192 research outputs found
Landau damping of partially incoherent Langmuir waves
It is shown that partial incoherence, in the form of stochastic phase noise,
of a Langmuir wave in an unmagnetized plasma gives rise to a Landau-type
damping. Starting from the Zakharov equations, which describe the nonlinear
interaction between Langmuir and ion-acoustic waves, a kinetic equation is
derived for the plasmons by introducing the Wigner-Moyal transform of the
complex Langmuir wave field. This equation is then used to analyze the
stability properties of small perturbations on a stationary solution consisting
of a constant amplitude wave with stochastic phase noise. The concomitant
dispersion relation exhibits the phenomenon of Landau-like damping. However,
this damping differs from the classical Landau damping in which a Langmuir
wave, interacting with the plasma electrons, loses energy. In the present
process, the damping is non-dissipative and is caused by the resonant
interaction between an instantaneously-produced disturbance, due to the
parametric interactions, and a partially incoherent Langmuir wave, which can be
considered as a quasi-particle composed of an ensemble of partially incoherent
plasmons.Comment: 12 page
Virial expansion with Feynman diagrams
We present a field theoretic method for the calculation of the second and
third virial coefficients b2 and b3 of 2-species fermions interacting via a
contact interaction. The method is mostly analytic. We find a closed expression
for b3 in terms of the 2 and 3-body T-matrices. We recover numerically, at
unitarity, and also in the whole BEC-BCS crossover, previous numerical results
for the third virial coefficient b3
Turbulence, magnetic fields and plasma physics in clusters of galaxies
Observations of galaxy clusters show that the intracluster medium (ICM) is
likely to be turbulent and is certainly magnetized. The properties of this
magnetized turbulence are determined both by fundamental nonlinear
magnetohydrodynamic interactions and by the plasma physics of the ICM, which
has very low collisionality. Cluster plasma threaded by weak magnetic fields is
subject to firehose and mirror instabilities. These saturate and produce
fluctuations at the ion gyroscale, which can scatter particles, increasing the
effective collision rate and, therefore, the effective Reynolds number of the
ICM. A simple way to model this effect is proposed. The model yields a
self-accelerating fluctuation dynamo whereby the field grows explosively fast,
reaching the observed, dynamically important, field strength in a fraction of
the cluster lifetime independent of the exact strength of the seed field. It is
suggested that the saturated state of the cluster turbulence is a combination
of the conventional isotropic magnetohydrodynamic turbulence, characterized by
folded, direction-reversing magnetic fields and an Alfv\'en-wave cascade at
collisionless scales. An argument is proposed to constrain the reversal scale
of the folded field. The picture that emerges appears to be in qualitative
agreement with observations of magnetic fields in clusters.Comment: revtex, 9 pages, 5 figures; invited talk for the 47th APS DPP
Meeting, Denver, CO, Oct 2005; minor corrections to match the published
versio
Downside risk in reservoir management
Downside risk, which refers to deviations below a threshold, is often important in
water management decisions, especially in areas with large and skewed variations in
precipitation patterns. In this paper, we present a model for a reservoir manager who
is downside risk averse and who performs a dynamic allocation of irrigation water,
taking into account the negative effects of droughts on farm profits and different
environmental constraints. We analyse the water stock, flows and agricultural profits
for alternative environmental restrictions and thresholds for irrigation levels and find
that stricter environmental constraints increase total water supply and carryover
stock, while higher penalty thresholds lead to their overall decrease. Furthermore,
increasing penalty thresholds leads to a higher emphasis on avoiding shortages, at the
expense of lower average profits.info:eu-repo/semantics/acceptedVersio
Identity of electrons and ionization equilibrium
It is perhaps appropriate that, in a year marking the 90th anniversary of
Meghnad Saha seminal paper (1920), new developments should call fresh attention
to the problem of ionization equilibrium in gases. Ionization equilibrium is
considered in the simplest "physical" model for an electronic subsystem of
matter in a rarefied state, consisting of one localized electronic state in
each nucleus and delocalized electronic states considered as free ones. It is
shown that, despite the qualitative agreement, there is a significant
quantitative difference from the results of applying the Saha formula to the
degree of ionization. This is caused by the fact that the Saha formula
corresponds to the "chemical" model of matter.Comment: 9 pages, 2 figure
Non-Markovian Levy diffusion in nonhomogeneous media
We study the diffusion equation with a position-dependent, power-law
diffusion coefficient. The equation possesses the Riesz-Weyl fractional
operator and includes a memory kernel. It is solved in the diffusion limit of
small wave numbers. Two kernels are considered in detail: the exponential
kernel, for which the problem resolves itself to the telegrapher's equation,
and the power-law one. The resulting distributions have the form of the L\'evy
process for any kernel. The renormalized fractional moment is introduced to
compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure
Nonlinear growth of firehose and mirror fluctuations in turbulent galaxy-cluster plasmas
In turbulent high-beta astrophysical plasmas (exemplified by the galaxy
cluster plasmas), pressure-anisotropy-driven firehose and mirror fluctuations
grow nonlinearly to large amplitudes, dB/B ~ 1, on a timescale comparable to
the turnover time of the turbulent motions. The principle of their nonlinear
evolution is to generate secularly growing small-scale magnetic fluctuations
that on average cancel the temporal change in the large-scale magnetic field
responsible for the pressure anisotropies. The presence of small-scale magnetic
fluctuations may dramatically affect the transport properties and, thereby, the
large-scale dynamics of the high-beta astrophysical plasmas.Comment: revtex, 4 pages, 1 figure; replaced to match published versio
Equation of state of a strongly magnetized hydrogen plasma
The influence of a constant uniform magnetic field on the thermodynamic
properties of a partially ionized hydrogen plasma is studied. Using the method
of Green' s function various interaction contributions to the thermodynamic
functions are calculated. The equation of state of a quantum magnetized plasma
is presented within the framework of a low density expansion up to the order
e^4 n^2 and, additionally, including ladder type contributions via the bound
states in the case of strong magnetic fields (2.35*10^{5} T << B << 2.35*10^{9}
T). We show that for high densities (n=10^{27-30} m^{-3}) and temperatures
T=10^5 - 10^6 K typical for the surface of neutron stars nonideality effects
as, e.g., Debye screening must be taken into account.Comment: 12 pages, 2 Postscript figures. uses revtex, to appear in Phys. Rev.
Landau Damping and Coherent Structures in Narrow-Banded 1+1 Deep Water Gravity Waves
We study the nonlinear energy transfer around the peak of the spectrum of
surface gravity waves by taking into account nonhomogeneous effects. In the
narrow-banded approximation the kinetic equation resulting from a
nonhomogeneous wave field is a Vlasov-Poisson type equation which includes at
the same time the random version of the Benjamin-Feir instability and the
Landau damping phenomenon. We analytically derive the values of the Phillips'
constant and the enhancement factor for which the
narrow-banded approximation of the JONSWAP spectrum is unstable. By performing
numerical simulations of the nonlinear Schr\"{o}dinger equation we check the
validity of the prediction of the related kinetic equation. We find that the
effect of Landau damping is to suppress the formation of coherent structures.
The problem of predicting freak waves is briefly discussed.Comment: 4 pages, 3 figure
Nonlinear theory of mirror instability near threshold
An asymptotic model based on a reductive perturbative expansion of the drift
kinetic and the Maxwell equations is used to demonstrate that, near the
instability threshold, the nonlinear dynamics of mirror modes in a magnetized
plasma with anisotropic ion temperatures involves a subcritical
bifurcation,leading to the formation of small-scale structures with amplitudes
comparable with the ambient magnetic field
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