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

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

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

Oligomorphic Dynamics for Analyzing the Quantitative Genetics of Adaptive Speciation

Ecological interaction, including competition for resources, often causes frequency-dependent disruptive selection, which, when accompanied by reproductive isolation, may act as driving forces of adaptive speciation. While adaptive dynamics models have added new perspectives to our understanding of the ecological dimensions of speciation processes, it remains an open question how best to incorporate and analyze genetic detail in such models. Conventional approaches, based on quantitative genetics theory, typically assume a unimodal character distribution and examine how its moments change over time. Such approximations inevitably fail when a character distribution becomes multimodal. Here, we propose a new approximation, oligomorphic dynamics, to the quantitative genetics of populations that include several morphs and that therefore exhibit multiple peaks in their character distribution. To this end we first decompose the character distribution into a sum of unimodal distributions corresponding to individual morphs. Characterizing these morphs by their frequency (fraction of individuals belonging to each morph), position (mean character of each morph), and width (standard deviation of each morph) we then derive the coupled eco-evolutionary dynamics of morphs through a double Taylor expansion. We show that the demographic, convergence, and evolutionary stability of a populations character distribution correspond, respectively, to the asymptotic stability of frequencies, positions, and widths under the oligomorphic dynamics introduced here. As first applications of oligomorphic dynamics theory we analytically derive the effects (a) of the strength of disruptive selection on waiting times until speciation, (b) of mutation on conditions for speciation, and (c) of the fourth moments of competition kernels on patterns of speciation

Resource heterogeneity can facilitate cooperation

Although social structure is known to promote cooperation, by locally exposing selfish agents to their own deeds, studies to date assumed that all agents have access to the same level of resources. This is clearly unrealistic. Here we find that cooperation can be maintained when some agents have access to more resources than others. Cooperation can then emerge even in populations in which the temptation to defect is so strong that players would act fully selfishly if their resources were distributed uniformly. Resource heterogeneity can thus be crucial for the emergence and maintenance of cooperation. We also show that resource heterogeneity can hinder cooperation once the temptation to defect is significantly lowered. In all cases, the level of cooperation can be maximized by managing resource heterogeneity

Disparate Maturation Adaptations to Size-dependent Mortality

Body size is an important determinant of resource use, fecundity, and mortality risk. Evolution of maturation size in response to size-dependent selection is thus a fundamental part of life-history theory. Increased mortality among small individuals has previously been predicted to cause larger maturation size, whereas increased mortality among large individuals is expected to have the opposite effect. Here we use a continuously size-structured model to demonstrate that, contrary to these widespread expectations, increased mortality among small individuals can have three alternative effects: maturation size may increase, decrease, or become evolutionarily bistable. We show that such complex responses must be reckoned with whenever mortality is size-dependent, growth is indeterminate, reproduction impairs growth, and fecundity increases with size. Predicting adaptive responses to altered size-dependent mortality is thus inherently difficult, since, as demonstrated here, such mortality can not only reverse the direction of adaptation, but also cause abrupt shifts in evolutionarily stable maturation sizes

Shocks in unmagnetized plasma with a shear flow: Stability and magnetic field generation

A pair of curved shocks in a collisionless plasma is examined with a two-dimensional particle-in-cell (PIC) simulation. The shocks are created by the collision of two electron-ion clouds at a speed that exceeds everywhere the threshold speed for shock formation. A variation of the collision speed along the initially planar collision boundary, which is comparable to the ion acoustic speed, yields a curvature of the shock that increases with time. The spatially varying Mach number of the shocks results in a variation of the downstream density in the direction along the shock boundary. This variation is eventually equilibrated by the thermal diffusion of ions. The pair of shocks is stable for tens of inverse ion plasma frequencies. The angle between the mean flow velocity vector of the inflowing upstream plasma and the shock's electrostatic field increases steadily during this time. The disalignment of both vectors gives rise to a rotational electron flow, which yields the growth of magnetic field patches that are coherent over tens of electron skin depths.Comment: 10 pages, 10 figures accepted for publication in Physics of Plasma