636 research outputs found
Timing mirror structures observed by Cluster with a magnetosheath flow model
The evolution of structures associated with mirror modes during their flow in
the Earth's magnetosheath is studied. The fact that the related magnetic
fluctuations can take distinct shapes, from deep holes to high peaks, has
been assessed in previous works on the observational, modeling and numerical
points of view. In this paper we present an analytical model for the flow
lines and velocity magnitude inside the magnetosheath. This model is used to
interpret almost 10 years of Cluster observations of mirror structures: by
back tracking each isolated observation to the shock, the "age", or flow
time, of these structures is determined together with the geometry of the
shock. Using this flow time the evolutionary path of the structures may be
studied with respect to different quantities: the distance to mirror
threshold, the amplitude of mirror fluctuations and the skewness of the
magnetic amplitude distribution as a marker of the shape of the structures.
These behaviours are confronted to numerical simulations which confirm the
dynamical perspective gained from the association of the statistical analysis
and the analytical model: magnetic peaks are mostly formed just behind the
shock and are quickly overwhelmed by magnetic holes as the plasma conditions
get more mirror stable. The amplitude of the fluctuations are found to
saturate before the skewness vanishes, i.e. when both structures
quantitatively balance each other, which typically occurs after a flow time
of 100–200 s in the Earth's magnetosheath. Comparison with other astrophysical
contexts is discussed
The role of parametric instabilities in turbulence generation and proton heating: Hybrid simulations of parallel propagating Alfv\'en waves
Large amplitude Alfv\'en waves tend to be unstable to parametric
instabilities which result in a decay process of the initial wave into
different daughter waves depending upon the amplitude of the fluctuations and
the plasma beta. The propagation angle with respect to the mean magnetic field
of the daughter waves plays an important role in determining the type of decay.
In this paper, we revisit this problem by means of multi-dimensional hybrid
simulations. In particular, we study the decay and the subsequent nonlinear
evolution of large-amplitude Alfv\'en waves by investigating the saturation
mechanism of the instability and its final nonlinear state reached for
different wave amplitudes and plasma beta conditions. As opposed to
one-dimensional simulations where the Decay instability is suppressed for
increasing plasma beta values, we find that the decay process in
multi-dimensions persists at large values of the plasma beta via the
filamentation/magnetosonic decay instabilities. In general, the decay process
acts as a trigger both to develop a perpendicular turbulent cascade and to
enhance mean field-aligned wave-particle interactions. We find indeed that the
saturated state is characterized by a turbulent plasma displaying a
field-aligned beam at the Alfv\'en speed and increased temperatures that we
ascribe to the Landau resonance and pitch angle scattering in phase space
Testing Conditional Independence of Discrete Distributions
We study the problem of testing \emph{conditional independence} for discrete
distributions. Specifically, given samples from a discrete random variable on domain , we want to distinguish,
with probability at least , between the case that and are
conditionally independent given from the case that is
-far, in -distance, from every distribution that has this
property. Conditional independence is a concept of central importance in
probability and statistics with a range of applications in various scientific
domains. As such, the statistical task of testing conditional independence has
been extensively studied in various forms within the statistics and
econometrics communities for nearly a century. Perhaps surprisingly, this
problem has not been previously considered in the framework of distribution
property testing and in particular no tester with sublinear sample complexity
is known, even for the important special case that the domains of and
are binary.
The main algorithmic result of this work is the first conditional
independence tester with {\em sublinear} sample complexity for discrete
distributions over . To complement our upper
bounds, we prove information-theoretic lower bounds establishing that the
sample complexity of our algorithm is optimal, up to constant factors, for a
number of settings. Specifically, for the prototypical setting when , we show that the sample complexity of testing conditional
independence (upper bound and matching lower bound) is
\[
\Theta\left({\max\left(n^{1/2}/\epsilon^2,\min\left(n^{7/8}/\epsilon,n^{6/7}/\epsilon^{8/7}\right)\right)}\right)\,.
\
Nonlinear evolution of the magnetized Kelvin-Helmholtz instability: from fluid to kinetic modeling
The nonlinear evolution of collisionless plasmas is typically a multi-scale
process where the energy is injected at large, fluid scales and dissipated at
small, kinetic scales. Accurately modelling the global evolution requires to
take into account the main micro-scale physical processes of interest. This is
why comparison of different plasma models is today an imperative task aiming at
understanding cross-scale processes in plasmas. We report here the first
comparative study of the evolution of a magnetized shear flow, through a
variety of different plasma models by using magnetohydrodynamic, Hall-MHD,
two-fluid, hybrid kinetic and full kinetic codes. Kinetic relaxation effects
are discussed to emphasize the need for kinetic equilibriums to study the
dynamics of collisionless plasmas in non trivial configurations. Discrepancies
between models are studied both in the linear and in the nonlinear regime of
the magnetized Kelvin-Helmholtz instability, to highlight the effects of small
scale processes on the nonlinear evolution of collisionless plasmas. We
illustrate how the evolution of a magnetized shear flow depends on the relative
orientation of the fluid vorticity with respect to the magnetic field direction
during the linear evolution when kinetic effects are taken into account. Even
if we found that small scale processes differ between the different models, we
show that the feedback from small, kinetic scales to large, fluid scales is
negligable in the nonlinear regime. This study show that the kinetic modeling
validates the use of a fluid approach at large scales, which encourages the
development and use of fluid codes to study the nonlinear evolution of
magnetized fluid flows, even in the colisionless regime
The oblique firehose instability in a bi-kappa magnetized plasma
In this work, we derive a dispersion equation that describes the excitation
of the oblique (or Alfv\'en) firehose instability in a plasma that contains
both electron and ion species modelled by bi-kappa velocity distribution
functions. The equation is obtained with the assumptions of low-frequency waves
and moderate to large values of the parallel (respective to the ambient
magnetic field) plasma beta parameter, but it is valid for any direction of
propagation and for any value of the particle gyroradius (or Larmor radius).
Considering values for the physical parameters typical to those found in the
solar wind, some solutions of the dispersion equation, corresponding to the
unstable mode, are presented. In order to implement the dispersion solver,
several new mathematical properties of the special functions occurring in a
kappa plasma are derived and included. The results presented here suggest that
the superthermal characteristic of the distribution functions leads to
reductions to both the maximum growth rate of the instability and of the
spectral range of its occurrence
A nonlinear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma
Weakly collisional plasmas dynamically develop pressure anisotropies with
respect to the magnetic field. These anisotropies trigger plasma instabilities
at scales just above the ion Larmor radius \rho_i and much below the mean free
path \lambda_{mfp}. They have growth rates of a fraction of the ion cyclotron
frequency - much faster than either the global dynamics or local turbulence.
The instabilities dramatically modify the transport properties and, therefore,
the macroscopic dynamics of the plasma. Their nonlinear evolution drives
pressure anisotropies towards marginal stability, controlled by the plasma beta
\beta_i. Here this nonlinear evolution is worked out for the simplest
analytically tractable example - the parallel firehose instability. In the
nonlinear regime, both analytical theory and the numerical solution predict
secular growth of magnetic fluctuations. They develop a k^{-3} spectrum,
extending from scales somewhat larger than \rho_i to the maximum scale that
grows secularly with time (~t^{1/2}); the relative pressure anisotropy
(\pperp-\ppar)/\ppar tends to the marginal value -2/\beta_i. The marginal state
is achieved via changes in the magnetic field, not particle scattering. When a
parallel ion heat flux is present, the firehose mutates into the new
gyrothermal instability (GTI), which continues to exist up to firehose-stable
values of pressure anisotropy, which can be positive and are limited by the
heat flux. The nonlinear evolution of the GTI also features secular growth of
magnetic fluctuations, but the spectrum is eventually dominated by modes around
the scale ~\rho_i l_T/\lambda_{mfp}, where l_T is the scale of the parallel
temperature variation. Implications for momentum and heat transport are
speculated about. This study is motivated by the dynamics of galaxy cluster
plasmas.Comment: 34 pages, replaced with the version published in MNRA
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