179 research outputs found
Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets
A 2D linear theory of the instability of Sweet-Parker (SP) current sheets is
developed in the framework of Reduced MHD. 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 {\bf 14},
100703 (2007)] is recovered, i.e., current sheets are unstable to the formation
of a large-wave-number chain of plasmoids (k_{\rm max}\Lsheet \sim S^{3/8},
where is the wave-number of fastest growing mode, S=\Lsheet
V_A/\eta is the Lundquist number, \Lsheet is the length of the sheet,
is the Alfv\'en speed and is the plasma resistivity), which grows
super-Alfv\'enically fast (\gmax\tau_A\sim S^{1/4}, where \gmax is the
maximum growth rate, and \tau_A=\Lsheet/V_A). For typical background
profiles, the growth rate and the wave-number are found to {\it 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 Alfv\'en speed associated with
the upstream magnetic field. The KH instability grows even faster than the
plasmoid instability, \gmax \tau_A \sim k_{\rm max} \Lsheet\sim S^{1/2}. The
effect of viscosity () on the plasmoid instability is also addressed. In
the limit of large magnetic Prandtl numbers, , it is found that
\gmax\sim S^{1/4}Pm^{-5/8} and k_{\rm max} \Lsheet\sim S^{3/8}Pm^{-3/16},
leading to the prediction that the critical Lundquist number for plasmoid
instability in the regime is \Scrit\sim 10^4Pm^{1/2}. These results
are verified via direct numerical simulation of the linearized equations, using
a new, analytical 2D SP equilibrium solution.Comment: 21 pages, 9 figures, submitted to Phys. Rev.
Self-Regulation of Solar Coronal Heating Process via Collisionless Reconnection Condition
I propose a new paradigm for solar coronal heating viewed as a
self-regulating process keeping the plasma marginally collisionless. The
mechanism is based on the coupling between two effects. First, coronal density
controls the plasma collisionality and hence the transition between the slow
collisional Sweet-Parker and the fast collisionless reconnection regimes. In
turn, coronal energy release leads to chromospheric evaporation, increasing the
density and thus inhibiting subsequent reconnection of the newly-reconnected
loops. As a result, statistically, the density fluctuates around some critical
level, comparable to that observed in the corona. In the long run, coronal
heating can be represented by repeating cycles of fast reconnection events
(nano-flares), evaporation episodes, and long periods of slow magnetic stress
build-up and radiative cooling of the coronal plasma.Comment: 4 pages; Phys. Rev. Lett., in pres
Fast Collisionless Reconnection Condition and Self-Organization of Solar Coronal Heating
I propose that solar coronal heating is a self-regulating process that keeps
the coronal plasma roughly marginally collisionless. The self-regulating
mechanism is based on the interplay of two effects. First, plasma density
controls coronal energy release via the transition between the slow collisional
Sweet-Parker regime and the fast collisionless reconnection regime. This
transition takes place when the Sweet--Parker layer becomes thinner than the
characteristic collisionless reconnection scale. I present a simple criterion
for this transition in terms of the upstream plasma density (n_e), the
reconnecting (B_0) and guide (B_z) magnetic field components, and the global
length (L) of the reconnection layer: L < 6.10^9 cm [n_e/(10^{10}/cm^3)]^(-3)
(B_0/30G)^4 (B_0/B_z)^2. Next, coronal energy release by reconnection raises
the ambient plasma density via chromospheric evaporation and this, in turn,
temporarily inhibits subsequent reconnection involving the newly-reconnected
loops. Over time, however, radiative cooling gradually lowers the density again
below the critical value and fast reconnection again becomes possible. As a
result, the density is highly inhomogeneous and intermittent but,
statistically, does not deviate strongly from the critical value which is
comparable with the observed coronal density. Thus, in the long run, the
coronal heating process can be represented by repeating cycles that consist of
fast reconnection events (i.e., nanoflares), followed by rapid evaporation
episodes, followed by relatively long periods (1-hour) during which magnetic
stresses build up and simultaneously the plasma cools down and precipitates.Comment: 17 pages, no figures; accepted to the Astrophysical Journal; replaced
to match the accepted versio
Magnetic reconnection and stochastic plasmoid chains in high-Lundquist-number plasmas
A numerical study of magnetic reconnection in the large-Lundquist-number
(), plasmoid-dominated regime is carried out for up to . The
theoretical model of Uzdensky {\it et al.} [Phys. Rev. Lett. {\bf 105}, 235002
(2010)] is confirmed and partially amended. The normalized reconnection rate is
\normEeff\sim 0.02 independently of for . The plasmoid flux
() and half-width () distribution functions scale as and . The joint distribution of and
shows that plasmoids populate a triangular region ,
where is the reconnecting field. It is argued that this feature is due to
plasmoid coalescence. Macroscopic "monster" plasmoids with % of the
system size are shown to emerge in just a few Alfv\'en times, independently of
, suggesting that large disruptive events are an inevitable feature of
large- reconnection.Comment: 5 pages, 6 figures, submitted for publicatio
From Solar and Stellar Flares to Coronal Heating: Theory and Observations of How Magnetic Reconnection Regulates Coronal Conditions
There is currently no explanation of why the corona has the temperature and
density it has. We present a model which explains how the dynamics of magnetic
reconnection regulates the conditions in the corona. A bifurcation in magnetic
reconnection at a critical state enforces an upper bound on the coronal
temperature for a given density. We present observational evidence from 107
flares in 37 sun-like stars that stellar coronae are near this critical state.
The model may be important to self-organized criticality models of the solar
corona.Comment: 13 pages, 2 figures, accepted to Ap. J. Lett., February 200
2D Numerical Simulation of the Resistive Reconnection Layer
In this paper we present a two-dimensional numerical simulation of a reconnection current layer in incompressible resistive magnetohydrodynamics with uniform resistivity in the limit of very large Lundquist numbers. We use realistic boundary conditions derived consistently from the outside magnetic field, and we also take into account the effect of the backpressure from the flow into the separatrix region. We find that within a few Alfven times the system reaches a steady state consistent with the Sweet--Parker model, even if the initial state is Petschek-like
Statistical Description of a Magnetized Corona above a Turbulent Accretion Disk
We present a physics-based statistical theory of a force-free magnetic field
in the corona above a turbulent accretion disk. The field is represented by a
statistical ensemble of loops tied to the disk. Each loop evolves under several
physical processes: Keplerian shear, turbulent random walk of the disk
footpoints, and reconnection with other loops. To build a statistical
description, we introduce the distribution function of loops over their sizes
and construct a kinetic equation that governs its evolution. This loop kinetic
equation is formally analogous to Boltzmann's kinetic equation, with loop-loop
reconnection described by a binary collision integral. A dimensionless
parameter is introduced to scale the (unknown) overall rate of reconnection
relative to Keplerian shear. After solving for the loop distribution function
numerically, we calculate self-consistently the distribution of the mean
magnetic pressure and dissipation rate with height, and the equilibrium shapes
of loops of different sizes. We also compute the energy and torque associated
with a given loop, as well as the total magnetic energy and torque in the
corona. We explore the dependence of these quantities on the reconnection
parameter and find that they can be greatly enhanced if reconnection between
loops is suppressed.Comment: 22 pages, 15 figures. Submitted to the Astrophysical Journa
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