Ion acoustic waves in collisionless plasma have a phase speed determined by the adiabatic constants of electrons and protons. Typically, the isothermal equation of state is assumed for electrons, resulting in an adiabatic constant γe=1⁠, while the adiabatic equation of state with one degree of freedom is applied to protons, yielding γp=3⁠. This selection has been experimentally validated in plasmas with hot electrons and cool ions. Here, we investigate whether this remains true in particle-in-cell (PIC) simulations, which generally exhibit noise levels significantly higher than those in real plasma. By comparing the power spectrum of simulation noise to the thermal noise spectrum and the dispersion relation of ion acoustic waves, we confirm that γe=1 and γp=3 are good approximations for the adiabatic constants that determine dispersive properties of ion acoustic waves in unmagnetized PIC simulation plasma with proton temperatures well below the electron temperature. 

The evolution of a deformed subcritical fast magnetosonic shock front is compared between two two-dimensional particle-in-cell simulations with different orientations of the magnetic field relative to the simulation box. All other initial and simulation conditions are kept identical. Shock boundary oscillations are observed in the simulation where the magnetic field direction is resolved. This oscillation is caused by the reformation of the shock front. One part of the front acts as a shock, while the other functions as a magnetic piston, with both halves changing their states in antiphase. The oscillation period corresponds to the time required for one shock wave to grow as the other collapses. In contrast, the corrugated fast magnetosonic shock does not oscillate in the second simulation, where the magnetic field is oriented out of the simulation plane. This dependence on magnetic field orientation suggests that the shock oscillation is induced by magnetic tension, which is only effective in the first simulation. In both simulations, the shock perturbation does not grow over time, indicating that the shocks are stable. The potential relevance of these findings for the Alfvénic oscillations of the supercritical Earth's bow shock, detected by the MMS multi-spacecraft mission, is also discussed.

We use a two-dimensional particle-in-cell (PIC) simulation to study the propagation of subcritical fast magnetosonic shocks in electron-nitrogen plasma and their stability against an initial deformation. A slab of dense plasma launches two planar blast waves into a surrounding ambient plasma, which is permeated by a magnetic field that points out of the simulation box and is spatially uniform at the start of the simulation. One shock propagates into a spatially uniform ambient plasma. This reference shock has a Mach number of 1.75, and the heating of ions only along the shock normal compresses the ions that cross the shock to twice the upstream density. Drift instabilities lead to rapidly growing electron-cyclotron harmonic waves ahead of the location where the shock's density overshoot peaks, and to slowly growing lower-hybrid waves with a longer wavelength behind it. The second shock wave enters a perturbation layer that deforms it into a sine shape. Once the shock leaves the perturbation layer, the deformation is weakly damped and non-oscillatory, and the shock remains stable. Even without an external perturbation, and for the plasma parameters considered here, drift instabilities will cause ripples in the shock wave. These instabilities lead to a spatially and temporally varying compression of the plasma that crosses the shock.

The role of thermal fluctuations on the stimulated Raman backscattering instability is investigated by means of Vlasov and particle-in-cell (PIC) simulations in a regime of strong linear Landau damping of the Langmuir wave. The instability is initially convective and amplifies thermal noise, leading to a low-amplitude back-scattered laser sideband. Linear Landau damping of the Langmuir sideband modifies and flattens the electron velocity distribution function at the resonant velocity, leading to a gradual decrease in the Landau damping rate and an increase in the convective amplification. The Langmuir wave traps electrons resulting in a rapid nonlinear absolute instability and large amplitude flashes of backscattered light off large amplitude Langmuir waves with trapped electrons, leading to the production of hot electrons. Conditions for simulating realistic thermal noise with Vlasov and PIC simulations are discussed and defined.

Ablating a target with an ultraintense laser pulse can create a cloud of collisionless plasma. A density ramp forms, in which the plasma density decreases and the ion's mean speed increases with distance from the plasma source. Its width increases with time. Electrons lose energy in the ion's expansion direction, which gives them a temperature anisotropy. We study with one-dimensional particle-in-cell simulations the expansion of a dense plasma into a dilute one, yielding a density ramp similar to that in laser-plasma experiments and a thermal-anisotropy-driven instability. Non-propagating Weibel-type wave modes grow in the simulation with no initial magnetic field. Their magnetic field diffuses across the shock and expands upstream. Circularly polarized propagating Whistler waves grow in a second simulation, in which a magnetic field is aligned with the ion expansion direction. Both wave modes are driven by non-resonant instabilities, they have similar exponential growth rates, and they can leave the density ramp and expand into the dilute plasma. Their large magnetic amplitude should make them detectable in experimental settings.

We examine with particle-in-cell simulations how a parallel shock in pair plasma reacts to upstream waves, which are driven by escaping downstream particles. Initially, the shock is sustained in the two-dimensional simulation by a magnetic filamentation (beam-Weibel) instability. Escaping particles drive an electrostatic beam instability upstream. Modifications of the upstream plasma by these waves hardly affect the shock. In time, a decreasing density and an increasing temperature of the escaping particles quench the beam instability. A larger thermal energy along than perpendicular to the magnetic field destabilizes the pair-Alfvén mode. In the rest frame of the upstream plasma, the group velocity of the growing pair-Alfvén waves is below that of the shock and the latter catches up with the waves. Accumulating pair-Alfvén waves gradually change the shock in the two-dimensional simulation from a Weibel-type shock into an Alfvénic shock with a Mach number that is about 6 for our initial conditions.

We study with a two-dimensional particle-in-cell simulation the stability of a discontinuity or piston, which separates an electron–positron cloud from a cooler electron–proton plasma. Such a piston might be present in the relativistic jets of accreting black holes separating the jet material from the surrounding ambient plasma and when pair clouds form during an x-ray flare and expand into the plasma of the accretion disk corona. We inject a pair plasma at a simulation boundary with a mildly relativistic temperature and mean speed. It flows across a spatially uniform electron–proton plasma, which is permeated by a background magnetic field. The magnetic field is aligned with one simulation direction and oriented orthogonally to the mean velocity vector of the pair cloud. The expanding pair cloud expels the magnetic field and piles it up at its front. It is amplified to a value large enough to trap ambient electrons. The current of the trapped electrons, which is carried with the expanding cloud front, drives an electric field that accelerates protons. A solitary wave grows and changes into a piston after it saturated. Our simulations show that this piston undergoes a collisionless instability similar to a Rayleigh–Taylor instability. The undular mode grows and we observe fingers in the proton density distribution. The effect of the instability is to deform the piston but it cannot destroy it.

We study with a one-dimensional particle-in-cell simulation the expansion of a pair cloud into a magnetized electron–proton plasma as well as the formation and subsequent propagation of a tangential discontinuity that separates both plasmas. Its propagation speed takes the value that balances the magnetic pressure of the discontinuity against the thermal pressure of the pair cloud and the ram pressure of the protons. Protons are accelerated by the discontinuity to a speed that exceeds the fast magnetosonic speed by the factor of 10. A supercritical fast magnetosonic shock forms at the front of this beam. An increasing proton temperature downstream of the shock and ahead of the discontinuity leaves the latter intact. We create the discontinuity by injecting a pair cloud at a simulation boundary into a uniform electron–proton plasma, which is permeated by a perpendicular magnetic field. Collisionless tangential discontinuities in the relativistic pair jets of x-ray binaries (microquasars) are in permanent contact with the relativistic leptons of their inner cocoon, and they become the sources of radio synchrotron emissions.

When two collisionless plasma shells collide, they interpenetrate and the overlapping region may turn Weibel unstable for some values of the collision parameters. This instability grows magnetic filaments which, at saturation, have to block the incoming flow if a Weibel shock is to form. In a recent paper (Bret, J. Plasma Phys., vol. 82, 2016b, 905820403), it was found by implementing a toy model for the incoming particle trajectories in the filaments, that a strong enough external magnetic field 𝘽𝘽0 can prevent the filaments blocking the flow if it is aligned with them. Denoting by Bf the peak value of the field in the magnetic filaments, all test particles stream through them if 𝛼𝛼=B0/Bf>1/2 . Here, this result is extended to the case of an oblique external field B0 making an angle 𝜃𝜃 with the flow. The result, numerically found, is simply 𝛼𝜅𝜃𝜃𝛼>𝜅(𝜃)/cos⁡𝜃 , where 𝜅𝜃𝜅(𝜃) is of order unity. Noteworthily, test particles exhibit chaotic trajectories.

Particle-in-cell simulations of jets of electrons and positrons in an ambient electron–proton plasma have revealed an acceleration of positrons at the expense of electron kinetic energy. We show that a filamentation instability, between an unmagnetized ambient electron–proton plasma at rest and a beam of pair plasma that moves through it at a non-relativistic speed, indeed results in preferential positron acceleration. Filaments form that are filled predominantly with particles with the same direction of their electric current vector. Positron filaments are separated by electromagnetic fields from beam electron filaments. Some particles can cross the field boundary and enter the filament of the other species. Positron filaments can neutralize their net charge by collecting the electrons of the ambient plasma, while protons cannot easily follow the beam electron filaments. Positron filaments can thus be compressed to a higher density and temperature than the beam electron filaments. Filament mergers, which take place after the exponential growth phase of the instability has ended, lead to an expansion of the beam electron filaments, which amplifies the magnetic field they generate and induces an electric field in this filament. Beam electrons lose a substantial fraction of their kinetic energy to the electric field. Some positrons in the beam electron filament are accelerated by the induced electric field to almost twice their initial speed. The simulations show that a weaker electric field is induced in the positron filament and particles in this filament hardly change their speed.