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By means of a particle-in-cell (PIC) simulation, we study the interaction between a uniform magnetized ambient electron-proton plasma at rest and an unmagnetized pair plasma, which we inject at one simulation boundary with a mildly relativistic mean speed and temperature. The magnetic field points out of the simulation plane. The injected pair plasma expels the magnetic field and piles it up at its front. It traps ambient electrons and drags them across the protons. An electric field grows, which accelerates protons into the pair cloud's expansion direction. This electromagnetic pulse separates the pair cloud from the ambient plasma. Electrons and positrons, which drift in the pulse's nonuniform field, trigger an instability that disrupts the current sheet ahead of the pulse. The wave vector of the growing perturbation is orthogonal to the magnetic field direction and magnetic tension cannot stabilize it. The electromagnetic pulse becomes permeable for pair plasma, which forms new electromagnetic pulses ahead of the initial one. A transition layer develops with a thickness of a few proton skin depths, in which protons and positrons are accelerated by strong electromagnetic fields. Protons form dense clumps surrounded by a strong magnetic field. The thickness of the transition layer grows less rapidly than we would expect from the typical speeds of the pair plasma particles and the latter transfer momentum to protons; hence, the transition layer acts as a discontinuity, separating the pair plasma from the ambient plasma. Such a discontinuity is an important building block for astrophysical pair plasma jets., Accepted for publication in Physics of Plasmas, 13 pages, 15 figures

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 are 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 collision-less 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., 13 pages, 11 figures, accepted for publication in Physics of Plasmas

We study with a one-dimensional particle-in-cell (PIC) 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 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 its inner cocoon and they become sources of radio synchrotron emissions., Comment: 10 pages, 11 figures, accepted for publication in Physics of Plasmas

The interaction between relativistic ion beams, electrostatic waves and particles in plasmas is studied numerically. This beam-particle interaction is important for the acceleration of electrons above the threshold, where they can perform Fermi acceleration across shocks perpendicular to the magnetic field direction. The electrons form Bernstein–Greene–Kruskal (BGK) modes, which are unstable due to a sideband instability. This process heats the electrons to relativistic temperatures and the electrons finally attain a flat-top momentum distribution with exponentially decreasing tails of the momentum distribution function. A scaling law, depending on the ion beam speed, is found for the electron distribution function. Furthermore, in the fully nonlinear phase, ion phase space vortices, or proton BGK modes are formed in the beam, which continue to interact with the electrons after the electron BGK modes have collapsed.

The expansion of a dense plasma into a dilute plasma across an initially uniform perpendicular magnetic field is followed with a one-dimensional particle-in-cell (PIC) simulation over MHD time scales. The dense plasma expands in the form of a fast rarefaction wave. The accelerated dilute plasma becomes separated from the dense plasma by a tangential discontinuity at its back. A fast magnetosonic shock with the Mach number 1.5 forms at its front. Our simulation demonstrates how wave dispersion widens the shock transition layer into a train of nonlinear fast magnetosonic waves., Comment: 5 pages, 4 figures, accepted for publication in Physics of Plasmas

The frequency maxima of electron cyclotron harmonic (ECH) waves provide strong responses to sounding in various plasma regimes in the solar system. The frequency maxima correspond to waves for which the group velocity and thus the energy propagation velocity in the plasma frame of reference is zero. A particle-in-cell (PIC) code is employed to show that the propagation of wave energy at a non-zero velocity, necessary to couple energy from a stationary antenna to the plasma, is accomplished by propagating wave precursors. The undamped waves at the frequency maxima of the ECH branches are nonpropagating hence the waves remain localized. It is demonstrated that the nonpropagating waves, built up by the wave precursors, are standing waves. The standing wave generation is followed from the linear to nonlinear regimes. For nonlinear emission amplitudes the emission causes a plasma density depletion close to the antenna. The depletion is shown to trigger a modulational instability in which the ECH wave collapses...

The plasma dynamics resulting from the simultaneous impact, of two equal, ultra-intense laser pulses, in two spatially separated spots, onto a dense target is studied via particle-in-cell (PIC) simulations. The simulations show that electrons accelerated to relativistic speeds, cross the target and exit at its rear surface. Most energetic electrons are bound to the rear surface by the ambipolar electric field and expand along it. Their current is closed by a return current in the target, and this current configuration generates strong surface magnetic fields. The two electron sheaths collide at the midplane between the laser impact points. The magnetic repulsion between the counter-streaming electron beams separates them along the surface normal direction, before they can thermalize through other beam instabilities. This magnetic repulsion is also the driving mechanism for the beam-Weibel (filamentation) instability, which is thought to be responsible for magnetic field growth close to the internal shocks of gamma-ray burst (GRB) jets. The relative strength of this repulsion compared to the competing electrostatic interactions, which is evidenced by the simulations, suggests that the filamentation instability can be examined in an experimental setting., 7 pages, 5 figures

A 2D particle simulation models the collision of two electron-ion plasma clouds along a quasi-parallel magnetic field. The collision speed is 0.9c and the density ratio 10. A current sheet forms at the front of the dense cloud, in which the electrons and the magnetic field reach energy equipartition with the ions. A structure composed of a solenoidal and a toroidal magnetic field grows in this sheet. It resembles that in the cross-section of the torus of a force-free spheromak, which may provide the coherent magnetic fields in gamma-ray burst (GRB) jets needed for their prompt emissions.

The electromagnetic instabilities driven by a relativistic electron beam, which moves through a magnetized plasma, are analyzed with a cold two-fluid model. It allows for any angle θB between the beam velocity vector and the magnetic field vector and considers any orientation of the wavevector in the two-dimensional plane spanned by these two vectors. If the magnetic field is strong, the two-stream instability dominates if θB=0 and the oblique modes grow faster at larger θB. A weaker magnetic field replaces the two-stream modes with oblique modes as the fastest-growing waves. The threshold value separating both magnetic regimes is estimated. A further dimensionless parameter is identified, which determines whether or not the wavevector of the most unstable wave is changed continuously, as θB is varied from 0 to π∕2. The fastest growing modes are always found for a transverse propagation of the beam with θB=π∕2, irrespective of the magnetic field strength.

A relativistic fluid model is implemented to assess the role of the ions motion in the linear phase of relativistic beam plasma electromagnetic instabilities. The all unstable wave vector spectrum is investigated, allowing us to assess how ion motions modify the competition between every possible instability. Beam densities up to the plasma one are considered. Due to the fluid approach, the temperatures must remain small, i.e., nonrelativistic. In the cold limit, ions motion affect the most unstable mode when the beam gamma factor γb≳αM∕mZi, α being the beam to plasma density ratio, Zi the ion charge, M their mass, and m the electrons. The return current plays an important role by prompting Buneman-type instabilities which remain in the nonrelativistic regime up to high beam densities. Nonrelativistic temperatures only slightly affect these conclusions, except in the diluted beam regime where they can stabilize the Buneman modes.

Particle-in-cell simulations confirm here that a mixed plasma mode is the fastest growing when a highly relativistic tenuous electron-proton beam interacts with an unmagnetized plasma. The mixed modes grow faster than the filamentation and two-stream modes in simulations with beam Lorentz factors Gamma of 4, 16, and 256, and are responsible for thermalizing the electrons. The mixed modes are followed to their saturation for the case of Gamma=4 and electron phase space holes are shown to form in the bulk plasma, while the electron beam becomes filamentary. The initial saturation is electrostatic in nature in the considered one- and two-dimensional geometries. Simulations performed with two different particle-in-cell simulation codes evidence that a finite grid instability couples energy into high-frequency electromagnetic waves, imposing simulation constraints.

The temperature-dependent fluid model from Phys. Plasmas 13, 042106 (2006) is expanded in order to explore the oblique electromagnetic instabilities, which are driven by a hot relativistic electron beam that is interpenetrating a hot and magnetized plasma. The beam velocity vector is parallel to the magnetic-field direction. The results are restricted to nonrelativistic temperatures. The growth rates of all instabilities but the two-stream instability can be reduced by a strong magnetic field so that the distribution of unstable waves becomes almost one dimensional. For high beam densities, highly unstable oblique modes dominate the spectrum of unstable waves as long as omega(c)/omega(p)less than or similar to 2 gamma(3/2)(b), where omega(c) is the electron gyrofrequency, omega(p) is the electron plasma frequency, and gamma(b) is the relativistic factor of the beam. A uniform stabilization over the entire k space cannot be achieved.

The ever increasing performance of supercomputers is now enabling kinetic simulations of extreme astrophysical and laser produced plasmas. Three-dimensional particle-in-cell (PIC) simulations of relativistic shocks have revealed highly filamented spatial structures and their ability to accelerate particles to ultrarelativistic speeds. However, these PIC simulations have not yet revealed mechanisms that could produce particles with tera-electron volt energies and beyond. In this work, PIC simulations in one dimension (1D) of the foreshock region of an internal shock in a gamma ray burst are performed to address this issue. The large spatiotemporal range accessible to a 1D simulation enables the self-consistent evolution of proton phase space structures that can accelerate particles to giga-electron volt energies in the jet frame of reference, and to tens of tera-electron volt in the Earth's frame of reference. One potential source of ultrahigh energy cosmic rays may thus be the thermalization of relativistically moving plasma.

The interaction of electrons with strong electrostatic waves and an external magnetic field, which is oriented obliquely to the wave vector, leads to stochastic acceleration and acceleration by the cross-field transport of trapped electrons. This wave-particle interaction involves three velocity components of the electrons and, for a plane wave, one spatial position. The phase-space evolution is also affected by nonlinear oscillations in the amplitude of the saturated wave, and the system becomes explicitly time dependent. Here, the wave-particle interactions are investigated with a particle-in-cell simulation, and the results are visualized by examining orbits of individual electrons and also time-evolving phase-space structures. Two clearly distinct electron populations are identified, one due to cross-field transport and the other due to stochastic interactions, which are robust against growing secondary modes.