2,511 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

### 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

### Current driven rotating kink mode in a plasma column with a non-line-tied free end

First experimental measurements are presented for the kink instability in a
linear plasma column which is insulated from an axial boundary by finite sheath
resistivity. Instability threshold below the classical Kruskal-Shafranov
threshold, axially asymmetric mode structure and rotation are observed. These
are accurately reproduced by a recent kink theory, which includes axial plasma
flow and one end of the plasma column that is free to move due to a
non-line-tied boundary condition.Comment: 4 pages, 6 figure

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