1,339 research outputs found
Isolated unstable Weibel modes in unmagnetized plasmas with tunable asymmetry
In this letter, an initially unmagnetized pair plasma with asymmetric
velocity distributions is investigated where any unstable Weibel mode must be
isolated, with discrete values for the growth rates and the unstable
wavenumbers. For both a non-relativistic distribution with thermal spread and a
high-relativistic two-stream distribution it is shown that isolated modes are
excited and that, as the asymmetry tends to zero, the growth rate remains
finite, as long as the distribution function is not precisely symmetric.Comment: Comments: references adde
Non-linear Weibel-type Soliton Modes
Discussion is given of non-linear soliton behavior including coupling between
electrostatic and electromagnetic potentials for non-relativistic, weakly
relativistic, and fully relativistic plasmas. For plasma distribution functions
that are independent of the canonical momenta perpendicular to the soliton
spatial structure direction there are, in fact, no soliton behaviors allowed
because transverse currents are zero. Dependence on the transverse canonical
momenta is necessary. When such is the case, it is shown that the presence or
absence of a soliton is intimately connected to the functional form assumed for
the particle distribution functions. Except for simple situations, the coupled
non-linear equations for the electrostatic and electromagnetic potentials would
seem to require numerical solution procedures. Examples are given to illustrate
all of these points for non-relativistic, weakly relativistic, and fully
relativistic plasmas.Comment: Accepted for publication at Journal of Physics A: Mathematical and
Theoretica
Pitch-angle scattering in magnetostatic turbulence. II. Analytical considerations and pitch-angle isotropization
Aims. The process of pitch-angle isotropization is important for many
applications ranging from diffusive shock acceleration to large-scale
cosmic-ray transport. Here, the basic analytical description is revisited on
the basis of recent simulation results. Methods. Both an analytical and a
numerical investigation were undertaken of the Fokker-Planck equation for
pitch-angle scattering. Additional test-particle simulations obtained with the
help of a Monte-Carlo code were used to verify the conclusions. Results. It is
shown that the usual definition of the pitch-angle Fokker-Planck coefficient
via the mean-square displacement is flawed. The reason can be traced back to
the assumption of homogeneity in time which does not hold for pitch-angle
scattering. Conclusions. Calculating the mean free path via the Fokker-Planck
coefficient has often proven to give an accurate description. For numerical
purposes, accordingly, it is the definition that has to be exchanged in favor
of the pitch-angle correlation function.Comment: 5 pages, 5 figures, accepted for publication in Astron. Astrophy
Cosmic-ray acceleration at collisionless astrophysical shocks using Monte-Carlo simulations
Context. The diffusive shock acceleration mechanism has been widely accepted
as the acceleration mechanism for galactic cosmic rays. While self-consistent
hybrid simulations have shown how power-law spectra are produced, detailed
information on the interplay of diffusive particle motion and the turbulent
electromagnetic fields responsible for repeated shock crossings are still
elusive. Aims. The framework of test-particle theory is applied to investigate
the effect of diffusive shock acceleration by inspecting the obtained
cosmic-ray energy spectra. The resulting energy spectra can be obtained this
way from the particle motion and, depending on the prescribed turbulence model,
the influence of stochastic acceleration through plasma waves can be studied.
Methods. A numerical Monte-Carlo simulation code is extended to include
collisionless shock waves. This allows one to trace the trajectories of test
particle while they are being accelerated. In addition, the diffusion
coefficients can be obtained directly from the particle motion, which allows
for a detailed understanding of the acceleration process. Results. The classic
result of an energy spectrum with is only reproduced for parallel
shocks, while, for all other cases, the energy spectral index is reduced
depending on the shock obliqueness. Qualitatively, this can be explained in
terms of the diffusion coefficients in the directions that are parallel and
perpendicular to the shock front.Comment: 12 pages, 15 figures, accepted for publication in A&
Modification of cosmic-ray energy spectra by stochastic acceleration
Context: Typical space plasmas contain spatially and temporally variable
turbulent electromagnetic fields. Understanding the transport of energetic
particles and the acceleration mechanisms for charged particles is an important
goal of today's astroparticle physics. Aims: To understand the acceleration
mechanisms at the particle source, subsequent effects have to be known.
Therefore, the modification of a particle energy distribution, due to
stochastic acceleration, needs to be investigated. Methods: The diffusion in
momentum space was investigated by using both a Monte-Carlo simulation code and
by analytically solving the momentum-diffusion equation. For simplicity, the
turbulence was assumed to consist of one-dimensional Alfven waves. Results:
Using both methods, it is shown that, on average, all particles with velocities
comparable to the Alfven speeds are accelerated. This influences the energy
distribution by significantly increasing the energy spectral index.
Conclusions: Because of electromagnetic turbulence, a particle energy spectrum
measured at Earth can drastically deviate from its initial spectrum. However,
for particles with velocities significantly above the Alfven speed, the effect
becomes negligible.Comment: 10 pages, 6 figures, accepted for publication in Astronomy &
Astrophysic
Pitch-angle scattering in magnetostatic turbulence. I. Test-particle simulations and the validity of analytical results
Context. Spacecraft observations have motivated the need for a refined
description of the phase-space distribution function. Of particular importance
is the pitch-angle diffusion coefficient that occurs in the Fokker-Planck
transport equation. Aims. Simulations and analytical test-particle theories are
compared to verify the diffusion description of particle transport, which does
not allow for non-Markovian behavior. Methods. A Monte-Carlo simulation code
was used to trace the trajectories of test particles moving in turbulent
magnetic fields. From the ensemble average, the pitch-angle Fokker-Planck
coefficient is obtained via the mean square displacement. Results. It is shown
that, while excellent agreement with analytical theories can be obtained for
slab turbulence, considerable deviations are found for isotropic turbulence. In
addition, all Fokker-Planck coefficients tend to zero for high time values.Comment: 8 pages, 10 figures, accepted for publication in Astron. Astrophy
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