584 research outputs found
Electron-scale reduced fluid models with gyroviscous effects
Reduced fluid models for collisionless plasmas including electron inertia and
finite Larmor radius corrections are derived for scales ranging from the ion to
the electron gyroradii. Based either on pressure balance or on the
incompressibility of the electron fluid, they respectively capture kinetic
Alfv\'en waves (KAWs) or whistler waves (WWs), and can provide suitable tools
for reconnection and turbulence studies. Both isothermal regimes and Landau
fluid closures permitting anisotropic pressure fluctuations are considered. For
small values of the electron beta parameter , a perturbative
computation of the gyroviscous force valid at scales comparable to the electron
inertial length is performed at order , which requires second-order
contributions in a scale expansion. Comparisons with kinetic theory are
performed in the linear regime. The spectrum of transverse magnetic
fluctuations for strong and weak turbulence energy cascades is also
phenomenologically predicted for both types of waves. In the case of moderate
ion to electron temperature ratio, a new regime of KAW turbulence at scales
smaller than the electron inertial length is obtained, where the magnetic
energy spectrum decays like , thus faster than the
spectrum of WW turbulence.Comment: 29 pages, 4 figure
Nonlinear Mirror Modes in Space Plasmas
Since the first observations by Kaufmann et al.\ (1970), special attention
has been paid to static pressure-balanced structures in the form of magnetic
holes or humps observed in regions of the solar wind and of planetary
magnetosheaths where the parameter is relatively large and the ion
perpendicular temperature exceeds the parallel one. Although alternative
interpretations have been proposed, these structures are usually viewed as
associated with the mirror instability discovered in 1957 by Vedenov and
Sagdeev. After reviewing observational results provided by satellite missions,
high-resolution numerical simulations of the Vlasov--Maxwell equations together
with asymptotic and phenomenological models of the nonlinear dynamics near the
instability threshold are discussed. The constraining effect of the mirror
instability on the temperature anisotropy associated with a dominant
perpendicular ion heating observed in the solar wind is reported, and recent
simulations of this phenomenon based on an elaborated fluid model including
low-frequency kinetic effects are briefly mentioned.Comment: 3rd School and Workshop on Space Plasma Physics, (1-12 September
2010,Kiten, Bulgaria),I. Zhelyazkov and T. Mishonov eds., AIP Conference
Proceedings 356, 159-176, ISBN 978-0-7354-0914-9 (American Institute of
Physics, 2011
Nonlinear mirror modes in the presence of hot electrons
A non-perturbative calculation of the gyrotropic pressures associated with
large-scale mirror modes is performed, taking into account a finite, possibly
anisotropic electron temperature. In the small-amplitude limit, this leads to
an extension of an asymptotic model previously derived for cold electrons. A
model equation for the profile of subcritical finite-amplitude large-scale
structures is also presented
Influence of the nonlinearity parameter on the solar-wind sub-ion magnetic energy spectrum: FLR-Landau fluid simulations
The cascade of kinetic Alfv\'en waves (KAWs) at the sub-ion scales in the
solar wind is numerically simulated using a fluid approach that retains ion and
electron Landau damping, together with ion finite Larmor radius corrections.
Assuming initially equal and isotropic ion and electron temperatures, and an
ion beta equal to unity, different simulations are performed by varying the
propagation direction and the amplitude of KAWs that are randomly driven at a
transverse scale of about one fifth of the proton gyroradius in order to
maintain a prescribed level of turbulent fluctuations. The resulting turbulent
regimes are characterized by the nonlinearity parameter, defined as the ratio
of the characteristic times of Alfv\'en wave propagation and of the transverse
nonlinear dynamics. The corresponding transverse magnetic energy spectra
display power laws with exponents spanning a range of values consistent with
spacecraft observations. The meandering of the magnetic field lines together
with the ion temperature homogenization along these lines are shown to be
related to the strength of the turbulence, measured by the nonlinearity
parameter. The results are interpreted in terms of a recently proposed
phenomenological model where the homogenization process along field lines
induced by Landau damping plays a central role
A fluid description for Landau damping of dispersive MHD waves
International audienceThe dynamics of long oblique MHD waves in a collisionless plasma permeated by a uniform magnetic field is addressed using a Landau-fluid model that includes Hall effect and electron-pressure gradient in a generalized Ohm's law and retains ion finite Larmor radius (FLR) corrections to the gyrotropic pressure (Phys. Plasmas 10, 3906, 2003). This one-fluid model, built to reproduce the weakly nonlinear dynamics of long dispersive Alfvén waves propagating along an ambient field, is shown to correctly capture the Landau damping of oblique magnetosonic waves predicted by a kinetic theory based on the Vlasov-Maxwell system. For oblique and kinetic Alfvén waves (for which second order FLR corrections are to be retained), the linear character of waves with small but finite amplitudes is established, and the dispersion relation reproduced in the regime of adiabatic protons and isothermal electrons, associated with the condition me/mp e/Tp, where ß is the squared ratio of the ion-acoustic to the Alfvén speeds. It is shown that in more general regimes, the heat fluxes are, to leading order, not gyrotropic and dependent on the Hall effect to leading order
Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow
In this paper, we prove the energy diminishing of a normalized gradient flow
which provides a mathematical justification of the imaginary time method used
in physical literatures to compute the ground state solution of Bose-Einstein
condensates (BEC). We also investigate the energy diminishing property for the
discretization of the normalized gradient flow. Two numerical methods are
proposed for such discretizations: one is the backward Euler centered finite
difference (BEFD), the other one is an explicit time-splitting sine-spectral
(TSSP) method. Energy diminishing for BEFD and TSSP for linear case, and
monotonicity for BEFD for both linear and nonlinear cases are proven.
Comparison between the two methods and existing methods, e.g. Crank-Nicolson
finite difference (CNFD) or forward Euler finite difference (FEFD), shows that
BEFD and TSSP are much better in terms of preserving energy diminishing
property of the normalized gradient flow. Numerical results in 1d, 2d and 3d
with magnetic trap confinement potential, as well as a potential of a stirrer
corresponding to a far-blue detuned Gaussian laser beam are reported to
demonstrate the effectiveness of BEFD and TSSP methods. Furthermore we observe
that the normalized gradient flow can also be applied directly to compute the
first excited state solution in BEC when the initial data is chosen as an odd
function.Comment: 28 pages, 6 figure
Scaling Properties of Weak Chaos in Nonlinear Disordered Lattices
The Discrete Nonlinear Schroedinger Equation with a random potential in one
dimension is studied as a dynamical system. It is characterized by the length,
the strength of the random potential and by the field density that determines
the effect of nonlinearity. The probability of the system to be regular is
established numerically and found to be a scaling function. This property is
used to calculate the asymptotic properties of the system in regimes beyond our
computational power.Comment: 4 pages, 5 figure
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