888 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 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
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
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
A Landau fluid model for warm collisionless plasmas
A Landau fluid model for a collisionless electron-proton magnetized plasma,
that accurately reproduces the dispersion relation and the Landau damping rate
of all the magnetohydrodynamic waves, is presented. It is obtained by an
accurate closure of the hydrodynamic hierarchy at the level of the fourth order
moments, based on linear kinetic theory. It retains non-gyrotropic corrections
to the pressure and heat flux tensors up to the second order in the ratio
between the considered frequencies and the ion cyclotron frequency.Comment: to appear in Phys. Plasma
Phase Space Models for Stochastic Nonlinear Parabolic Waves: Wave Spread and Singularity
We derive several kinetic equations to model the large scale, low Fresnel
number behavior of the nonlinear Schrodinger (NLS) equation with a rapidly
fluctuating random potential. There are three types of kinetic equations the
longitudinal, the transverse and the longitudinal with friction. For these
nonlinear kinetic equations we address two problems: the rate of dispersion and
the singularity formation.
For the problem of dispersion, we show that the kinetic equations of the
longitudinal type produce the cubic-in-time law, that the transverse type
produce the quadratic-in-time law and that the one with friction produces the
linear-in-time law for the variance prior to any singularity.
For the problem of singularity, we show that the singularity and blow-up
conditions in the transverse case remain the same as those for the homogeneous
NLS equation with critical or supercritical self-focusing nonlinearity, but
they have changed in the longitudinal case and in the frictional case due to
the evolution of the Hamiltonian
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