141 research outputs found
Fast magnetic reconnection in the plasmoid-dominated regime
A conceptual model of resistive magnetic reconnection via a stochastic
plasmoid chain is proposed. The global reconnection rate is shown to be
independent of the Lundquist number. The distribution of fluxes in the
plasmoids is shown to be an inverse square law. It is argued that there is a
finite probability of emergence of abnormally large plasmoids, which can
disrupt the chain (and may be responsible for observable large abrupt events in
solar flares and sawtooth crashes). A criterion for the transition from
magnetohydrodynamic to collisionless regime is provided.Comment: 4 pages, 1 figur
Effects of Line-tying on Magnetohydrodynamic Instabilities and Current Sheet Formation
An overview of some recent progress on magnetohydrodynamic stability and
current sheet formation in a line-tied system is given. Key results on the
linear stability of the ideal internal kink mode and resistive tearing mode are
summarized. For nonlinear problems, a counterexample to the recent
demonstration of current sheet formation by Low \emph{et al}. [B. C. Low and
\AA. M. Janse, Astrophys. J. \textbf{696}, 821 (2009)] is presented, and the
governing equations for quasi-static evolution of a boundary driven, line-tied
magnetic field are derived. Some open questions and possible strategies to
resolve them are discussed.Comment: To appear in Phys. Plasma
Oscillatory disintegration of a trans-Alfvenic shock: A magnetohydrodynamic simulation
Nonlinear evolution of a trans-Alfvenic shock wave (TASW), at which the flow
velocity passes over the Alfven velocity, is computed in a magnetohydrodynamic
approximation. The analytical theory suggests that an infinitesimal
perturbation of a TASW results in its disintegration, i.e., finite variation of
the flow, or transformation into some other unsteady configuration. In the
present paper, this result is confirmed by numerical simulations. It is shown
that the disintegration time is close to its minimum value equal to the shock
thickness divided by a relative velocity of the emerging secondary structures.
The secondary TASW that appears after the disintegration is again unstable with
respect to disintegration. When the perturbation has a cyclic nature, the TASW
undergoes oscillatory disintegration, during which it repeatedly transforms
into another TASW. This process manifests itself as a train of shock and
rarefaction waves, which consecutively emerge at one edge of the train and
merge at the other edge.Comment: REVTEX, 8 pages, 13 PostScript figures, uses epsfig.st
Diffusive propagation of UHECR and the propagation theorem
We present a detailed analytical study of the propagation of ultra high
energy (UHE) particles in extragalactic magnetic fields. The crucial parameter
which affects the diffuse spectrum is the separation between sources. In the
case of a uniform distribution of sources with a separation between them much
smaller than all characteristic propagation lengths, the diffuse spectrum of
UHE particles has a {\em universal} form, independent of the mode of
propagation. This statement has a status of theorem. The proof is obtained
using the particle number conservation during propagation, and also using the
kinetic equation for the propagation of UHE particles. This theorem can be also
proved with the help of the diffusion equation. In particular, it is shown
numerically, how the diffuse fluxes converge to this universal spectrum, when
the separation between sources diminishes. We study also the analytic solution
of the diffusion equation in weak and strong magnetic fields with energy losses
taken into account. In the case of strong magnetic fields and for a separation
between sources large enough, the GZK cutoff can practically disappear, as it
has been found early in numerical simulations. In practice, however, the source
luminosities required are too large for this possibility.Comment: 16 pages, 13 eps figures, discussion of the absence of the GZK
cut-off in strong magnetic field added, a misprint in figure 6 corrected,
version accepted for publication in Ap
Small scale structures in three-dimensional magnetohydrodynamic turbulence
We investigate using direct numerical simulations with grids up to 1536^3
points, the rate at which small scales develop in a decaying three-dimensional
MHD flow both for deterministic and random initial conditions. Parallel current
and vorticity sheets form at the same spatial locations, and further
destabilize and fold or roll-up after an initial exponential phase. At high
Reynolds numbers, a self-similar evolution of the current and vorticity maxima
is found, in which they grow as a cubic power of time; the flow then reaches a
finite dissipation rate independent of Reynolds number.Comment: 4 pages, 3 figure
Indeterminacy and instability in Petschek reconnection
We explain two puzzling aspects of Petschek's model for fast reconnection. One is its failure to occur in plasma simulations with uniform resistivity. The other is its inability to provide anything more than an upper limit for the reconnection rate. We have found that previously published analytical solutions based on Petschek's model are structurally unstable if the electrical resistivity is uniform. The structural instability is associated with the presence of an essential singularity at the X-line that is unphysical. By requiring that such a singularity does not exist, we obtain a formula that predicts a specific rate of reconnection. For uniform resistivity, reconnection can only occur at the slow, Sweet-Parker rate. For nonuniform resistivity, reconnection can occur at a much faster rate provided that the resistivity profile is not too flat near the X-line. If this condition is satisfied, then the scale length of the nonuniformity determines the reconnection rate
ATIC, PAMELA, HESS, Fermi and nearby Dark Matter subhalos
We study the local flux of electrons and positrons from annihilating Dark
Matter (DM), and investigate how its spectrum depends on the choice of DM model
and inhomogeneities in the DM distribution. Below a cutoff energy, the flux is
expected to have a universal power-law form with an index n ~ -2. The cutoff
energy and the behavior of the flux near the cutoff is model dependent. The
dependence on the DM host halo profile may be significant at energies E < 100
GeV and leads to softening of the flux, n < -2. There may be additional
features at high energies due to the presence of local clumps of DM, especially
for models in which the Sommerfeld effect boosts subhalo luminosities. In
general, the flux from a nearby clump gives rise to a harder spectrum of
electrons and positrons, with an index n > -2. Using the Via Lactea II
simulation, we estimate the probability of such subhalo effects in a generic
Sommerfeld-enhanced model to be at least 4%, and possibly as high as 15% if
subhalos below the simulation's resolution limit are accounted for. We discuss
the consequences of these results for the interpretation of the ATIC, PAMELA,
HESS, and Fermi data, as well as for future experiments.Comment: v1: 15 pages, 7 figures; v2: 16 pages, 8 figures, title changed,
figures 3 and 5 corrected, Fermi-LAT and HESS data added; v3: minor changes,
figure 8 correcte
Pulsars versus Dark Matter Interpretation of ATIC/PAMELA
In this paper, we study the flux of electrons and positrons injected by
pulsars and by annihilating or decaying dark matter in the context of recent
ATIC, PAMELA, Fermi, and HESS data. We review the flux from a single pulsar and
derive the flux from a distribution of pulsars. We point out that the particle
acceleration in the pulsar magnetosphere is insufficient to explain the
observed excess of electrons and positrons with energy E ~ 1 TeV and one has to
take into account an additional acceleration of electrons at the termination
shock between the pulsar and its wind nebula. We show that at energies less
than a few hundred GeV, the flux from a continuous distribution of pulsars
provides a good approximation to the expected flux from pulsars in the
Australia Telescope National Facility (ATNF) catalog. At higher energies, we
demonstrate that the electron/positron flux measured at the Earth will be
dominated by a few young nearby pulsars, and therefore the spectrum would
contain bumplike features. We argue that the presence of such features at high
energies would strongly suggest a pulsar origin of the anomalous contribution
to electron and positron fluxes. The absence of features either points to a
dark matter origin or constrains pulsar models in such a way that the
fluctuations are suppressed. Also we derive that the features can be partially
smeared due to spatial variation of the energy losses during propagation.Comment: 23 pages, 15 figures, 1 table; v2: minor corrections, references
added; v3: 20 pages, 10 figures, 1 table, major changes in presentation, main
conclusions unchanged; v4: minor correction
On the viscous boundary layer near the center of the resistive reconnection region
This paper studies the behavior of the magnetic field near the center of the reconnection layer in the framework of two-dimensional incompressible resistive magnetohydrodynamics with uniform resistivity in a steady state. Priest and Cowley have presented an argument [1] showing that when the viscosity is zero, the magnetic separatrices do not cross at a finite angle but osculate at the X-point. In the present paper, it is shown that this conclusion is in fact not correct. First, some results of numerical simulations of the reconnection layer are presented. These results contradict the conclusions of Priest and Cowley. In order to explain this contradiction, an analytical theory for the neighborhood of the X-point is developed in the second part of the paper. It is found that, if the viscosity is exactly equal to zero, then one of the critical assumptions of the above mentioned argument, namely the assumption that the stream function can be Taylor-expanded near the X-point, breaks down. In the case of small but finite viscosity, a boundary layer analysis in the vicinity of the neutral point is carried out. Some of the higher derivatives of the stream function become very large near the X-point, leading to a non-zero angle between the separatrices. As viscosity goes to zero, the boundary layer shrinks and one can see the emergence of the non-analytic logarithmic terms in the expansion of the stream function in the outer region. The results of the boundary layer analysis are found to be in good agreement with the numerical simulations
Steady Hall Magnetohydrodynamics Near a X-type Magnetic Neutral Line
Hall magnetohydrodynamics (MHD) properties near a two-dimensional (2D) X-type
magnetic neutral line in the steady state are considered via heuristic and
rigorous developments. Upon considering the steady-state as the asymptotic
limit of the corresponding \textit{time-dependent} problem and using a rigorous
development, Hall effects are shown to be able to sustain the hyperbolicity of
the magnetic field (and hence a more open X-point configuration) near the
neutral line in the steady state. The heuristic development misses this subtle
connection of the steady state with the corresponding \textit{time-dependent}
problem and predicts only an elongated current-sheet configuration (as in
resistive MHD). However, the heuristic development turns out to be useful in
providing insight into the lack of dependence of the reconnection rate on the
mechanism breaking the frozen-in condition of the magnetic field lines. The
latter result can be understood in terms of the ability of the ions and
electrons to transport equal amounts of magnetic flux per unit time out of the
reconnection region.Comment: 1-10 page
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