2,998 research outputs found
Instability of toroidal magnetic field in jets and plerions
Jets and pulsar-fed supernova remnants (plerions) tend to develop highly
organized toroidal magnetic field. Such a field structure could explain the
polarization properties of some jets, and contribute to their lateral
confinement. A toroidal field geometry is also central to models for the Crab
Nebula - the archetypal plerion - and leads to the deduction that the Crab
pulsar's wind must have a weak magnetic field. Yet this `Z-pinch' field
configuration is well known to be locally unstable, even when the magnetic
field is weak and/or boundary conditions slow or suppress global modes. Thus,
the magnetic field structures imputed to the interiors of jets and plerions are
unlikely to persist.
To demonstrate this, I present a local analysis of Z-pinch instabilities for
relativistic fluids in the ideal MHD limit. Kink instabilities dominate,
destroying the concentric field structure and probably driving the system
toward a more chaotic state in which the mean field strength is independent of
radius (and in which resistive dissipation of the field may be enhanced). I
estimate the timescales over which the field structure is likely to be
rearranged and relate these to distances along relativistic jets and radii from
the central pulsar in a plerion.
I conclude that a concentric toroidal field is unlikely to exist well outside
the Crab pulsar's wind termination shock. There is thus no dynamical reason to
conclude that the magnetic energy flux carried by the pulsar wind is much
weaker than the kinetic energy flux. Abandoning this inference would resolve a
long-standing puzzle in pulsar wind theory.Comment: 28 pages, plain TeX. Accepted for publication in Ap
Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decomposition
Successful applications of the Kruskal-Segur approach to interfacial pattern
formation have remained limited due to the necessity of an integral formulation
of the problem. This excludes nonlinear bulk equations, rendering convection
intractable. Combining the method with Zauderer's asymptotic decomposition
scheme, we are able to strongly extend its scope of applicability and solve
selection problems based on free boundary formulations in terms of partial
differential equations alone. To demonstrate the technique, we give the first
analytic solution of the problem of velocity selection for dendritic growth in
a forced potential flow.Comment: Submitted to Europhys. Letters, No figures, 5 page
Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations
The truncation method is a collective name for techniques that arise from
truncating a Laurent series expansion (with leading term) of generic solutions
of nonlinear partial differential equations (PDEs). Despite its utility in
finding Backlund transformations and other remarkable properties of integrable
PDEs, it has not been generally extended to ordinary differential equations
(ODEs). Here we give a new general method that provides such an extension and
show how to apply it to the classical nonlinear ODEs called the Painleve
equations. Our main new idea is to consider mappings that preserve the
locations of a natural subset of the movable poles admitted by the equation. In
this way we are able to recover all known fundamental Backlund transformations
for the equations considered. We are also able to derive Backlund
transformations onto other ODEs in the Painleve classification.Comment: To appear in Nonlinearity (22 pages
The first correction to the second adiabatic invariant of charged-particle motion
First correction to second adiabatic invariant of charged particle motion in magnetic fiel
Understanding complex dynamics by means of an associated Riemann surface
We provide an example of how the complex dynamics of a recently introduced
model can be understood via a detailed analysis of its associated Riemann
surface. Thanks to this geometric description an explicit formula for the
period of the orbits can be derived, which is shown to depend on the initial
data and the continued fraction expansion of a simple ratio of the coupling
constants of the problem. For rational values of this ratio and generic values
of the initial data, all orbits are periodic and the system is isochronous. For
irrational values of the ratio, there exist periodic and quasi-periodic orbits
for different initial data. Moreover, the dependence of the period on the
initial data shows a rich behavior and initial data can always be found such
the period is arbitrarily high.Comment: 25 pages, 14 figures, typed in AMS-LaTe
A list of all integrable 2D homogeneous polynomial potentials with a polynomial integral of order at most 4 in the momenta
We searched integrable 2D homogeneous polynomial potential with a polynomial
first integral by using the so-called direct method of searching for first
integrals. We proved that there exist no polynomial first integrals which are
genuinely cubic or quartic in the momenta if the degree of homogeneous
polynomial potentials is greater than 4.Comment: 22 pages, no figures, to appear in J. Phys. A: Math. Ge
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