arXiv subjects

M. Lazar

Publications and source records attributed to M. Lazar.

At least 55 records · Page 3Linked to original sources

arXiv2018

Regularized $κ$-distributions with non-diverging moments

For various plasma applications the so-called (non-relativistic) $κ$-distribution is widely used to reproduce and interpret the suprathermal particle populations exhibiting a power-law distribution in velocity or energy. Despite its reputation the standard $κ$-distribution as a concept is still disputable, mainly due to the velocity moments $M_{l}$ which make possible a macroscopic characterization, but whose existence is restricted only to low orders $l < 2κ-1$. In fact, the definition of the $κ$-distribution itself is conditioned by the existence of the moment of order $l=2$ (i.e., kinetic temperature) satisfied only for $κ> 3/2$. In order to resolve these critical limitations we introduce the regularized $κ$-distribution with non-diverging moments. For the evaluation of all velocity moments a general analytical expression is provided enabling a significant step towards a macroscopic (fluid-like) description of space plasmas, and, in general, any system of $κ$-distributed particles.

physics.plasm-ph↗

arXiv2017

Instability constraints for the electron temperature anisotropy in the slow solar wind. Thermal core vs. suprathermal halo

This letter presents the results of an advanced parametrization of the solar wind electron temperature anisotropy and the instabilities resulting from the interplay of the (bi-)Maxwellian core and (bi-)Kappa halo populations in the slow solar wind. A large set of observational data (from the Ulysses, Helios and Cluster missions) is used to parametrize these components and establish their correlations. The instabilities are significantly stimulated in the presence of suprathermals, and the instability thresholds shape the limits of the temperature anisotropy for both the core and halo populations re-stating the incontestable role that the selfgenerated instabilities can play in constraining the electron anisotropy. These results confirm a particular implication of the suprathermal electrons which are less dense but hotter than thermal electrons.

astro-ph.SR↗

arXiv2017

Dual Maxwellian-Kappa modelling of the solar wind electrons: new clues on the temperature of Kappa populations

Context. Recent studies on Kappa distribution functions invoked in space plasma applications have emphasized two alternative approaches which may assume the temperature parameter either dependent or independent of the power-index $κ$. Each of them can obtain justification in different scenarios involving Kappa-distributed plasmas, but direct evidences supporting any of these two alternatives with measurements from laboratory or natural plasmas are not available yet. Aims. This paper aims to provide more facts on this intriguing issue from direct fitting measurements of suprathermal electron populations present in the solar wind, as well as from their destabilizing effects predicted by these two alternating approaches. Methods. Two fitting models are contrasted, namely, the global Kappa and the dual Maxwellian-Kappa models, which are currently invoked in theory and observations. The destabilizing effects of suprathermal electrons are characterized on the basis of a kinetic approach which accounts for the microscopic details of the velocity distribution. Results. In order to be relevant, the model is chosen to accurately reproduce the observed distributions and this is achieved by a dual Maxwellian-Kappa distribution function. A statistical survey indicates a $κ$-dependent temperature of the suprathermal (halo) electrons for any heliocentric distance. Only for this approach the instabilities driven by the temperature anisotropy are found to be systematically stimulated by the abundance of suprathermal populations, i.e., lowering the values of $κ$-index.

physics.plasm-ph↗

arXiv2017

Towards parallelizable sampling-based Nonlinear Model Predictive Control

This paper proposes a new sampling-based nonlinear model predictive control (MPC) algorithm, with a bound on complexity quadratic in the prediction horizon N and linear in the number of samples. The idea of the proposed algorithm is to use the sequence of predicted inputs from the previous time step as a warm start, and to iteratively update this sequence by changing its elements one by one, starting from the last predicted input and ending with the first predicted input. This strategy, which resembles the dynamic programming principle, allows for parallelization up to a certain level and yields a suboptimal nonlinear MPC algorithm with guaranteed recursive feasibility, stability and improved cost function at every iteration, which is suitable for real-time implementation. The complexity of the algorithm per each time step in the prediction horizon depends only on the horizon, the number of samples and parallel threads, and it is independent of the measured system state. Comparisons with the fmincon nonlinear optimization solver on benchmark examples indicate that as the simulation time progresses, the proposed algorithm converges rapidly to the "optimal" solution, even when using a small number of samples.

eess.SY↗

arXiv2016

Shaping the solar wind temperature anisotropy by the interplay of electron and proton instabilities

A variety of nonthermal characteristics like kinetic, e.g., temperature, anisotropies and suprathermal populations (enhancing the high energy tails of the velocity distributions) are revealed by the in-situ observations in the solar wind indicating quasistationary states of plasma particles out of thermal equilibrium. Large deviations from isotropy generate kinetic instabilities and growing fluctuating fields which should be more efficient than collisions in limiting the anisotropy (below the instability threshold) and explain the anisotropy limits reported by the observations. The present paper aims to decode the principal instabilities driven by the temperature anisotropy of electrons and protons in the solar wind, and contrast the instability thresholds with the bounds observed at 1~AU for the temperature anisotropy. The instabilities are characterized using linear kinetic theory to identify the appropriate (fastest) instability in the relaxation of temperature anisotropies $A_{e,p} = T_{e,p,\perp}/ T_{e,p,\parallel} \ne 1$. The analysis focuses on the electromagnetic instabilities driven by the anisotropic protons ($A_p \lessgtr 1$) and invokes for the first time a dynamical model to capture the interplay with the anisotropic electrons by correlating the effects of these two species of plasma particles, dominant in the solar wind.

astro-ph.SR↗

arXiv2016

Effects of suprathermal electrons on the proton temperature anisotropy in space plasmas: Electromagnetic ion-cyclotron instability

In collision-poor plasmas from space, e.g., the solar wind and planetary magnetospheres, the kinetic anisotropy of the plasma particles is expected to be regulated by the kinetic instabilities. Driven by an excess of ion (proton) temperature perpendicular to the magnetic field $(~T_\perp >T_\parallel)$, the electromagnetic ion-cyclotron (EMIC) instability is fast enough to constrain the proton anisotropy, but the observations do not conform to the instability thresholds predicted by the standard theory for bi-Maxwellian models of the plasma particles. This paper presents an extended investigation of the EMIC instability in the presence of suprathermal electrons which are ubiquitous in these environments. The analysis is based on the kinetic (Vlasov-Maxwell) theory assuming that both species, protons and electrons, may be anisotropic, and the EMIC unstable solutions are derived numerically providing an accurate description for conditions typically encountered in space plasmas. The effects of suprathermal populations are triggered by the electron anisotropy and the temperature contrast between electrons and protons. For certain conditions the anisotropy thresholds exceed the limits of the proton anisotropy measured in the solar wind considerably restraining the unstable regimes of the EMIC modes.

physics.space-ph↗

arXiv2016

Firehose constraints for the solar wind suprathermal electrons

The indefinite increase of temperature predicted by the solar wind expansion in the direction parallel to the interplanetary magnetic field is already notorious for not being confirmed by the observations. In hot and dilute plasmas from space particle-particle collisions are not efficient in constraining large deviations from isotropy, but the resulting firehose instability provides in this case plausible limitations for the temperature anisotropy of the thermal (core) populations of both the electron and proton species. The present paper takes into discussion the suprathermal (halo) electrons, which are ubiquitous in the solar wind. Less dense but hotter than the core, suprathermals may be highly anisotropic and susceptible to the firehose instability. The main features of the instability are here derived from a first-order theory for conditions specific to the suprathermal electrons in the solar wind and terrestrial magnetospheres. Unveiled here, new regimes of the electron firehose instability may be exclusively controlled by the suprathermals. The instability is found to be systematically stimulated by the suprathermal electrons, with thresholds that approach the limits of the temperature anisotropy reported by the observations. These results represent new and valuable evidences for the implication of the firehose instability in the relaxation of the temperature anisotropy in space plasmas.

astro-ph.SR↗

arXiv2016

The Electron Temperature and Anisotropy in the Solar Wind. I. Comparison of the Core and Halo Populations

Estimating the temperature of the solar wind particles and their anisotropies is particularly important for understanding the origin of these deviations from thermal equilibrium as well as their effects. In the absence of energetic events the velocity distribution of electrons reveal a dual structure with a thermal (Maxwellian) core and a suprathermal (Kappa) halo. This paper presents a detailed observational analysis of these two components, providing estimations of their temperatures and temperature anisotropies and decoding any potential interdependence that their properties may indicate. The data set used in this study includes more than 120$\,$000 the events detected by three missions in the ecliptic within an extended range of heliocentric distances from 0.3 to over 4~AU. The anti-correlation found for the core and halo temperatures is consistent with the radial evolution of the Kappa model, clarifying an apparent contradiction in previous observational analysis and providing valuable clues about the temperature of the Kappa-distributed populations. However, these two components manifest a clear tendency to deviate from isotropy in the same direction, that seems to confirm the existence of mechanisms with similar effects on both components, e.g., the solar wind expansion, or the particle heating by the fluctuations. On the other hand, the existence of plasma states with anti-correlated anisotropies of the core and halo populations suggests a dynamic interplay of these components, mediated, most probably, by the anisotropy-driven instabilities.

physics.space-ph↗

arXiv2016

On the interpretation and applicability of $κ$-distributions

The generally accepted representation of $κ$-distributions in space plasma physics allows for two different alternatives, namely assuming either the temperature or the thermal velocity to be $κ$-independent. The present paper aims to clarify the issue concerning which of the two possible choices and the related physical interpretation is the correct one. A quantitative comparison of the consequences of the use of both distributions for specific physical systems leads to their correct interpretation. It is found that both alternatives can be realized, but are valid for principally different physical systems. The investigation demonstrates that, before employing one of the two alternatives, one should be conscious about the nature of the physical system one intends to describe, otherwise one would possibly obtain unphysical results.

astro-ph.SR↗

arXiv2014

Constraints for the aperiodic O-mode streaming instability

In plasmas where the thermal energy density exceeds the magnetic energy density ($β_\parallel > 1$), the aperiodic ordinary mode (O-mode) instability is driven by an excess of parallel temperature $A = T_\perp /T_\parallel < 1$ (where $\parallel$ and $\perp$ denote directions relative to the uniform magnetic field). When stimulated by parallel plasma streams the instability conditions extend to low beta states, i.e., $β_\parallel <1$, and recent studies have proven the existence of a new regime, where the anisotropy threshold decreases steeply with lowering $β_\parallel \to 0$ if the streaming velocity is sufficiently high. However, the occurrence of this instability is questionable especially in the low-beta plasmas, where the electrostatic two-stream instabilities are expected to develop much faster in the process of relaxation of the counterstreams. It is therefore proposed here to identify the instability conditions for the O-mode below those required for the onset of the electrostatic instability. An hierarchy of these two instabilities is established for both the low $β_\parallel <1$ and large $β_\parallel > 1$ plasmas. The conditions where the O-mode instability can operate efficiently are markedly constrained by the electrostatic instabilities especially in the low-beta plasmas.

physics.plasm-ph↗

arXiv2014

Solar Wind Electron Strahls Associated with a High-Latitude CME: \emph{Ulysses} Observations

Counterstreaming beams of electrons are ubiquitous in coronal mass ejections (CMEs) - although their existence is not unanimously accepted as a necessary and/or sufficient signature of these events. We continue the investigations of a high-latitude CME registered by the \emph{Ulysses} spacecraft on January 18\,--\,19, 2002 (Dumitrache, Popescu, and Oncica, Solar Phys. {\bf 272}, 137, 2011), by surveying the solar wind electron distributions associated with this event. The temporal-evolution of the pitch-angle distributions reveal populations of electrons distinguishable through their anisotropy, with clear signatures of i) electron strahls, ii) counter-streaming in the magnetic clouds and their precursors, and iii) unidirectional in the fast wind preceding the CME. The analysis of the counter-streams inside the CME allows us to elucidate the complexity of the magnetic-cloud structures embeded in the CME and to refine the borders of the event. Identifying such strahls in CMEs, which preserve properties of the low $β< 1$ coronal plasma, gives more support to the hypothesis that these populations are remnants of the hot coronal electrons that escape from the electrostatic potential of the Sun into the heliosphere.

astro-ph.SR↗

arXiv2013

The Electron Firehose and Ordinary-Mode Instabilities in Space Plasmas

The selfgenerated wave fluctuations are particularly interesting in the solar wind and magnetospheric plasmas, where Coulomb collisions are rare and cannot explain the observed states of quasi-equilibrium. Linear theory predicts that the firehose and the ordinary-mode instabilities can develop under the same conditions, confusing the role of these instabilities in conditioning the space-plasma properties. The hierarchy of these two instabilities is reconsidered here for nonstreaming plasmas with an electron temperature anisotropy $T_\parallel > T_\perp$, where $\parallel$ and $\perp$ denote directions with respect to the local mean magnetic field. In addition to the previous comparative analysis, here the entire 3D wave-vector spectrum of the competing instabilities is investigated, paying particular attention to the oblique firehose instability and the relatively poorly known ordinary-mode instability. Results show a dominance of the oblique firehose instability with a threshold lower than the parallel firehose instability and lower than the ordinary-mode instability. For larger anisotropies, the ordinary mode can grow faster, with maximum growth rates exceeding the ones of the oblique firehose instability. In contrast to previous studies that claimed a possible activity of the ordinary-mode in the small $β[< 1]$ regimes, here it is rigorously shown that only the large $β[> 1]$ regimes are susceptible to these instabilities.

astro-ph.SR↗

arXiv2012

Modeling space plasma dynamics with anisotropic Kappa distributions

Space plasmas are collisionpoor and kinetic effects prevail leading to wave fluctuations, which transfer the energy to small scales: wave-particle interactions replace collisions and enhance dispersive effects heating particles and producing suprathermal populations observed at any heliospheric distance in the solar wind. At large distances collisions are not efficient, and the selfgenerated instabilities constrain the solar wind anisotropy including the thermal core and the suprathermal components. The generalized power-laws of Kappa-type are the best fitting model for the observed distributions of particles, and a convenient mathematical tool for modeling their dynamics. But the anisotropic Kappa models are not correlated with the observations leading, in general, to inconsistent effects. This review work aims to reconcile some of the existing Kappa models with the observations.

astro-ph.SR↗

arXiv2012

In-beam spectroscopic studies of $^{44}$S nucleus

The structure of the $^{44}$S nucleus has been studied at GANIL through the one proton knock-out reaction from a $^{45}$Cl secondary beam at 42 A$\cdot$MeV. The $γ$ rays following the de-excitation of $^{44}$S were detected in flight using the 70 BaF${_2}$ detectors of the Château de Cristal array. An exhaustive $γγ$-coincidence analysis allowed an unambiguous construction of the level scheme up to an excitation energy of 3301 keV. The existence of the spherical 2$^+_2$ state is confirmed and three new $γ$-ray transitions connecting the prolate deformed 2$^+_1$ level were observed. Comparison of the experimental results to shell model calculations further supports a prolate and spherical shape coexistence with a large mixing of states built on the ground state band in $^{44}$S.

nucl-ex↗

arXiv2010

Is the Weibel instability enhanced by the suprathermal populations, or not?

The kinetic instabilities of the Weibel-type are presently invoked in a large variety of astrophysical scenarios because anisotropic plasma structures are ubiquitous in space. The Weibel instability is driven by a temperature anisotropy which is commonly modeled by a bi-axis distribution function, such as a bi-Maxwellian or a generalized bi-Kappa. Previous studies have been limited to a bi-Kappa distribution and found a suppression of this instability in the presence of suprathermal tails. In the present paper it is shown that the Weibel growth rate is rather more sensitive to the shape of the anisotropic distribution function. In order to illustrate the distinguishing properties of this instability a \emph{product-bi-Kappa distribution} is introduced, with the advantage that this distribution function enables the use of different values of the spectral index in the two directions, $κ_{\parallel} \ne κ_{\perp}$. The growth rates and the instability threshold are derived and contrasted with those for a simple bi-Kappa and a bi-Maxwellian. Thus, while the maximum growth rates reached at the saturation are found to be higher, the threshold is drastically reduced making the anisotropic product-bi-Kappa (with small kappas) highly susceptible to the Weibel instability. This effect could also rise questions on the temperature or the temperature anisotropy that seems to be not an exclusive source of free energy for this instability, and definition of these notions for such Kappa distributions must probably be reconsidered.

physics.plasm-ph↗

arXiv2010

Kappa distributions: theory and applications in space plasmas

Particle velocity distribution functions (VDF) in space plasmas often show non Maxwellian suprathermal tails decreasing as a power law of the velocity. Such distributions are well fitted by the so-called Kappa distribution. The presence of such distributions in different space plasmas suggests a universal mechanism for the creation of such suprathermal tails. Different theories have been proposed and are recalled in this review paper. The suprathermal particles have important consequences concerning the acceleration and the temperature that are well evidenced by the kinetic approach where no closure requires the distributions to be nearly Maxwellians. Moreover, the presence of the suprathermal particles take an important role in the wave-particle interactions.

physics.space-ph↗

arXiv2010

Flexible Lyapunov Functions and Applications to Fast Mechatronic Systems

The property that every control system should posses is stability, which translates into safety in real-life applications. A central tool in systems theory for synthesizing control laws that achieve stability are control Lyapunov functions (CLFs). Classically, a CLF enforces that the resulting closed-loop state trajectory is contained within a cone with a fixed, predefined shape, and which is centered at and converges to a desired converging point. However, such a requirement often proves to be overconservative, which is why most of the real-time controllers do not have a stability guarantee. Recently, a novel idea that improves the design of CLFs in terms of flexibility was proposed. The focus of this new approach is on the design of optimization problems that allow certain parameters that define a cone associated with a standard CLF to be decision variables. In this way non-monotonicity of the CLF is explicitly linked with a decision variable that can be optimized on-line. Conservativeness is significantly reduced compared to classical CLFs, which makes \emph{flexible CLFs} more suitable for stabilization of constrained discrete-time nonlinear systems and real-time control. The purpose of this overview is to highlight the potential of flexible CLFs for real-time control of fast mechatronic systems, with sampling periods below one millisecond, which are widely employed in aerospace and automotive applications.

cs.OH↗

arXiv2008

Cumulative effect of Weibel-type instabilities in counterstreaming plasmas with non-Maxwellian anisotropies

Counterstreaming plasma structures are widely present in laboratory experiments and astrophysical systems, and they are investigated either to prevent unstable modes arising in beam-plasma experiments or to prove the existence of large scale magnetic fields in astrophysical objects. Filamentation instability arises in a counterstreaming plasma and is responsible for the magnetization of the plasma. Filamentationally unstable mode is described by assuming that each of the counterstreaming plasmas has an isotropic Lorentzian (kappa) distribution. In this case, the filamentation instability growth rate can reach a maximum value markedly larger than that for a a plasma with a Maxwellian distribution function. This behaviour is opposite to what was observed for the Weibel instability growth rate in a bi-kappa plasma, which is always smaller than that obtained for a bi-Maxwellian plasma. The approach is further generalized for a counterstreaming plasma with a bi-kappa temperature anisotropy. In this case, the filamentation instability growth rate is enhanced by the Weibel effect when the plasma is hotter in the streaming direction, and the growth rate becomes even larger. These effects improve significantly the efficiency of the magnetic field generation, and provide further support for the potential role of the Weibel-type instabilities in the fast magnetization scenarios.

physics.plasm-ph↗