Electric field generation by the electron beam filamentation instability: Filament size effects

The filamentation instability (FI) of counter-propagating beams of electrons is modelled with a particle-in-cell simulation in one spatial dimension and with a high statistical plasma representation. The simulation direction is orthogonal to the beam velocity vector. Both electron beams have initially equal densities, temperatures and moduli of their nonrelativistic mean velocities. The FI is electromagnetic in this case. A previous study of a small filament demonstrated, that the magnetic pressure gradient force (MPGF) results in a nonlinearly driven electrostatic field. The probably small contribution of the thermal pressure gradient to the force balance implied, that the electrostatic field performed undamped oscillations around a background electric field. Here we consider larger filaments, which reach a stronger electrostatic potential when they saturate. The electron heating is enhanced and electrostatic electron phase space holes form. The competition of several smaller filaments, which grow simultaneously with the large filament, also perturbs the balance between the electrostatic and magnetic fields. The oscillations are damped but the final electric field amplitude is still determined by the MPGF.Comment: 14 pages, 10 plots, accepted for publication in Physica Script

Diffusive radiation in Langmuir turbulence produced by jet shocks

Anisotropic distributions of charged particles including two-stream distributions give rise to generation of either stochastic electric fields (in the form of Langmuir waves, Buneman instability) or random quasi-static magnetic fields (Weibel and filamentation instabilities) or both. These two-stream instabilities are known to play a key role in collisionless shock formation, shock-shock interactions, and shock-induced electromagnetic emission. This paper applies the general non-perturbative stochastic theory of radiation to study electromagnetic emission produced by relativistic particles, which random walk in the stochastic electric fields of the Langmuir waves. This analysis takes into account the cumulative effect of uncorrelated Langmuir waves on the radiating particle trajectory giving rise to angular diffusion of the particle, which eventually modifies the corresponding radiation spectra. We demonstrate that the radiative process considered is probably relevant for emission produced in various kinds of astrophysical jets, in particular, prompt gamma-ray burst spectra, including X-ray excesses and prompt optical flashes.Comment: 9 pages, 5 figures, MNRAS, accepte

Shock creation and particle acceleration driven by plasma expansion into a rarefied medium

The expansion of a dense plasma through a more rarefied ionised medium is a phenomenon of interest in various physics environments ranging from astrophysics to high energy density laser- matter laboratory experiments. Here this situation is modeled via a 1D Particle-In-Cell simulation; a jump in the plasma density of a factor of 100 is introduced in the middle of an otherwise equally dense electron-proton plasma with an uniform proton and electron temperature of 10eV and 1keV respectively. The diffusion of the dense plasma, through the rarified one, triggers the onset of different nonlinear phenomena such as a strong ion-acoustic shock wave and a rarefaction wave. Secondary structures are detected, some of which are driven by a drift instability of the rarefaction wave. Efficient proton acceleration occurs ahead of the shock, bringing the maximum proton velocity up to 60 times the initial ion thermal speed

The filamentation instability driven by warm electron beams: Statistics and electric field generation

The filamentation instability of counterpropagating symmetric beams of electrons is examined with 1D and 2D particle-in-cell (PIC) simulations, which are oriented orthogonally to the beam velocity vector. The beams are uniform, warm and their relative speed is mildly relativistic. The dynamics of the filaments is examined in 2D and it is confirmed that their characteristic size increases linearly in time. Currents orthogonal to the beam velocity vector are driven through the magnetic and electric fields in the simulation plane. The fields are tied to the filament boundaries and the scale size of the flow-aligned and the perpendicular currents are thus equal. It is confirmed that the electrostatic and the magnetic forces are equally important, when the filamentation instability saturates in 1D. Their balance is apparently the saturation mechanism of the filamentation instability for our initial conditions. The electric force is relatively weaker but not negligible in the 2D simulation, where the electron temperature is set higher to reduce the computational cost. The magnetic pressure gradient is the principal source of the electrostatic field, when and after the instability saturates in the 1D simulation and in the 2D simulation.Comment: 10 pages, 6 figures, accepted by the Plasma Physics and Controlled Fusion (Special Issue EPS 2009

Particle-in-cell simulation of a mildly relativistic collision of an electron-ion plasma carrying a quasi-parallel magnetic field: Electron acceleration and magnetic field amplification at supernova shocks

Plasma processes close to SNR shocks result in the amplification of magnetic fields and in the acceleration of electrons, injecting them into the diffusive acceleration mechanism. The acceleration of electrons and the B field amplification by the collision of two plasma clouds, each consisting of electrons and ions, at a speed of 0.5c is investigated. A quasi-parallel guiding magnetic field, a cloud density ratio of 10 and a plasma temperature of 25 keV are considered. A quasi-planar shock forms at the front of the dense plasma cloud. It is mediated by a circularly left-hand polarized electromagnetic wave with an electric field component along the guiding magnetic field. Its propagation direction is close to that of the guiding field and orthogonal to the collision boundary. It has a low frequency and a wavelength that equals several times the ion inertial length, which would be indicative of a dispersive Alfven wave close to the ion cyclotron resonance frequency of the left-handed mode (ion whistler), provided that the frequency is appropriate. However, it moves with the super-alfvenic plasma collision speed, suggesting that it is an Alfven precursor or a nonlinear MHD wave such as a Short Large-Amplitude Magnetic Structure (SLAMS). The growth of the magnetic amplitude of this wave to values well in excess of those of the quasi-parallel guiding field and of the filamentation modes results in a quasi-perpendicular shock. We present evidence for the instability of this mode to a four wave interaction. The waves developing upstream of the dense cloud give rise to electron acceleration ahead of the collision boundary. Energy equipartition between the ions and the electrons is established at the shock and the electrons are accelerated to relativistic speeds.Comment: 16 pages, 18 figures, Accepted for publication by Astron & Astrophy

Systemic-risk Dilemmas Emerging from Reactive Investments

The stability and prosperity of human societies depend on cooperative exchanges at many levels. While the emergence and stability of such exchanges has been studied extensively, the majority of these investigations have relied on the prisoner’s dilemma game. However, cooperative exchanges are typically more complex and involve decisions about continuous investments, instead of simple choices between cooperation and non-cooperation. Our aim here is to understand the factors promoting the emergence and stability of cooperative exchanges based on continuous investments, performed by individuals with reactive strategies. Through such strategies, agents continuously re-evaluate and adjust their investments according to the gains obtained from an exchange. Such reactivity provides a natural safeguard against exploitation, as it allows agents to fade out unprofitable investments. Here we show that these benefits of reactivity, which are so crucial at the level of agents, exact a high price at the level of the society, by exacerbating systemic risk. In particular, the spread of exuberant investors causes the emergence of boom-bust cycles, characterized by an increase in investment levels followed by a decline. We demonstrate that an optimal level of reactivity can stabilize cooperation while offering safeguards against both exploitation and exuberance. We also study three other fundamental factors: the pace of innovation enhancing strategy diversity, the modularity arising from dividing the collective of agents into smaller groups with sparse interactions between them, and the heterogeneity of such groups structuring social exchanges. We demonstrate how intermediate levels of these additional factors are optimal in terms of stabilizing cooperation while minimizing systemic risk. Our study identifies generally applicable countermeasures against ubiquitous threats to the stability of cooperative exchanges, with a view towards facilitating the design of corresponding future policies

PIC Simulations of the Temperature Anisotropy-Driven Weibel Instability: Analyzing the perpendicular mode

An instability driven by the thermal anisotropy of a single electron species is investigated in a 2D particle-in-cell (PIC) simulation. This instability is the one considered by Weibel and it differs from the beam driven filamentation instability. A comparison of the simulation results with analytic theory provides similar exponential growth rates of the magnetic field during the linear growth phase of the instability. We observe in accordance with previous works the growth of electric fields during the saturation phase of the instability. Some components of this electric field are not accounted for by the linearized theory. A single-fluid-based theory is used to determine the source of this nonlinear electric field. It is demonstrated that the magnetic stress tensor, which vanishes in a 1D geometry, is more important in this 2-dimensional model used here. The electric field grows to an amplitude, which yields a force on the electrons that is comparable to the magnetic one. The peak energy density of each magnetic field component in the simulation plane agrees with previous estimates. Eddy currents develop, which let the amplitude of the third magnetic field component grow, which is not observed in a 1D simulation.Comment: accepted by Plasma Physics and Controlled Fusio

How large can the electron to proton mass ratio be in Particle-In-Cell simulations of unstable systems?

Particle-in-cell (PIC) simulations are widely used as a tool to investigate instabilities that develop between a collisionless plasma and beams of charged particles. However, even on contemporary supercomputers, it is not always possible to resolve the ion dynamics in more than one spatial dimension with such simulations. The ion mass is thus reduced below 1836 electron masses, which can affect the plasma dynamics during the initial exponential growth phase of the instability and during the subsequent nonlinear saturation. The goal of this article is to assess how far the electron to ion mass ratio can be increased, without changing qualitatively the physics. It is first demonstrated that there can be no exact similarity law, which balances a change of the mass ratio with that of another plasma parameter, leaving the physics unchanged. Restricting then the analysis to the linear phase, a criterion allowing to define a maximum ratio is explicated in terms of the hierarchy of the linear unstable modes. The criterion is applied to the case of a relativistic electron beam crossing an unmagnetized electron-ion plasma.Comment: To appear in Physics of Plasma

The origin of green icebergs in Antarctica

A comparison of samples from a translucent green iceberg with a core from the Ronne Ice Shelf revealed an excellent agreement in isotopic composition, crystal structure, and incorporated sediment particles. Marine shelf ice which constitutes the basal portion of some ice shelves is considered to be the source of green icebergs. It most likely results from "ice pump" processes which produce large amounts of ice platelets in the water column beneath ice shelves. These subsequently accumulate and become compacted into bubble-free, desalinated ice. Iceberg and drift-buoy trajectories indicate that green icebergs observed in the Weddell Sea originate from the Amery Ice Shelf rather than from the Ronne Ice Shelf, although the latter ice shelf is also a potential source