52 research outputs found
A Numerical Simulation of the Reconnection Layer in 2D Resistive MHD
In this paper we present a two-dimensional, time dependent, 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 back pressure from flow into the the separatrix region. We find that within
a few Alfven times the system evolves from an arbitrary initial state to a
steady state consistent with the Sweet--Parker model, even if the initial state
is Petschek-like.Comment: 33 pages, 17 figure
Hydrodynamic Stability and Magnetic Reconnection in Disks and Stars
The purpose of this grant is to study parametric instability. The simplest example of parametric instability is a harmonic oscillator with a periodic modulation of the spring constant. If the modulation frequency is close to twice the natural frequency of the oscillator, the amplitude of oscillation tends to grow exponentially. The growth rate is proportional to the strength of the modulation, but it also depends upon the closeness to resonance of the two frequencies, and upon natural damping rate or "Q" of the oscillator. Parametric instabilities are very common in physics. A familiar example is a jogger's ponytail--normally a very strongly damped pendulum, it can be destabilized by the variation in effective gravity during the jogger's stride. Observation confirms that the period of the pendulum is half that of the jogger's vertical motion. In astrophysics, parametric instability may occur by external tidal forcing, or by interaction among eigenmodes. In the latter case, an energetic eigenmode may destabilize modes of half its frequency, provided some weak nonlinearity exists to couple them. Under a previous Astrophysical Theory grant (NAGW-2419), the PI discovered a parametric instability of tidally forced disks such as the accretion disks in cataclysmic variables and X ray binaries [2]. The destabilized modes are tightly-wound, incompressible, three-dimensional waves analogous to g-modes and r-modes in stars. Later work has confirmed our analysis [4]. It was hoped that these modes might provide a source of turbulence and angular momentum transport in accretion disks. However, a follow-up investigation of this instability by local numerical simulations, although confirming the analytically estimated growth rates, found negligible angular momentum flux [3]. Other work, partly supported by the ATP, now strongly indicates that the transport mechanism in such disks is magnetohydrodynamic turbulence [6]. Nevertheless, the parametric mechanism may truncate the outer edges of disks in close binaries [2], and it may be important in disks of very low ionization such as protostellar disks, or even cataclysmic-variable disks in quiescence where the MHD mechanism may be ineffective [5]. All analyses up to 1996 were done in a local approximation where the orbital frequency, shear rate, and tidal field were treated as constants. The locally computed growth rate turns out to depend strongly on radius, and it was unclear how to average these local rates to obtain the correct global rate. This is a critical issue for accretion disks in close binaries, because the local growth rate is comparable to the orbital frequency towards the outer edge of the disk but decreases rapidly inwards. Paper #1 examined this issue in a simplified global model where the destabilizing terms vary with position. We found that the global growth rate is essentially equal to the maximum local rate, provided that the latter is smoothed over a radial range equal to the distance that the destabilized wave propagates at its group speed in one growth time. Thus, in an accretion disk, waves would grow rapidly in the outer parts but would propagate both inwards and outwards at a maximum group speed of order the disk thickness divided by the orbital period
Magnetic reconnection with anomalous resistivity in two-and-a-half dimensions I: Quasi-stationary case
In this paper quasi-stationary, two-and-a-half-dimensional magnetic
reconnection is studied in the framework of incompressible resistive
magnetohydrodynamics (MHD). A new theoretical approach for calculation of the
reconnection rate is presented. This approach is based on local analytical
derivations in a thin reconnection layer, and it is applicable to the case when
resistivity is anomalous and is an arbitrary function of the electric current
and the spatial coordinates. It is found that a quasi-stationary reconnection
rate is fully determined by a particular functional form of the anomalous
resistivity and by the local configuration of the magnetic field just outside
the reconnection layer. It is also found that in the special case of constant
resistivity reconnection is Sweet-Parker and not Petschek.Comment: 15 pages, 4 figures, minor changes as compared to the 1st versio
Spectra and Growth Rates of Fluctuating Magnetic Fields in the Kinematic Dynamo Theory with Large Magnetic Prandtl Numbers
The existence of a weak galactic magnetic field has been repeatedly confirmed
by observational data. The origin of this field has not as yet been explained
in a fully satisfactory way and represents one of the main challenges of the
astrophysical dynamo theory. In both the galactic dynamo theory and the
primordial-origin theory, a major influence is exerted by the small-scale
magnetic fluctuations. This article is devoted to constructing a systematic
second-order statistical theory of such small-scale fields. The statistics of
these fields are studied in the kinematic approximation and for the case of
large Prandtl numbers, which is relevant for the galactic and protogalactic
plasma. The advecting velocity field is assumed to be Gaussian and short-time
correlated. Theoretical understanding of this kinematic dynamo model is a
necessary prerequisite for any prospective nonlinear dynamo theory. The theory
is developed for an arbitrary degree of compressibility and formally in d
dimensions, which generalizes the previously known results, elicits the
structure of the solutions, and uncovers a number of new effects. The magnetic
energy spectra are studied as they grow and spread over scales during the
initial stage of the field amplification. Exact Green's-function solutions are
obtained. The spectral theory is supplemented by the study of magnetic-field
correlation functions in the configuration space, where the dynamo problem can
be mapped onto a particular one-dimensional quantum-mechanical problem. The
latter approach is most suitable for the description of the kinematic dynamo in
the long-time limit, i.e. when the magnetic excitation has spread over all
scales present in the system. A simple way of calculating the growth rates of
the magnetic fields in this long-time limit is proposed.Comment: aastex, 52 pages, 10 figures; final version of the paper as published
in Ap
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Cold Fusion Catalyzed by Muons and Electrons
Two alternative methods have been suggested to produce fusion power at low temperature. The first, muon catalyzed fusion or MCF, uses muons to spontaneously catalyze fusion through the muon mesomolecule formation. Unfortunately, this method fails to generate enough fusion energy to supply the muons, by a factor of about ten. The physics of MCF is discussed, and a possible approach to increasing the number of MCF fusions generated by each muon is mentioned. The second method, which has become known as Cold Fusion,'' involves catalysis by electrons in electrolytic cells. The physics of this process, if it exists, is more mysterious than MCF. However, it now appears to be an artifact, the claims for its reality resting largely on experimental errors occurring in rather delicate experiments. However, a very low level of such fusion claimed by Jones may be real. Experiments in cold fusion will also be discussed
On the two-dimensional magnetic reconnection with nonuniform resistivity
In this paper two theoretical approaches for the calculation of the rate of
quasi-stationary, two-dimensional magnetic reconnection with nonuniform
anomalous resistivity are considered in the framework of incompressible
magnetohydrodynamics (MHD). In the first, ``global'' equations approach the MHD
equations are approximately solved for a whole reconnection layer, including
the upstream and downstream regions and the layer center. In the second,
``local'' equations approach the equations are solved across the reconnection
layer, including only the upstream region and the layer center. Both approaches
give the same approximate answer for the reconnection rate. Our theoretical
model is in agreement with the results of recent simulations of reconnection
with spatially nonuniform resistivity by Baty, Priest and Forbes (2006),
contrary to their conclusions.Comment: 7 pages, 1 figur
Magnetic reconnection with Sweet-Parker characteristics in two-dimensional laboratory plasmas
Magnetic reconnection has been experimentally studied in a well-controlled, two-dimensional laboratory magnetohydrodynamic plasma. The observations are found to be both qualitatively and quantitatively consistent with a generalized Sweet-Parker model which incorporates compressibility, downstream pressure, and the effective resistivity. The latter is significantly enhanced over its classical values in the collisionless limit. This generalized Sweet-Parker model also applies to the case in which an unidirectional, sizable third magnetic component is present
Transport phenomena in stochastic magnetic mirrors
Parallel thermal conduction along stochastic magnetic field lines may be
reduced because the heat conducting electrons become trapped and detrapped
between regions of strong magnetic field (magnetic mirrors). The problem
reduces to a simple but realistic model for diffusion of mono-energetic
electrons based on the fact that when there is a reduction of diffusion, it is
controlled by a subset of the mirrors, the principle mirrors. The diffusion
reduction can be considered as equivalent to an enhancement of the pitch angle
scattering rate. Therefore, in deriving the collision integral, we modify the
pitch angle scattering term. We take into account the full perturbed
electron-electron collision integral, as well as the electron-proton collision
term. Finally, we obtain the four plasma transport coefficients and the
effective thermal conductivity. We express them as reductions from the
classical values. We present these reductions as functions of the ratio of the
magnetic field decorrelation length to the electron mean free path at the
thermal speed . We briefly discuss an application of our
results to clusters of galaxies.
Key words: magnetic fields: conduction --- magnetic fields: diffusion ---
methods: analytical --- plasmasComment: 25 pages, 7 figures, 3 appendice
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