Particle-in-cell simulations of electron acceleration by a simple capacitative antenna in collisionless plasma

We examine the electron acceleration by a localized electrostatic potential oscillating at high frequencies by means of particle‐in‐cell (PIC) simulations, in which we apply oscillating electric fields to two neighboring simulation cells. We derive an analytic model for the direct electron heating by the externally driven antenna electric field, and we confirm that it approximates well the electron heating obtained in the simulations. In the simulations, transient waves accelerate electrons in a sheath surrounding the antenna. This increases the Larmor radii of the electrons close to the antenna, and more electrons can reach the antenna location to interact with the externally driven fields. The resulting hot electron sheath is dense enough to support strong waves that produce high‐energy sounder‐accelerated electrons (SAEs) by their nonlinear interaction with the ambient electrons. By increasing the emission amplitudes in our simulations to values that are representative for the ones of the sounder on board the OEDIPUS C (OC) satellites, we obtain electron acceleration into the energy range which is comparable to the 20 keV energies of the SAE observed by the OC mission. The emission also triggers stable electrostatic waves oscillating at frequencies close to the first harmonic of the electron cyclotron frequency. We find this to be an encouraging first step of examining SAE generation with kinetic numerical simulation codes

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

Quasi-perpendicular fast magnetosonic shock with wave precursor in collisionless plasma

A one-dimensional particle-in-cell (PIC) simulation tracks a fast magnetosonic shock over time scales comparable to an inverse ion gyrofrequency. The magnetic pressure is comparable to the thermal pressure upstream. The shock propagates across a uniform background magnetic field with a pressure that equals the thermal pressure upstream at the angle 85$^\circ$ at a speed that is 1.5 times the fast magnetosonic speed in the electromagnetic limit. Electrostatic contributions to the wave dispersion increase its phase speed at large wave numbers, which leads to a convex dispersion curve. A fast magnetosonic precursor forms ahead of the shock with a phase speed that exceeds the fast magnetosonic speed by about $\sim 30 \%$. The wave is slower than the shock and hence it is damped.Comment: 4 pages, 3 figure

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

Simulation study of the filamentation of counter-streaming beams of the electrons and positrons in plasmas

The filamentation instability driven by two spatially uniform and counter-streaming beams of charged particles in plasmas is modelled by a particle-in-cell (PIC) simulation. Each beam consists of the electrons and positrons. The four species are equally dense and they have the same temperature. The one-dimensional simulation direction is orthogonal to the beam velocity vector. The magnetic field grows spontaneously and rearranges the particles in space, such that the distributions of the electrons of one beam and the positrons of the second beam match. The simulation demonstrates that as a result no electrostatic field is generated by the magnetic field through its magnetic pressure gradient prior to its saturation. This electrostatic field would be repulsive at the centres of the filaments and limit the maximum charge and current density. The filaments of electrons and positrons in this simulation reach higher charge and current densities than in one with no positrons. The oscillations of the magnetic field strength induced by the magnetically trapped particles result in an oscillatory magnetic pressure gradient force. The latter interplays with the statistical fluctuations in the particle density and it probably enforces a charge separation, by which electrostatic waves grow after the filamentation instability has saturated.Comment: 13 pages, 8 figure

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

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

Multidimensional simulations of magnetic field amplification and electron acceleration to near-energy equipartition with ions by a mildly relativistic quasi-parallel plasma collision

The energetic electromagnetic eruptions observed during the prompt phase of gamma-ray bursts are attributed to synchrotron emissions. The internal shocks moving through the ultrarelativistic jet, which is ejected by an imploding supermassive star, are the likely source of this radiation. Synchrotron emissions at the observed strength require the simultaneous presence of powerful magnetic fields and highly relativistic electrons. We explore with one and three-dimensional relativistic particle-in-cell simulations the transition layer of a shock, that evolves out of the collision of two plasma clouds at a speed 0.9c and in the presence of a quasi-parallel magnetic field. The cloud densities vary by a factor of 10. The number densities of ions and electrons in each cloud, which have the mass ratio 250, are equal. The peak Lorentz factor of the electrons is determined in the 1D simulation, as well as the orientation and the strength of the magnetic field at the boundary of the two colliding clouds. The relativistic masses of the electrons and ions close to the shock transition layer are comparable as in previous work. The 3D simulation shows rapid and strong plasma filamentation behind the transient precursor. The magnetic field component orthogonal to the initial field direction is amplified in both simulations to values that exceed those expected from the shock compression by over an order of magnitude. The forming shock is quasi-perpendicular due to this amplification. The simultaneous presence of highly relativistic electrons and strong magnetic fields will give rise to significant synchrotron emissions.Comment: 8 pages, 5 figures. This work was presented at 21st International Conference on Numerical Simulation of Plasmas (ICNSP'09). Accepted for publication IEEE Trans. on Plasma Scienc

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