243 research outputs found
Stellar Oscillons
We study the weakly nonlinear evolution of acoustic instability of a plane-
parallel polytrope with thermal dissipation in the form of Newton's law of
cooling. The most unstable horizontal wavenumbers form a band around zero and
this permits the development of a nonlinear pattern theory leading to a complex
Ginzburg-Landau equation (CGLE). Numerical solutions for a subcritical, quintic
CGLE produce vertically oscillating, localized structures that resemble the
oscillons observed in recent experiments of vibrated granular material.Comment: 12 Latex pages using aasms4.sty, 2 postscript figures, submitted to
the proceedings of the Florida Workshop in Nonlinear Astrophysics and Physic
The Collisonal Tearing Mode Instability in a Quasi-stational Plasma
The behaviour of a small perturbation in the diffuse neutral sheet is analysed in a frame of MHD equations. It is shown that the normal magnetic component perpendicular to the current sheet does not contribute to the stability of the tearing instability in both the cases of high coductivity limit and low conductivity limit.The plasma flow expanding along the sheet can effectively stabilize the tearing instability.The nonlinear stage of this mode is estimated. It is shown that the secondary stationary flow with a hyperbolic pattern is structed.Tearing不安定は,天体プラズマ及び実験室プラズマでの応用と関連して,多くの研究がある。この不安定は,MHD的扱いのみならずCollisionlessプラズマでも起こる。又,この不安定は,太陽大気でのフレアー現象や,地球磁気圏での爆発的現象(substorm)と関連して,そして又,トカマクプラズマでのdisruptive不安定と関連しており,重要な不安定として研究されている。我々は,本稿で,MIlD領域でtearingmodeが安定化されないことを示す。論文の終わりで,tearing modeの非線形段階で現われる2次的な流れの効果についても述べる
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
Stability of an MHD shear flow with a piecewise linear velocity profile
In this paper we present the results of the stability analysis of a simple shear flow of an incompressible fluid with a piecewise linear velocity profile in the presence of a magnetic field. In the flow, a finite transitional magnetic-free layer with a linear velocity profile is sandwiched by two semi-infinite regions. One of these regions is magnetic-free and the flow velocity in the region is constant. The other region is magnetic and the fluid in it is quiescent. The magnetic field is constant and parallel to the flow in the transitional layer. The fluid density is constant both in the magnetic as well as the magnetic-free regions, while it has a jump-type discontinuity at the boundary between the transitional layer and the magnetic region. The effect of gravity is included in the model, and it is assumed that the lighter fluid is overlaying the heavier one, thus no Rayleigh-Taylor instability is present. The dispersion equation governing the normal-mode stability of the flow is derived and its properties are analysed. We study stability of two cases: (i) magnetic-free flow in the presence of gravity, and (ii) magnetic flow without gravity. In the first case, the flow stability is controlled by the Rayleigh number, R. In the second case, the control parameter is the inverse squared Alfvénic Mach number, H . Stability of a particular monochromatic perturbation also depends on its dimensionless wavenumber α. We combine the analytical and numerical approaches to obtain the neutral stability curves in the (α,R)-plane in the case of the magnetic-free flow, and in the (α,H)-plane in the case of the magnetic flow. The dependence of the instability increment on R in the first case, and on H in the second case is treated. We apply the results of the analysis to the stability of a strongly subsonic portion of the heliopause. Our main conclusion is as follows: The inclusion of a transitional layer near the heliopause into the model increases by an order of magnitude the strength of the interstellar magnetic field required to stabilize this portion of the heliopause in comparison with the corresponding stabilizing strength of the magnetic field required when modelling the heliopause as a tangential discontinuity
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
Dynamics of an Alfven surface in core collapse supernovae
We investigate the dynamics of an Alfven surface (where the Alfven speed
equals the advection velocity) in the context of core collapse supernovae
during the phase of accretion on the proto-neutron star. Such a surface should
exist even for weak magnetic fields because the advection velocity decreases to
zero at the center of the collapsing core. In this decelerated flow, Alfven
waves created by the standing accretion shock instability (SASI) or convection
accumulate and amplify while approaching the Alfven surface. We study this
amplification using one dimensional MHD simulations with explicit physical
dissipation. In the linear regime, the amplification continues until the Alfven
wavelength becomes as small as the dissipative scale. A pressure feedback that
increases the pressure in the upstream flow is created via a non linear
coupling. We derive analytic formulae for the maximum amplification and the non
linear coupling and check them with numerical simulations to a very good
accuracy. We also characterize the non linear saturation of this amplification
when compression effects become important, leading to either a change of the
velocity gradient, or a steepening of the Alfven wave. Applying these results
to core collapse supernovae shows that the amplification can be fast enough to
affect the dynamics, if the magnetic field is strong enough for the Alfven
surface to lie in the region of strong velocity gradient just above the
neutrinosphere. This requires the presence of a strong magnetic field in the
progenitor star, which would correspond to the formation of a magnetar under
the assumption of magnetic flux conservation. An extrapolation of our analytic
formula (taking into account the nonlinear saturation) suggests that the Alfven
wave could reach an amplitude of B ~ 10^15 G, and that the pressure feedback
could significantly contribute to the pressure below the shock.Comment: 18 pages, 14 figures, accepted for publication in ApJ. Added a
discussion of the energy budget in subsection 7.
Toward a magnetohydrodynamic theory of the stationary accretion shock: toy model of the advective-acoustic cycle in a magnetized flow
The effect of a magnetic field on the linear phase of the advective-acoustic
instability is investigated, as a first step toward a magnetohydrodynamic (MHD)
theory of the stationary accretion shock instability taking place during
stellar core collapse. We study a toy model where the flow behind a planar
stationary accretion shock is adiabatically decelerated by an external
potential. Two magnetic field geometries are considered: parallel or
perpendicular to the shock. The entropy-vorticity wave, which is simply
advected in the unmagnetized limit, separates into five different waves: the
entropy perturbations are advected, while the vorticity can propagate along the
field lines through two Alfven waves and two slow magnetosonic waves. The two
cycles existing in the unmagnetized limit, advective-acoustic and purely
acoustic, are replaced by up to six distinct MHD cycles. The phase differences
among the cycles play an important role in determining the total cycle
efficiency and hence the growth rate. Oscillations in the growth rate as a
function of the magnetic field strength are due to this varying phase shift. A
vertical magnetic field hardly affects the cycle efficiency in the regime of
super-Alfvenic accretion that is considered. In contrast, we find that a
horizontal magnetic field strongly increases the efficiencies of the vorticity
cycles that bend the field lines, resulting in a significant increase of the
growth rate if the different cycles are in phase. These magnetic effects are
significant for large-scale modes if the Alfven velocity is a sizable fraction
of the flow velocity.Comment: 13 pages, 9 figures, accepted for publication in ApJ. Cosmetic
changes after proof reading corrections
On the Mechanical Energy Available to Drive Solar Flares
Where does solar flare energy come from? More specifically, assuming that the
ultimate source of flare energy is mechanical energy in the convection zone,
how is this translated into energy dissipated or stored in the corona? This
question appears to have been given relatively little thought, as attention has
been focussed predominantly on mechanisms for the rapid dissipation of coronal
magnetic energy by way of MHD instabilities and plasma micro instabilities. We
consider three types of flare theory: the steady state "photospheric dynamo"
model in which flare power represents coronal dissipation of currents generated
simultaneously by sub-photospheric flows; the "magnetic energy storage" model
where sub-photospheric flows again induce coronal currents but which in this
case are built up over a longer period before being released suddenly; and
"emerging flux" models, in which new magnetic flux rising to the photosphere
already contains free energy, and does not require subsequent stressing by
photospheric motions. We conclude that photospheric dynamos can power only very
minor flares; that coronal energy storage can in principle meet the
requirements of a major flare, although perhaps not the very largest flares,
but that difficulties in coupling efficiently to the energy source may limit
this mechanism to moderate sized flares; and that emerging magnetic flux tubes,
generated in the solar interior, can carry sufficient free energy to power even
the largest flares ever observed.Comment: 14 pages, 1 figur
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