.e., dissipative processes
representing sets of interacting coherent structures, which correspond to
flares in astrophysical systems. We develop methods for identifying and
characterizing these processes, and then perform a statistical analysis of
dissipative processes in numerical simulations of driven magnetohydrodynamic
turbulence. We find that processes are often highly complex, long-lived, and
weakly asymmetric in time. They exhibit robust power-law probability
distributions and scaling relations, including a distribution of dissipated
energy with power-law index near -1.75, indicating that intense dissipative
events dominate the overall energy dissipation. We compare our results with the
previously observed statistical properties of solar flares.
The Astrophysical Journal 06/2015; 811(1). DOI:10.1088/0004-637X/811/1/6 · 5.99 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We carry out a systematic study of the dispersion relation for linear
electrostatic waves in an arbitrarily degenerate quantum electron plasma. We
solve for the complex frequency spectrum for arbitrary values of wavenumber $k$
and level of degeneracy $\mu$. Our finding is that for large $k$ and high $\mu$
the real part of the frequency $\omega_{r}$ grows linearly with $k$ and scales
with $\mu$ only because of the scaling of the Fermi energy. In this regime the
relative Landau damping rate $\gamma/\omega_{r}$ becomes independent of $k$ and
varies inversly with $\mu$. Thus, damping is weak but finite at moderate levels
of degeneracy for short wavelengths.
[Show abstract][Hide abstract] ABSTRACT: We live in an age in which high-performance computing is transforming the way
we do science. Previously intractable problems are now becoming accessible by
means of increasingly realistic numerical simulations. One of the most enduring
and most challenging of these problems is turbulence. Yet, despite these
advances, the extreme parameter regimes encountered in astrophysics and space
physics (as in atmospheric and oceanic physics) still preclude direct numerical
simulation. Numerical models must take a Large Eddy Simulation (LES) approach,
explicitly computing only a fraction of the active dynamical scales. The
success of such an approach hinges on how well the model can represent the
subgrid-scales (SGS) that are not explicitly resolved. In addition to the
parameter regime, astrophysical and heliophysical applications must also face
an equally daunting challenge: magnetism. The presence of magnetic fields in a
turbulent, electrically conducting fluid flow can dramatically alter the
coupling between large and small scales, with potentially profound implications
for LES/SGS modeling. In this review article, we summarize the state of the art
in LES modeling of turbulent magnetohydrodynamic (MHD) flows. After discussing
the nature of MHD turbulence and the small-scale processes that give rise to
energy dissipation, plasma heating, and magnetic reconnection, we consider how
these processes may best be captured within an LES/SGS framework. We then
consider several specific applications in astrophysics and heliophysics,
assessing triumphs, challenges, and future directions.
Space Science Reviews 05/2015; DOI:10.1007/s11214-015-0190-7 · 6.28 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Energy dissipation in magnetohydrodynamic (MHD) turbulence is known to be
highly intermittent in space, being concentrated in sheet-like coherent
structures. Much less is known about intermittency in time, another fundamental
aspect of turbulence which has great importance for observations of solar
flares and other space/astrophysical phenomena. In this Letter, we investigate
the temporal intermittency of energy dissipation in numerical simulations of
MHD turbulence. We consider four-dimensional spatiotemporal structures, "flare
events", responsible for a large fraction of the energy dissipation. We find
that although the flare events are often highly complex, they exhibit robust
power-law distributions and scaling relations. We find that the probability
distribution of dissipated energy has a power law index close to -1.75, similar
to observations of solar flares, indicating that intense dissipative events
dominate the heating of the system. We also discuss the temporal asymmetry of
flare events as a signature of the turbulent cascade.
[Show abstract][Hide abstract] ABSTRACT: The recent realization that Sweet-Parker current sheets are violently
unstable to the secondary tearing (plasmoid) instability implies that such
current sheets cannot occur in real systems. This suggests that, in order to
understand the onset of magnetic reconnection, one needs to consider the growth
of the tearing instability in a current layer as it is being formed. Such an
analysis is performed here in the context of nonlinear resistive MHD for a
generic time-dependent equilibrium representing a gradually forming current
sheet. It is shown that two regimes, single-island and multi-island, are
possible, depending on the rate of current sheet formation. A simple model is
used to compute the criterion for transition between these two regimes, as well
as the reconnection onset time and the current sheet parameters at that moment.
For typical solar corona parameters this model yields results consistent with
observations.
[Show abstract][Hide abstract] ABSTRACT: Using two-dimensional particle-in-cell simulations, we characterize the
energy spectra of particles accelerated by relativistic magnetic reconnection
(without guide field) in collisionless electron-positron plasmas, for a wide
range of upstream magnetizations $\sigma$ and system sizes $L$. The particle
spectra are well-represented by a power law $\gamma^{-\alpha}$, with a
combination of exponential and super-exponential high-energy cutoffs,
proportional to $\sigma$ and $L$, respectively. For large $L$ and $\sigma$, the
power-law index $\alpha$ approaches about 1.2.
[Show abstract][Hide abstract] ABSTRACT: Certain classes of astrophysical objects, namely magnetars and central
engines of supernovae and gamma-ray bursts (GRBs), are characterized by extreme
physical conditions not encountered elsewhere in the Universe. In particular,
they possess magnetic fields that exceed the critical quantum field of 44
teragauss. Figuring out how these complex ultra-magnetized systems work
requires understanding various plasma processes, both small-scale kinetic and
large-scale magnetohydrodynamic (MHD). However, an ultra-strong magnetic field
modifies the underlying physics to such an extent that many relevant
plasma-physical problems call for building QED-based relativistic quantum
plasma physics. In this review, after describing the extreme astrophysical
systems of interest and identifying the key relevant plasma-physical problems,
we survey the recent progress in the development of such a theory. We discuss
how a super-critical field modifies the properties of vacuum and matter and
outline the basic theoretical framework for describing both non-relativistic
and relativistic quantum plasmas. We then turn to astrophysical applications of
relativistic QED plasma physics relevant to magnetar magnetospheres and central
engines of supernovae and long GRBs. Specifically, we discuss propagation of
light through a magnetar magnetosphere; large-scale MHD processes driving
magnetar activity and GRB jet launching and propagation; energy-transport
processes governing the thermodynamics of extreme plasma environments;
micro-scale kinetic plasma processes important in the interaction of intense
magnetospheric electric currents with a magnetar's surface; and magnetic
reconnection of ultra-strong magnetic fields. Finally, we point out that future
progress will require the development of numerical modeling capabilities.
Reports on Progress in Physics 03/2014; 77(3):036902. DOI:10.1088/0034-4885/77/3/036902 · 17.06 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The Crab Nebula was formed after the collapse of a massive star about a
thousand years ago, leaving behind a pulsar that inflates a bubble of
ultra-relativistic electron-positron pairs permeated with magnetic field. The
observation of brief but bright flares of energetic gamma rays suggests that
pairs are accelerated to PeV energies within a few days; such rapid
acceleration cannot be driven by shocks. Here, it is argued that the flares may
be the smoking gun of magnetic dissipation in the Nebula. Using 2D and 3D
particle-in-cell simulations, it is shown that the observations are consistent
with relativistic magnetic reconnection, where pairs are subject to strong
radiative cooling. The Crab flares may highlight the importance of relativistic
magnetic reconnection in astrophysical sources.
Physics of Plasmas 01/2014; 21(5). DOI:10.1063/1.4872024 · 2.14 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The discovery of rapid synchrotron gamma-ray flares above 100 MeV from the
Crab Nebula has attracted new interest in alternative particle acceleration
mechanisms in pulsar wind nebulae. Diffuse shock-acceleration fails to explain
the flares because particle acceleration and emission occur during a single or
even sub-Larmor timescale. In this regime, the synchrotron energy losses induce
a drag force on the particle motion that balances the electric acceleration and
prevents the emission of synchrotron radiation above 160 MeV. Previous
analytical studies and 2D particle-in-cell (PIC) simulations indicate that
relativistic reconnection is a viable mechanism to circumvent the above
difficulties. The reconnection electric field localized at X-points linearly
accelerates particles with little radiative energy losses. In this paper, we
check whether this mechanism survives in 3D, using a set of large PIC
simulations with radiation reaction force and with a guide field. In agreement
with earlier works, we find that the relativistic drift kink instability
deforms and then disrupts the layer, resulting in significant plasma heating
but few non-thermal particles. A moderate guide field stabilizes the layer and
enables particle acceleration. We report that 3D magnetic reconnection can
accelerate particles above the standard radiation reaction limit, although the
effect is less pronounced than in 2D with no guide field. We confirm that the
highest energy particles form compact bunches within magnetic flux ropes, and a
beam tightly confined within the reconnection layer, which could result in the
observed Crab flares when, by chance, the beam crosses our line of sight.
The Astrophysical Journal 11/2013; 782(2). DOI:10.1088/0004-637X/782/2/104 · 5.99 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In this paper, we consider two outstanding intertwined problems in modern high-energy astrophysics: (1) the vertical-thermal structure of an optically thick accretion disk heated by the dissipation of magnetohydrodynamic turbulence driven by the magnetorotational instability (MRI), and (2) determining the fraction of the accretion power released in the corona above the disk. For simplicity, we consider a gas-pressure-dominated disk and assume a constant opacity. We argue that the local turbulent dissipation rate due to the disruption of the MRI channel flows by secondary parasitic instabilities should be uniform across most of the disk, almost up to the disk photosphere. We then obtain a self-consistent analytical solution for the vertical thermal structure of the disk, governed by the balance between the heating by MRI turbulence and the cooling by radiative diffusion. Next, we argue that the coronal power fraction is determined by the competition between the Parker instability, viewed as a parasitic instability feeding off of MRI channel flows, and other parasitic instabilities. We show that the Parker instability inevitably becomes important near the disk surface, leading to a certain lower limit on the coronal power. While most of the analysis in this paper focuses on the case of a disk threaded by an externally imposed vertical magnetic field, we also discuss the zero net flux case, in which the magnetic field is produced by the MRI dynamo itself, and show that most of our arguments and conclusions should be valid in this case as well.
The Astrophysical Journal 09/2013; 775(2):103. DOI:10.1088/0004-637X/775/2/103 · 5.99 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A second-order accurate semi-implicit Lorentz force ions, fluid electrons δfδf hybrid model has been developed using a “current closure” scheme. The model assumes quasi-neutrality and is fully electromagnetic. The implicit field solver improves numerical accuracy by separating the equilibrium terms in the presence of small perturbations. The equilibrium part of the generalized Ohm’s law is solved by direct matrix inversion along the direction of gradients for every Fourier mode in the other two directions, while the nonlinear part is solved iteratively. The simulation has been benchmarked on Alfvén waves, ion sound waves and whistler waves against analytical dispersion relation in a slab. In particular, the first-order and second-order schemes are compared by studying the numerical damping of whistler waves. The full evolution of the resistive tearing mode using the Harris sheet equilibrium is also investigated. The linear growth rate and mode structure are compared with the resistive MHD theory. Important tearing mode nonlinear phenomena such as the Rutherford regime and saturation are demonstrated. We also presented systematic study of Rutherford growth rates and saturation island width, which is consistent with previous MHD studies.
[Show abstract][Hide abstract] ABSTRACT: Magnetic reconnection converts magnetic field energy into particle
kinetic energy, accelerating particles to sufficient energies to emit
gamma-ray synchrotron radiation in astrophysical contexts, possibly
including pulsar wind nebulae, Gamma-Ray Bursts, and blazar jets. A
balance between acceleration (by the electric field E) and synchrotron
braking (while orbiting a B-field line) limits particle energy so that
synchrotron processes cannot emit photons above about 160 MeV, unless E
> B. However, short, intense gamma-ray flares of much higher energies
have recently been observed in the Crab nebula. This work demonstrates,
using 2D simulations, that reconnection in relativistic
electron-positron pair plasmas can accelerate particles in Speiser
orbits around the magnetic null (where E > B) such that the particles
can emit synchrotron photons above the 160 MeV limit. Furthermore,
reconnection bunches particles and focuses them into beams; high-energy
synchrotron radiation is also strongly beamed, and the sweeping of the
beam across the observer's line of sight can explain the fast time
variability of the flares.
[Show abstract][Hide abstract] ABSTRACT: It is generally accepted that astrophysical sources cannot emit synchrotron
radiation above 160 MeV in their rest frame. This limit is given by the balance
between the accelerating electric force and the radiation reaction force acting
on the electrons. The discovery of synchrotron gamma-ray flares in the Crab
Nebula, well above this limit, challenges this classical picture of particle
acceleration. To overcome this limit, particles must accelerate in a region of
high electric field and low magnetic field. This is possible only with a
non-ideal magnetohydrodynamic process, like magnetic reconnection. We present
the first numerical evidence of particle acceleration beyond the synchrotron
burnoff limit, using a set of 2D particle-in-cell simulations of
ultra-relativistic pair plasma reconnection. We use a new code, Zeltron, that
includes self-consistently the radiation reaction force in the equation of
motion of the particles. We demonstrate that the most energetic particles move
back and forth across the reconnection layer, following relativistic Speiser
orbits. These particles then radiate >160 MeV synchrotron radiation rapidly,
within a fraction of a full gyration, after they exit the layer. Our analysis
shows that the high-energy synchrotron flux is highly variable in time because
of the strong anisotropy and inhomogeneity of the energetic particles. We
discover a robust positive correlation between the flux and the cut-off energy
of the emitted radiation, mimicking the effect of relativistic Doppler
amplification. A strong guide field quenches the emission of >160 MeV
synchrotron radiation. Our results are consistent with the observed properties
of the Crab flares, supporting the reconnection scenario.
The Astrophysical Journal 02/2013; 770(2). DOI:10.1088/0004-637X/770/2/147 · 5.99 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We develop a framework for studying the statistical properties of current
sheets in numerical simulations of 3D magnetohydrodynamic (MHD) turbulence. We
describe an algorithm that identifies current sheets in a simulation snapshot
and then determines their geometrical properties (including length, width, and
thickness) and intensities (peak current density and total energy dissipation
rate). We then apply this procedure to simulations of reduced MHD turbulence
and perform a statistical analysis on the obtained population of current
sheets. We evaluate the role of reconnection by separately studying the
populations of current sheets which contain magnetic X-points and those which
do not. We find that the statistical properties of the two populations are
different in general. We compare the scaling of these properties to
phenomenological predictions obtained for the inertial range of MHD turbulence.
Finally, we test whether the reconnecting current sheets are consistent with
the Sweet-Parker model.
The Astrophysical Journal 02/2013; 771(2). DOI:10.1088/0004-637X/771/2/124 · 5.99 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A two-dimensional (2D) linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of reduced magnetohydrodynamics. A local analysis is performed taking into account the dependence of a generic equilibrium profile on the outflow coordinate. The plasmoid instability [Loureiro et al., Phys. Plasmas 14, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids (k_{max}L_{CS}∼S^{3/8}, where k_{max} is the wave number of fastest growing mode, S=L_{CS}V_{A}/η is the Lundquist number, L_{CS} is the length of the sheet, V_{A} is the Alfvén speed, and η is the plasma resistivity), which grows super Alfvénically fast (γ_{max}τ_{A}∼S^{1/4}, where γ_{max} is the maximum growth rate, and τ_{A}=L_{CS}/V_{A}). For typical background profiles, the growth rate and the wave number are found to increase in the outflow direction. This is due to the presence of another mode, the Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the layer, where the outflow velocity exceeds the Alfvén speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability γ_{max}τ_{A}∼k_{max}L_{CS}∼S^{1/2}. The effect of viscosity (ν) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers Pm=ν/η, it is found that γ_{max}∼S^{1/4}Pm^{-5/8} and k_{max}L_{CS}∼S^{3/8}Pm^{-3/16}, leading to the prediction that the critical Lundquist number for plasmoid instability in the Pm≫1 regime is S_{crit}∼10^{4}Pm^{1/2}. These results are verified via direct numerical simulation of the linearized equations, using an analytical 2D SP equilibrium solution.
Physical Review E 01/2013; 87(1-1):013102. DOI:10.1103/PhysRevE.87.013102 · 2.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We report on the first study of energetic particles and radiation
angular distributions generated in relativistic collisionless pair
plasma reconnection, using 2.5-dimensional particle-incell simulations.
We have discovered that the energetic particles are focused within a
small solid angle, and bunched into compact regions inside magnetic
islands. In addition, we find that the synchrotron radiation emitted by
these particles, as seen by an external observer, is tightly beamed and
variable on time scales much shorter than the light-crossing time of the
system. This energy dependent "kinetic beaming" differs fundamentally
from the achromatic Doppler beaming usually ascribed to relativistic
jets. Our findings can account for the puzzling discoveries of bright,
short flares seen in high-energy gamma rays, especially from the Crab
Nebula and from blazars.
[Show abstract][Hide abstract] ABSTRACT: The magnetosphere of a rotating pulsar naturally develops a current sheet
beyond the light cylinder (LC). Magnetic reconnection in this current sheet
inevitably dissipates a nontrivial fraction of the pulsar spin-down power
within a few LC radii. We develop a basic physical picture of reconnection in
this environment and discuss its implications for the observed pulsed gamma-ray
emission. We argue that reconnection proceeds in the plasmoid-dominated regime,
via an hierarchical chain of multiple secondary islands/flux ropes. The
inter-plasmoid reconnection layers are subject to strong synchrotron cooling,
leading to significant plasma compression. Using the conditions of pressure
balance across these current layers, the balance between the heating by
magnetic energy dissipation and synchrotron cooling, and Ampere's law, we
obtain simple estimates for key parameters of the layers --- temperature,
density, and layer thickness. In the comoving frame of the relativistic pulsar
wind just outside of the equatorial current sheet, these basic parameters are
uniquely determined by the strength of the reconnecting upstream magnetic
field. For the case of the Crab pulsar, we find them to be of order 10 GeV,
$10^{13} cm^{-3}$, and 10 cm, respectively. After accounting for the bulk
Doppler boosting due to the pulsar wind, the synchrotron and inverse-Compton
emission from the reconnecting current sheet can explain the observed pulsed
high-energy (GeV) and VHE (~100 GeV) radiation, respectively. Also, we suggest
that the rapid relative motions of the secondary plasmoids in the hierarchical
chain may contribute to the production of the pulsar radio emission.
The Astrophysical Journal 10/2012; 780(1). DOI:10.1088/0004-637X/780/1/3 · 5.99 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Magnetic reconnection is one of a few astrophysical mechanisms that can
accelerate particles to energies sufficient to emit observable
high-energy radiation. This work reports on 2D simulations of
reconnection in relativistic electron-positron pair plasmas, which may
power gamma-ray emission from pulsar wind nebulae (PWNe), Gamma-Ray
Bursts (GRBs), and blazar jets. The most important new discovery is the
strong, energy-dependent angular anisotropy and spatial inhomogeneity of
accelerated particles: high-energy particles are bunched in space and
focused into beams mostly confined to the reconnection layer midplane.
Another important advance is the calculation of the associated radiative
signatures (spectra and light curves) seen by a distant observer. The
synchrotron and inverse Compton radiation from the high-energy particles
is likewise focused in narrow beams. The beams sweep back and forth
within the midplane, so that an observer sees intense bursts (only) when
a beam crosses the line of sight. The resulting rapid variability, on
timescales much shorter than the light-crossing time of the reconnection
region, could explain the short, intense gamma-ray flares observed in
blazar jets and PWNe, including the GeV flares recently discovered in
the Crab nebula.