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Vencels J.,KTH Royal Institute of Technology | Delzanno G.L.,Los Alamos National Laboratory | Johnson A.,Center for Mathematical Plasma Astrophysics | Peng I.B.,KTH Royal Institute of Technology | And 2 more authors.
Procedia Computer Science | Year: 2015

A spectral method for kinetic plasma simulations based on the expansion of the velocity distribution function in a variable number of Hermite polynomials is presented. The method is based on a set of non-linear equations that is solved to determine the coefficients of the Hermite expansion satisfying the Vlasov and Poisson equations. In this paper, we first show that this technique combines the fluid and kinetic approaches into one framework. Second, we present an adaptive strategy to increase and decrease the number of Hermite functions dynamically during the simulation. The technique is applied to the Landau damping and two-stream instability test problems. Performance results show 21% and 47% saving of total simulation time in the Landau and two-stream instability test cases, respectively. © The Authors. Published by Elsevier B.V.


Lazar M.,Ruhr University Bochum | Lazar M.,Center for Mathematical Plasma Astrophysics
Astronomy and Astrophysics | Year: 2012

Context. Observations regularly show low-frequency fluctuations of the interplanetary magnetic field (IMF), which are attributed to the electromagnetic ion-cyclotron (EMIC) waves generated either locally and self-consistently by the kinetic anisotropies of ions, or closer to the Sun (through a nonlinear cascade from long to short wavelengths), and transported by the super-Alfvenic solar wind. As a back reaction, ions can be pitch-angle scattered and accelerated, leading to the observed suprathermal populations, which are invariably anisotropic and are well described by the generalized Kappa models. Aims. A refined analysis is proposed for the EMIC wave instability as one of the most plausible constraints for the proton temperature anisotropy T p, < T p, where and denote directions relative to the stationary IMF. In the context of a strong, but not clear competition with the mirror instability that can develop in the same conditions, an advanced Kappa model is expected to provide the first realistic insights into the EMIC instability conditions in the solar wind. Methods. Because the solar wind is a poor-collisional plasma, the dispersion/stability formalism is based on the fundamental kinetic Vlasov-Maxwell equations for an nonthermal bi-Kappa distributed plasma. EMIC solutions are derived exactly numerically, providing accurate physical correlations between the maximum growth rates and the instability threshold conditions, which are here derived for the full range of values of the plasma beta, including the solar wind and magnetospheric plasma conditions. Results. The lowest thresholds (close to the marginal stability), which are the most relevant for the instability conditions, decrease with the increase in density of suprathermal populations. This is contrary to what was found before in a less general model, but it is fully predicted by the enhanced fluctuations of this instability for sufficiently low temperature anisotropies. These results furthermore support a fast and efficient EMIC instability involving the relaxation of kinetic anisotropies and (re)heating plasma particles. © 2012 ESO.


Ibscher D.,Ruhr University Bochum | Lazar M.,Ruhr University Bochum | Lazar M.,Center for Mathematical Plasma Astrophysics | Michno M.J.,Ruhr University Bochum | Schlickeiser R.,Ruhr University Bochum
Physics of Plasmas | Year: 2013

The ordinary mode instability can be driven by drifting bi-Maxwellian plasma particle distributions with and without temperature anisotropy. Here, the linear instability analysis is generalized for realistic settings, when the plasma streams are magnetized and hot enough. The new parametrization proposed in this study enables a better understanding of the interplay of counterstreaming and temperature anisotropy, providing the derivation of new regimes of the ordinary mode instability. Accurate analytical forms are derived for the instability conditions for general values of the temperature anisotropy, the streaming velocity, and the parallel plasma beta. To keep the analysis straightforward, the role of ions is minimized. © 2013 American Institute of Physics.


Keppens R.,Center for Mathematical Plasma Astrophysics | Porth O.,University of Leeds | Galsgaard K.,Copenhagen University | Frederiksen J.T.,Copenhagen University | And 3 more authors.
Physics of Plasmas | Year: 2013

In this paper, we address the long-term evolution of an idealised double current system entering reconnection regimes where chaotic behavior plays a prominent role. Our aim is to quantify the energetics in high magnetic Reynolds number evolutions, enriched by secondary tearing events, multiple magnetic island coalescence, and compressive versus resistive heating scenarios. Our study will pay particular attention to the required numerical resolutions achievable by modern (grid-adaptive) computations, and comment on the challenge associated with resolving chaotic island formation and interaction. We will use shock-capturing, conservative, grid-adaptive simulations for investigating trends dominated by both physical (resistivity) and numerical (resolution) parameters, and confront them with (visco-)resistive magnetohydrodynamic simulations performed with very different, but equally widely used discretization schemes. This will allow us to comment on the obtained evolutions in a manner irrespective of the adopted discretization strategy. Our findings demonstrate that all schemes used (finite volume based shock-capturing, high order finite differences, and particle in cell-like methods) qualitatively agree on the various evolutionary stages, and that resistivity values of order 0.001 already can lead to chaotic island appearance. However, none of the methods exploited demonstrates convergence in the strong sense in these chaotic regimes. At the same time, nonperturbed tests for showing convergence over long time scales in ideal to resistive regimes are provided as well, where all methods are shown to agree. Both the advantages and disadvantages of specific discretizations as applied to this challenging problem are discussed. © 2013 AIP Publishing LLC.


Lapenta G.,Center for Mathematical Plasma Astrophysics | Ashour-Abdalla M.,University of California at Los Angeles | Walker R.J.,University of California at Los Angeles | El Alaoui M.,University of California at Los Angeles
Geophysical Research Letters | Year: 2016

Ion heating during a substorm on 15 February 2008, starting at 0348UT, is studied with a new approach recently described in Ashour-Abdalla et al. (2015). The general conditions of the magnetotail are obtained from a global magnetohydrodynamic (MHD) model and are used to drive a full kinetic particle-in-cell (PIC) simulation of a 3-D region of the tail. Within the kinetic box, the ions, the electrons, and the fields evolve self-consistently. The large scales are captured by the MHD model and the small scales by the PIC model based on the MHD state. This approach is used to study ion heating. Different heating mechanisms were analyzed by examining the velocity distributions at different locations. In the x direction heating occurs as the reconnection-generated ion jet interacts with the environment in which it propagates. The heating is found mostly in the separatrices and increases downstream of the reconnection region. In the y direction the heating is less intense and is found near the dipolarization fronts. It occurs as ions become magnetized and gyrotropize the distribution function. In addition, ions can be heated in the y direction by the reconnection electric field near the reconnection site. In the z direction the ions are heated by the formation of beams moving along z between the separatrices. ©2015. American Geophysical Union.


Felten T.,Ruhr University Bochum | Schlickeiser R.,Ruhr University Bochum | Yoon P.H.,University of Maryland University College | Yoon P.H.,Kyung Hee University | Lazar M.,Center for Mathematical Plasma Astrophysics
Physics of Plasmas | Year: 2013

General expressions for the electromagnetic fluctuation spectra in unmagnetized plasmas are derived using fully relativistic dispersion functions and form factors for the important class of isotropic plasma particle distribution functions including in particular relativistic Maxwellian distributions. In order to obtain fluctuation spectra valid in the entire complex frequency plane, the proper analytical continuations of the unmagnetized form factors and dispersion functions are presented. The results are illustrated for the important special case of isotropic Maxwellian particle distribution functions providing in particular the thermal fluctuations of aperiodic modes. No restriction to the plasma temperature value is made, and the electromagnetic fluctuation spectra of ultrarelativistic thermal plasmas are calculated. The fully relativistic calculations also provide more general results in the limit of nonrelativistic plasma temperatures being valid in the entire complex frequency plane. They complement our earlier results in paper I and III of this series for negative values of the imaginary part of the frequency. A new collective, transverse, damped aperiodic mode with the damping rate γ ∝ - k - 5 / 3 is discovered in an isotropic thermal electron-proton plasma with nonrelativistic temperatures. © 2013 AIP Publishing LLC.


Liang H.,University of California at Los Angeles | Ashour-Abdalla M.,University of California at Los Angeles | Lapenta G.,Center for Mathematical Plasma Astrophysics | Walker R.J.,University of California at Los Angeles
Journal of Geophysical Research A: Space Physics | Year: 2016

Spacecraft observations near a magnetotail X line show that oxygen (O+) ions are minor species during nonstorm substorms, but they can become major species during some of the storm time substorms. Dipolarization fronts (DFs), which are characterized by a sharp increase northward magnetic field in the magnetotail, are commonly observed during magnetospheric substorms. In this study, we investigated the O+ effects on DFs and the reconnection rate during magnetotail reconnection. We used a 2.5-D implicit particle-in-cell simulation in a 2-D Harris current sheet in the presence of H+ and O+ ions. Simulation runs with equal number densities of O+ and H+ (O+ run) and with pure H+ ion species (H+ run) were performed. Comparing the two different runs, we found that both the reconnection rate and the DF speed in the O+ run were much less than those in the H+ run. By studying the force balance and plasma composition at the DF, we found that the outflow magnetic flux and DF propagation were encumbered by the current sheet O+ inertia, which reduced the DF speed and delayed the reconnection rate in the O+ run. We also found an ambipolar electric field in the O+ run due to the different inflow and outflow speeds of O+ and electrons in the O+ diffusion region. As a result, this ambipolar electric field induced O+ drag on the convective magnetic field in the O+ diffusion region. The small reconnection rate determined in the O+ run can be attributed to the current sheet inertia and the O+ drag on the convective magnetic flux. ©2016. American Geophysical Union.


Eliasson B.,University of Strathclyde | Lazar M.,Center for Mathematical Plasma Astrophysics | Lazar M.,Ruhr University Bochum
Physics of Plasmas | Year: 2015

This paper presents a numerical study of the linear and nonlinear evolution of the electromagnetic electron-cyclotron (EMEC) instability in a bi-Kappa distributed plasma. Distributions with high energy tails described by the Kappa power-laws are often observed in collision-less plasmas (e.g., solar wind and accelerators), where wave-particle interactions control the plasma thermodynamics and keep the particle distributions out of Maxwellian equilibrium. Under certain conditions, the anisotropic bi-Kappa distribution gives rise to plasma instabilities creating low-frequency EMEC waves in the whistler branch. The instability saturates nonlinearly by reducing the temperature anisotropy until marginal stability is reached. Numerical simulations of the Vlasov-Maxwell system of equations show excellent agreement with the growth-rate and real frequency of the unstable modes predicted by linear theory. The wave-amplitude of the EMEC waves at nonlinear saturation is consistent with magnetic trapping of the electrons. © 2015 Author(s).


Lazar M.,Center for Mathematical Plasma Astrophysics | Lazar M.,Ruhr University Bochum | Poedts S.,Center for Mathematical Plasma Astrophysics | Michno M.J.,Ruhr University Bochum
Astronomy and Astrophysics | Year: 2013

Context. Recent studies of the electromagnetic electron whistler-cyclotron instability in anisotropic bi-Kappa distributed plasmas claim that the instability threshold conditions do not depend on the power index, êe, of the electron distribution function, but that the maximum growth rate (ãm) strongly depends on this parameter. But these two statements contradict each other because the instability threshold conditions are derived with respect to the threshold levels of the maximum growth rates (e.g.,γm/ω = 10-1, 10-2, etc.). Aims. This paper proposes to clarify this inconsistency, refining the analysis of the electron-whistler cyclotron instability. In anisotropic plasmas far from Maxwellian equilibrium, this instability represents one of the most plausible constraints for the electron temperature anisotropy Te,Te,(where and denote directions relative to the local stationary magnetic field). Methods. In the context of a suprathermal solar wind, where the electron populations are well fitted by the advanced Kappa distribution functions, these models are expected to provide a more realistic description for the critical stability conditions. The unstable solutions are derived exactly numerically, providing accurate physical correlations between the maximum growth rates and the threshold conditions. Results. Thresholds of the temperature anisotropy are derived for the full range of values of the plasma beta including both the solar wind and magnetospheric plasma conditions. The lowest thresholds, which are the most relevant for the marginal stability, are found to decrease with the increase in density of the suprathermal populations. This result is correlated with an opposite effect on the corresponding growth rates (at low anisotropies), because their maximum values are enhanced in the presence of suprathermal electrons. The new marginal thresholds calculated with a bi-Kappa model are expected to provide better predictions for the limits of the temperature anisotropy in the solar wind. © 2013 ESO.


Goossens M.,Center for Mathematical Plasma Astrophysics | Van Doorsselaere T.,Center for Mathematical Plasma Astrophysics | Soler R.,University of the Balearic Islands | Verth G.,University of Sheffield
Astrophysical Journal | Year: 2013

Recently, a significant amount of transverse wave energy has been estimated propagating along solar atmospheric magnetic fields. However, these estimates have been made with the classic bulk Alfvén wave model which assumes a homogeneous plasma. In this paper, the kinetic, magnetic, and total energy densities and the flux of energy are computed for transverse MHD waves in one-dimensional cylindrical flux tube models with a piecewise constant or continuous radial density profile. There are fundamental deviations from the properties for classic bulk Alfvén waves. (1) There is no local equipartition between kinetic and magnetic energy. (2) The flux of energy and the velocity of energy transfer have, in addition to a component parallel to the magnetic field, components in the planes normal to the magnetic field. (3) The energy densities and the flux of energy vary spatially, contrary to the case of classic bulk Alfvén waves. This last property has the important consequence that the energy flux computed with the well known expression for bulk Alfvén waves could overestimate the real flux by a factor in the range 10-50, depending on the flux tube equilibrium properties. © 2013. The American Astronomical Society. All rights reserved.

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