3,455 research outputs found
Cosmic Ray Acceleration at Relativistic Shock Waves with a "Realistic" Magnetic Field Structure
The process of cosmic ray first-order Fermi acceleration at relativistic
shock waves is studied with the method of Monte Carlo simulations. The
simulations are based on numerical integration of particle equations of motion
in a turbulent magnetic field near the shock. In comparison to earlier studies,
a few "realistic" features of the magnetic field structure are included. The
upstream field consists of a mean field component inclined at some angle to the
shock normal with finite-amplitude sinusoidal perturbations imposed upon it.
The perturbations are assumed to be static in the local plasma rest frame.
Their flat or Kolmogorov spectra are constructed with randomly drawn wave
vectors from a wide range . The downstream field structure
is derived from the upstream one as compressed at the shock. We present
particle spectra and angular distributions obtained at mildly relativistic sub-
and superluminal shocks and also parallel shocks. We show that particle spectra
diverge from a simple power-law, the exact shape of the spectrum depends on
both the amplitude of the magnetic field perturbations and the wave power
spectrum. Features such as spectrum hardening before the cut-off at oblique
subluminal shocks and formation of power-law tails at superluminal ones are
presented and discussed. At parallel shocks, the presence of finite-amplitude
magnetic field perturbations leads to the formation of locally oblique field
configurations at the shock and the respective magnetic field compressions.
This results in the modification of the particle acceleration process,
introducing some features present in oblique shocks, e.g., particle reflections
from the shock. We demonstrate for parallel shocks a (nonmonotonic) variation
of the particle spectral index with the turbulence amplitude.Comment: revised version (37 pages, 13 figures
Cosmic-Ray Momentum Diffusion In Magnetosonic Versus Alfvenic Turbulent Field
Energetic particle transport in a finite amplitude magnetosonic and Alfvenic
turbulence is considered using Monte Carlo particle simulations, which involve
an integration of particle equation of motion. We show that in a low-Betha
plasma cosmic ray can be the most important damping process for magnetosonic
waves. Assuming such conditions we derive the momentum diffusion coefficient
for relativistic particles in the presence of anisotropic finite-amplitude
turbulent wave field, for flat and Kolmogorov-type turbulence spectra. We
confirm the possibility of larger values of a momentum diffusion coefficient
occuring due to transit-time damping resonance interaction in the presence of
isotropic fast-mode waves in comparison to the Alfven waves of the same
amplitude.Comment: 16 pages, 2 fig, macro for Solar Physcs, accepted for Solar Physic
Cosmic-ray Acceleration at Ultrarelativistic Shock Waves: Effects of a "Realistic" Magnetic Field Structure
First-order Fermi acceleration processes at ultrarelativistic shocks are
studied with Monte Carlo simulations. The accelerated particle spectra are
derived by integrating the exact particle trajectories in a turbulent magnetic
field near the shock. ''Realistic'' features of the field structure are
included. We show that the main acceleration process at superluminal shocks is
the particle compression at the shock. Formation of energetic spectral tails is
possible in a limited energy range only for highly perturbed magnetic fields,
with cutoffs occuring at low energies within the resonance energy range
considered. These spectral features result from the anisotropic character of
particle transport in the downstream magnetic field, where field compression
produces effectively 2D perturbations. Because of the downstream field
compression, the acceleration process is inefficient in parallel shocks for
larger turbulence amplitudes, and features observed in oblique shocks are
recovered. For small-amplitude turbulence, wide-energy range particle spectra
are formed and modifications of the process due to the existence of long-wave
perturbations are observed. In both sub- and superluminal shocks, an increase
of \gamma leads to steeper spectra with lower cut-off energies. The spectra
obtained for the ``realistic'' background conditions assumed here do not
converge to the ``universal'' spectral index claimed in the literature. Thus
the role of the first-order Fermi process in astrophysical sources hosting
relativistic shocks requires serious reanalysis.Comment: submitted to Ap
Discovery of a tight correlation for gamma ray burst afterglows with `canonical' light curves
Gamma Ray Bursts (GRB) observed up to redshifts are fascinating objects
to study due to their still unexplained relativistic outburst mechanisms and a
possible use to test cosmological models. Our analysis of 77 GRB afterglows
with known redshifts revealed a physical subsample of long GRBs with canonical
{\it plateau breaking to power-law} light curves with a significant {\it
luminosity - break time } correlation in the GRB rest frame.
This subsample forms approximately the {\it upper envelope} of the studied
distribution. We have also found a similar relation for a small sample of GRB
afterglows that belong to the intermediate class (IC) between the short and the
long ones. It proves that within the full sample of afterglows there exist
physical subclasses revealed here by tight correlations of their afterglow
properties. The afterglows with regular (`canonical') light curves obey not
only a mentioned tight physical scaling, but -- for a given -- the more
regular progenitor explosions lead to preferentially brighter afterglows.Comment: 15 pages, 5 figures accepted to ApJ
Self-Similar Collisionless Shocks
Observations of gamma-ray burst afterglows suggest that the correlation
length of magnetic field fluctuations downstream of relativistic non-magnetized
collisionless shocks grows with distance from the shock to scales much larger
than the plasma skin depth. We argue that this indicates that the plasma
properties are described by a self-similar solution, and derive constraints on
the scaling properties of the solution. For example, we find that the scaling
of the characteristic magnetic field amplitude with distance from the shock is
B \propto D^{s_B} with -1<s_B<=0, that the spectrum of accelerated particles is
dn/dE \propto E^{-2/(s_B+1)}, and that the scaling of the magnetic correlation
function is \propto x^{2s_B} (for x>>D). We show that the
plasma may be approximated as a combination of two self-similar components: a
kinetic component of energetic particles and an MHD-like component representing
"thermal" particles. We argue that the latter may be considered as infinitely
conducting, in which case s_B=0 and the scalings are completely determined
(e.g. dn/dE \propto E^{-2} and B \propto D^0). Similar claims apply to non-
relativistic shocks such as in supernova remnants, if the upstream magnetic
field can be neglected. Self-similarity has important implications for any
model of particle acceleration and/or field generation. For example, we show
that the diffusion function in the angle \mu of momentum p in diffusive shock
acceleration models must satisfy D_{\mu\mu}(p,D) = D^{-1}D'_{\mu\mu}(p/D), and
that a previously suggested model for the generation of large scale magnetic
fields through a hierarchical merger of current-filaments should be
generalized. A numerical experiment testing our analysis is outlined
(Abridged).Comment: 16 pages, 1 figure, accepted for publication in Ap
Symmetry Reduction of Optimal Control Systems and Principal Connections
This paper explores the role of symmetries and reduction in nonlinear control
and optimal control systems. The focus of the paper is to give a geometric
framework of symmetry reduction of optimal control systems as well as to show
how to obtain explicit expressions of the reduced system by exploiting the
geometry. In particular, we show how to obtain a principal connection to be
used in the reduction for various choices of symmetry groups, as opposed to
assuming such a principal connection is given or choosing a particular symmetry
group to simplify the setting. Our result synthesizes some previous works on
symmetry reduction of nonlinear control and optimal control systems. Affine and
kinematic optimal control systems are of particular interest: We explicitly
work out the details for such systems and also show a few examples of symmetry
reduction of kinematic optimal control problems.Comment: 23 pages, 2 figure
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