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1.	Ahmed, Hamad, et al. (författare) Experimental Observation of Thin-shell Instability in a Collisionless Plasma 2017 Ingår i: Astrophysical Journal Letters. - : Institute of Physics Publishing (IOPP). - 2041-8205 .- 2041-8213. ; 834:2 Tidskriftsartikel (refereegranskat)abstract We report on the experimental observation of the instability of a plasma shell, which formed during the expansion of a laser-ablated plasma into a rarefied ambient medium. By means of a proton radiography technique, the evolution of the instability is temporally and spatially resolved on a timescale much shorter than the hydrodynamic one. The density of the thin shell exceeds that of the surrounding plasma, which lets electrons diffuse outward. An ambipolar electric field grows on both sides of the thin shell that is antiparallel to the density gradient. Ripples in the thin shell result in a spatially varying balance between the thermal pressure force mediated by this field and the ram pressure force that is exerted on it by the inflowing plasma. This mismatch amplifies the ripples by the same mechanism that drives the hydrodynamic nonlinear thin-shell instability (NTSI). Our results thus constitute the first experimental verification that the NTSI can develop in colliding flows.
2.	Bret, Antoine, et al. (författare) Departure from MHD prescriptions in shock formation over a guiding magnetic field 2017 Ingår i: Laser and particle beams (Print). - : Cambridge University Press. - 0263-0346 .- 1469-803X. ; 35, s. 513-519 Tidskriftsartikel (refereegranskat)abstract In plasmas where the mean-free-path is much larger than the size of the system, shock waves can arise with a front much shorter than the mean-free path. These so-called "collisionless shocks" are mediated y collective plasma interactions. Studies conducted so far on these shocks found that although binary collisions are absent, the distribution functions are thermalized downstream by scattering on the fields, so that magnetohydrodynamic prescriptions may apply. Here we show a clear departure from this pattern in the case of Weibel shocks forming over a flow-aligned magnetic field. A micro-physical analysis of the particle motion in the Weibel filaments shows how they become unable to trap the flow in the presence of too strong a field, inhibiting the mechanism of shock formation. Particle-in-cell simulations confirm these results.
3.	Bret, Antoine, et al. (författare) Hierarchy of instabilities for two counter-streaming magnetized pair beams: Influence of field obliquity 2017 Ingår i: Physics of Plasmas. - : A I P Publishing LLC. - 1070-664X .- 1089-7674. ; 24:6 Tidskriftsartikel (refereegranskat)abstract The hierarchy of unstable modes when two counter-streaming pair plasmas interact over a flow-aligned magnetic field has been recently investigated [Phys. Plasmas 23, 062122 (2016)]. The analysis is here extended to the case of an arbitrarily tilted magnetic field. The two plasma shells are initially cold and identical. For any angle θ ∈ [0, π/2] between the field and the initial flow, the hierarchy of unstable modes is numerically determined in terms of the initial Lorentz factor of the shells γ0, and the field strength as measured by a parameter denoted σ. For θ = 0, four different kinds of mode are likely to lead the linear phase. The hierarchy simplifies for larger θ's, partly because the Weibel instability can no longer be cancelled in this regime. For θ > 0.78 (44°) and in the relativistic regime, the Weibel instability always govern the interaction. In the non-relativistic regime, the hierarchy becomes θ-independent because the interaction turns to be field-independent. As a result, the two-stream instability becomes the dominant one, regardless of the field obliquity.
4.	Bret, Antoine, et al. (författare) How large can the electron to proton mass ratio be in particle-in-cell simulations of unstable systems? 2010 Ingår i: Physics of Plasmas. - : American Institute of Physics. - 1070-664X .- 1089-7674. ; 17:3, s. 032109- Tidskriftsartikel (refereegranskat)abstract Particle-in-cell 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 in 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.
5.	Bret, Antoine, et al. (författare) Ions motion effects on the full unstable spectrum in relativistic electron beam plasma interaction 2008 Ingår i: Physics of Plasmas. - : AIP Publishing. - 1070-664X .- 1089-7674. ; 15:1, s. 012104-1-12104-13 Tidskriftsartikel (refereegranskat)abstract 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 bM/mi, being the beam to plasma density ratio, i 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.
6.	Bret, Antoine, et al. (författare) Magnetic field effects on instabilities driven by a field-aligned relativistic warm electron beam and warm bulk electrons 2007 Ingår i: 34th European Physical Society Conference on Plasma Physics,2007. - Warsaw : European Physical Society. ; , s. P2.079- Konferensbidrag (refereegranskat)abstract Instabilities driven by relativistic electron beams are being investigated due to their importance for plasma heating and electromagnetic field generation in astrophysical and laboratory plasmas. Particle-in-cell (PIC) simulations of initially unmagnetized colliding plasmas have demonstrated the generation of strong magnetic fields and a moderate electron acceleration. The inclusion of a flow-aligned magnetic field suppresses the electromagnetic filamentation instability and PIC simulations have shown that the plasma dynamics turns quasi-electrostatic. To quantify the impact of the magnetic field, we have analyzed numerically a magnetized multi-fluid model that includes a kinetic pressure term. This fluid model allows us to examine the beam-driven instability at all angles between the wavevector and the magnetic field vector. More accurate kinetic models typically focus only on the filamentation instability, due to the increased analytical complexity. We present here the fluid model and a growth rate map of the entire k-space for a beam Lorentz factor 4. We verify that the two-stream, mixed mode and filamentation instability belong to the same wave branch and that the magnetic field selects the fastest-growing mode. We estimate the magnetic fields required to suppress the filamentation and the mixed mode instabilities.
7.	Bret, Antoine, et al. (författare) Multidimensional electron beam-plasma instabilities in the relativistic regime 2010 Ingår i: Physics of Plasmas. - : AIP Publishing. - 1070-664X .- 1089-7674. ; 17:12, s. 120501-1-120501-36 Forskningsöversikt (refereegranskat)abstract The interest in relativistic beam-plasma instabilities has been greatly rejuvenated over the past two decades by novel concepts in laboratory and space plasmas. Recent advances in this long-standing field are here reviewed from both theoretical and numerical points of view. The primary focus is on the two-dimensional spectrum of unstable electromagnetic waves growing within relativistic, unmagnetized, and uniform electron beam-plasma systems. Although the goal is to provide a unified picture of all instability classes at play, emphasis is put on the potentially dominant waves propagating obliquely to the beam direction, which have received little attention over the years. First, the basic derivation of the general dielectric function of a kinetic relativistic plasma is recalled. Next, an overview of two-dimensional unstable spectra associated with various beam-plasma distribution functions is given. Both cold-fluid and kinetic linear theory results are reported, the latter being based on waterbag and Maxwell–Jüttner model distributions. The main properties of the competing modes (developing parallel, transverse, and oblique to the beam) are given, and their respective region of dominance in the system parameter space is explained. Later sections address particle-in-cell numerical simulations and the nonlinear evolution of multidimensional beam-plasma systems. The elementary structures generated by the various instability classes are first discussed in the case of reduced-geometry systems. Validation of linear theory is then illustrated in detail for large-scale systems, as is the multistaged character of the nonlinear phase. Finally, a collection of closely related beam-plasma problems involving additional physical effects is presented, and worthwhile directions of future research are outlined.
8.	Bret, Antoine, et al. (författare) Oblique electromagnetic instabilities for a hot relativistic beam interacting with a hot and magnetized plasma 2006 Ingår i: Physics of Plasmas. - : AIP Publishing. - 1070-664X .- 1089-7674. ; 13:8, s. 082109-1-082109-8 Tidskriftsartikel (refereegranskat)abstract 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.
9.	Bret, Antoine, et al. (författare) On the proton to electron mass ratio in particle-in-cell simulations 2011 Ingår i: Europhysics conference abstracts. ; , s. O4.310-1-O4.310-4 Konferensbidrag (refereegranskat)
10.	Bret, Antoine, et al. (författare) Particle trajectories in Weibel filaments: influence of external field obliquity and chaos 2020 Ingår i: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 86:3 Tidskriftsartikel (refereegranskat)abstract 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 ??0 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 ??=B0/Bf>1/2 . Here, this result is extended to the case of an oblique external field B0 making an angle ?? with the flow. The result, numerically found, is simply ?????>?(?)/cos⁡? , where ???(?) is of order unity. Noteworthily, test particles exhibit chaotic trajectories.
11.	Bret, Antoine, et al. (författare) Recent progresses in relativistic beam-plasma instability theory 2010 Ingår i: Annales Geophysicae. - : Copernicus GmbH. - 0992-7689 .- 1432-0576. ; 28:11, s. 2127-2132 Tidskriftsartikel (refereegranskat)abstract Beam-plasma instabilities are a key physical process in many astrophysical phenomena. Within the fireball model of Gamma ray bursts, they first mediate a relativistic collisionless shock before they produce upstream the turbulence needed for the Fermi acceleration process. While non-relativistic systems are usually governed by flow-aligned unstable modes, relativistic ones are likely to be dominated by normally or even obliquely propagating waves. After reviewing the basis of the theory, results related to the relativistic kinetic regime of the poorly-known oblique unstable modes will be presented. Relevant systems besides the well-known electron beam-plasma interaction are presented, and it is shown how the concept of modes hierarchy yields a criterion to assess the proton to electron mass ratio in Particle in cell simulations.
12.	Bret, Antoine, et al. (författare) Relativistic electron beam driven instabilities in the presence of an arbitrarily oriented magnetic field 2008 Ingår i: Physics of Plasmas. - : AIP Publishing. - 1070-664X .- 1089-7674. ; 15:6, s. 062102-1- Tidskriftsartikel (refereegranskat)abstract 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 B 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 B=0 and the oblique modes grow faster at larger B. 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 B is varied from 0 to /2. The fastest growing modes are always found for a transverse propagation of the beam with B=/2, irrespective of the magnetic field strength. ©2008 American Institute of Physics
13.	Bret, Antoine, et al. (författare) Theory of the formation of a collisionless Weibel shock: pair vs. electron/proton plasmas 2016 Ingår i: Laser and particle beams (Print). - 0263-0346 .- 1469-803X. ; 34:2, s. 362-367 Tidskriftsartikel (refereegranskat)abstract Collisionless shocks are shocks in which the mean-free path is much larger than the shock front. They are ubiquitous in astrophysics and the object of much current attention as they are known to be excellent particle accelerators that could be the key to the cosmic rays enigma. While the scenario leading to the formation of a fluid shock is well known, less is known about the formation of a collisionless shock. We present theoretical and numerical results on the formation of such shocks when two relativistic and symmetric plasma shells (pair or electron/proton) collide. As the two shells start to interpenetrate, the overlapping region turns Weibel unstable. A key concept is the one of trapping time τp, which is the time when the turbulence in the central region has grown enough to trap the incoming flow. For the pair case, this time is simply the saturation time of the Weibel instability. For the electron/proton case, the filaments resulting from the growth of the electronic and protonic Weibel instabilities, need to grow further for the trapping time to be reached. In either case, the shock formation time is 2τp in two-dimensional (2D), and 3τp in 3D. Our results are successfully checked by particle-in-cell simulations and may help designing experiments aiming at producing such shocks in the laboratory.
14.	Dieckmann, Mark E, 1969-, et al. (författare) Comparing electrostatic instabilities driven by mildly and highly relativistic proton beams 2007 Ingår i: Plasma Physics and Controlled Fusion. - : IOP Publishing. - 0741-3335 .- 1361-6587. ; 49:December, s. 1989-2004 Tidskriftsartikel (refereegranskat)abstract An electrostatic instability driven by counter-propagating tenuous proton beams that traverse a bulk plasma consisting of electrons and protons is considered. The system is spatially homogeneous and is evolved in time with a one-dimensional particle-in-cell simulation, which allows for a good statistical plasma representation. Mildly and highly relativistic beam speeds are modeled. The proton beams with a speed of 0.9c result in waves that saturate by the trapping of electrons. The collapse of the phase space holes in the electron distribution scatters these to a flat-top momentum distribution. The final electric fields are weak and the proton beams are weakly modulated. No secondary instabilities are likely to form that could thermalize the proton beams. The proton beams moving with 0.99c initially heat the bulk plasma through a three-wave interaction. Coalescing phase space holes in the bulk proton distribution arising from the saturation of ion acoustic waves transport wave energy to low wavenumbers. Highly relativistic phase space holes form in the electron distribution, which are not spatially homogeneous. The spatial envelope of these electron phase space holes interacts with the fluctuations driven by the phase space holes in the bulk protons, triggering a modulational instability. A Langmuir wave condensate forms that gives rise to strong and long electrostatic wave packets, as well as to a substantial modulation of the proton beams. The final state of the system with the highly relativistic proton beams is thus more unstable to further secondary instabilities that may transfer a larger beam energy fraction to the electrons and thermalize the proton beams more rapidly
15.	Dieckmann, Mark Eric, 1969-, et al. (författare) Electric field generation by the electron beam filamentation instability: filament size effects 2010 Ingår i: Physica Scripta. - BRISTOL, ENGLAND : IOP PUBLISHING LTD. - 0031-8949 .- 1402-4896. ; 81:1, s. 015502- Tidskriftsartikel (refereegranskat)abstract 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 non-relativistic 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.
16.	Dieckmann, Mark E, 1969-, et al. (författare) Electron surfing acceleration by mildly relativistic beams : wave magnetic field effects 2008 Ingår i: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 10:Januar, s. 013029-1-13029-2 Tidskriftsartikel (refereegranskat)abstract Electron surfing acceleration (ESA) is based on the trapping of electrons by a wave and the transport of the trapped electrons across a perpendicular magnetic field. ESA can accelerate electrons to relativistic speeds and it may thus produce hot electrons in plasmas supporting fast ion beams, like close to astrophysical shocks. One-dimensional (1D) particle-in-cell (PIC) simulations have demonstrated that trapped electron structures (phase space holes) are stabilized by relativistic phase speeds of the waves, by which ESA can accelerate electrons to ultrarelativistic speeds. The 2(1/2)D electromagnetic and relativistic PIC simulations performed in the present paper model proton beam driven instabilities in the presence of a magnetic field perpendicular to the simulation plane. This configuration represents the partially electromagnetic mixed modes and the filamentation modes, in addition to the Buneman waves. The waves are found to become predominantly electromagnetic and nonplanar for beam speeds that would result in stable trapped electron structures. The relativistic boost of ESA reported previously is cancelled by this effect. For proton beam speeds of 0.6 and 0.8c, the electrons reach only million electron volt energies. The system with the slower beam is followed sufficiently long in time to reveal the development of a secondary filamentation instability. The instability forms a channel in the simulation domain that is void of any magnetic field. Proton beams may thereby cross perpendicular magnetic fields for distances beyond their gyroradius.
17.	Dieckmann, Mark E, 1969-, et al. (författare) Electrostatic and magnetic instabilities in the transition layer of a collisionless weakly relativistic pair shock 2018 Ingår i: Monthly notices of the Royal Astronomical Society. - : Oxford University Press. - 0035-8711 .- 1365-2966. ; 473:1, s. 198-209 Tidskriftsartikel (refereegranskat)abstract Energetic electromagnetic emissions by astrophysical jets like those that are launched during the collapse of a massive star and trigger gamma-ray bursts are partially attributed to relativistic internal shocks. The shocks are mediated in the collisionless plasma of such jets by the filamentation instability of counterstreaming particle beams. The filamentation instability grows fastest only if the beams move at a relativistic relative speed. We model here with a particle-in-cell simulation, the collision of two cold pair clouds at the speed c/2 (c: speed of light). We demonstrate that the two-stream instability outgrows the filamentation instability for this speed and is thus responsible for the shock formation. The incomplete thermalization of the upstream plasma by its quasi-electrostatic waves allows other instabilities to grow. A shock transition layer forms, in which a filamentation instability modulates the plasma far upstream of the shock. The inflowing upstream plasma is progressively heated by a two-stream instability closer to the shock and compressed to the expected downstream density by the Weibel instability. The strong magnetic field due to the latter is confined to a layer 10 electron skin depths wide.
18.	Dieckmann, Mark E, 1969-, et al. (författare) Emergence of MHD structures in a collisionless PIC simulation plasma 2017 Ingår i: Physics of Plasmas. - Melville, NY, United States : A I P Publishing LLC. - 1070-664X .- 1089-7674. ; 24:9 Tidskriftsartikel (refereegranskat)abstract 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 simulation over magnetohydrodynamics 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.
19.	Dieckmann, Mark E, 1969-, et al. (författare) Evolution of the fastest-growing relativistic mixed mode instability driven by a tenuous plasma beam in one and two dimensions 2006 Ingår i: Physics of Plasmas. - : AIP Publishing. - 1070-664X .- 1089-7674. ; 13:11, s. 112110-1-112110-8 Tidskriftsartikel (refereegranskat)abstract 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.
20.	Dieckmann, Mark E, 1969-, et al. (författare) Expansion of a radial plasma blast shell into an ambient plasma 2017 Ingår i: Physics of Plasmas. - Melville, NY, United States : A I P Publishing LLC. - 1070-664X .- 1089-7674. ; 24:9 Tidskriftsartikel (refereegranskat)abstract The expansion of a radial blast shell into an ambient plasma is modeled with a particle-in-cell simulation. The unmagnetized plasma consists of electrons and protons. The formation and evolution of an electrostatic shock is observed, which is trailed by ion-acoustic solitary waves that grow on the beam of the blast shell ions in the post-shock plasma. In spite of the initially radial symmetric outflow, the solitary waves become twisted and entangled and, hence, they break the radial symmetry of the flow. The waves and their interaction with the shocked ambient ions slow down the blast shell protons and bring the post-shock plasma closer to equilibrium.
21.	Dieckmann, Mark E, 1969-, et al. (författare) Particle-in-cell simulation of a strong double layer in a nonrelativistic plasma flow : Electron acceleration to ultrarelativistic speeds 2009 Ingår i: Astrophysical Journal. - 0004-637X .- 1538-4357. ; 694:1, s. 154-164 Tidskriftsartikel (refereegranskat)abstract Two charge- and current-neutral plasma beams are modeled with a one-dimensional particle-in-cell simulation. The beams are uniform and unbounded. The relative speed between both beams is 0.4c. One beam is composed of electrons and protons, and the other of protons and negatively charged oxygen (dust). All species have the temperature 9.1 keV. A Buneman instability develops between the electrons of the first beam and the protons of the second beam. The wave traps the electrons, which form plasmons. The plasmons couple energy into the ion acousticwaves, which trap the protons of the second beam. Astructure similar to a proton phase-space hole develops, which grows through its interaction with the oxygen and the heated electrons into a rarefaction pulse. This pulse drives a double layer, which accelerates a beam of electrons to about 50 MeV, which is comparable to the proton kinetic energy. The proton distribution eventually evolves into an electrostatic shock. Beams of charged particles moving at such speeds may occur in the foreshock of supernova remnant (SNR) shocks. This double layer is thus potentially relevant for the electron acceleration (injection) into the diffusive shock acceleration by SNR shocks.
22.	Dieckmann, Mark Eric, et al. (författare) Particle simulation study of electron heating by counter-streaming ion beams ahead of supernova remnant shocks 2012 Ingår i: Plasma Physics and Controlled Fusion. - : Institute of Physics Publishing (IOPP). - 0741-3335 .- 1361-6587. ; 54:8, s. 085015- Tidskriftsartikel (refereegranskat)abstract The growth and saturation of Buneman-type instabilities is examined with a particle-in-cell (PIC) simulation for parameters that are representative for the foreshock region of fast supernova remnant shocks. A dense ion beam and the electrons correspond to the upstream plasma and a fast ion beam to the shock-reflected ions. The purpose of the 2D simulation is to identify the nonlinear saturation mechanisms, the electron heating and potential secondary instabilities that arise from anisotropic electron heating and result in the growth of magnetic fields. We confirm that the instabilities between both ion beams and the electrons saturate by the formation of phase space holes by the beam-aligned modes. The slower oblique modes accelerate some electrons, but they cannot heat up the electrons significantly before they are trapped by the faster beam-aligned modes. Two circular electron velocity distributions develop, which are centred around the velocity of each ion beam. They develop due to the scattering of the electrons by the electrostatic wave potentials. The growth of magnetic fields is observed, but their amplitude remains low.
23.	Dieckmann, Mark Eric, et al. (författare) PIC simulation of a thermal anisotropy-driven Weibel instability in a circular rarefaction wave 2012 Ingår i: New Journal of Physics. - London : Institute of Physics (IOP). - 1367-2630. ; 14:023007 Tidskriftsartikel (refereegranskat)abstract The expansion of an initially unmagnetized planar rarefaction wave has recently been shown to trigger a thermal anisotropy-driven Weibel instability (TAWI), which can generate magnetic fields from noise levels. It is examined here whether the TAWI can also grow in a curved rarefaction wave. The expansion of an initially unmagnetized circular plasma cloud, which consists of protons and hot electrons, into a vacuum is modelled for this purpose with a two-dimensional particle-in-cell (PIC) simulation. It is shown that the momentum transfer from the electrons to the radially accelerating protons can indeed trigger a TAWI. Radial current channels form and the aperiodic growth of a magnetowave is observed, which has a magnetic field that is oriented orthogonal to the simulation plane. The induced electric field implies that the electron density gradient is no longer parallel to the electric field. Evidence is presented here that this electric field modification triggers a second magnetic instability, which results in a rotational low-frequency magnetowave. The relevance of the TAWI is discussed for the growth of small-scale magnetic fields in astrophysical environments, which are needed to explain the electromagnetic emissions by astrophysical jets. It is outlined how this instability could be examined experimentally.
24.	Dieckmann, Mark E, 1969-, et al. (författare) PIC simulations of relativistic electron flows : The fastest-growing mixed mode and the electromagnetic finite grid instability 2007 Ingår i: 34th European Physical Society Conference on Plasma Physics,2007. - Warsaw : European Physical Society. ; , s. P2.078- Konferensbidrag (refereegranskat)abstract Instabilities driven by two electron beams that stream at the relativistic relative velocity vb are important as a plasma thermalization and magnetic field generation mechanism in astrophysics and in inertial confinement fusion. The time-evolution of such instabilities, which are subdivided into the two-stream, mixed mode and filamentation (beam-Weibel) instability, is multi-dimensional and nonlinear and the instabilities are usually modelled with particle-in-cell (PIC) simulations. We examine the wave spectrum we obtain, if both beams have a density ratio 9 and (1-vb^2/c^2)^(-1/2)=4. The mixed mode dominates and grows fastest for highly relativistic vb. An electromagnetic finite grid instability is shown to generate artificial magnetic fields, imposing a simulation constraint.
25.	Dieckmann, Mark Eric, et al. (författare) PIC simulations of stable surface waves on a subcritical fast magnetosonic shock front 2023 Ingår i: Physica Scripta. - : IOP Publishing Ltd. - 0031-8949 .- 1402-4896. ; 98:9 Tidskriftsartikel (refereegranskat)abstract We study with particle-in-cell (PIC) simulations the stability of fast magnetosonic shocks. They expand across a collisionless plasma and an orthogonal magnetic field that is aligned with one of the directions resolved by the 2D simulations. The shock speed is 1.6 times the fast magnetosonic speed when it enters a layer with a reduced density of mobile ions, which decreases the shock speed by up to 15% in 1D simulations. In the 2D simulations, the density of mobile ions in the layer varies sinusoidally perpendicularly to the shock normal. We resolve one sine period. This variation only leads to small changes in the shock speed evidencing a restoring force that opposes a shock deformation. As the shock propagates through the layer, the ion density becomes increasingly spatially modulated along the shock front and the magnetic field bulges out where the mobile ion density is lowest. The perturbed shock eventually reaches a steady state. Once it leaves the layer, the perturbations of the ion density and magnetic field oscillate along its front at a frequency close to the lower-hybrid frequency; the shock is mediated by a standing wave composed of obliquely propagating lower-hybrid waves. We perform three 2D simulations with different box lengths along the shock front. The shock front oscillations are aperiodically damped in the smallest box with the fastest variation of the ion density, strongly damped in the intermediate one, and weakly damped in the largest box. The shock front oscillations perturb the magnetic field in a spatial interval that extends by several electron skin depths upstream and downstream of the shock front and could give rise to Whistler waves that propagate along the shock's magnetic field overshoot. Similar waves were observed in hybrid and PIC simulations and by the MMS satellite mission.
26.	Dieckmann, Mark E, 1969-, et al. (författare) Simulation studies of temperature anisotropy driven pair-Alfvén and aperiodic instabilities in magnetized pair plasma 2019 Ingår i: Plasma Physics and Controlled Fusion. - : Institute of Physics Publishing (IOPP). - 0741-3335 .- 1361-6587. ; 61:8 Tidskriftsartikel (refereegranskat)abstract We compare with one-dimensional particle-in-cell simulations the aperiodically growing instabilities driven by a bi-Maxwellian velocity distribution in unmagnetized electron plasma (Weibel instability) and in pair plasma. The simulation box is aligned with the cool direction. The waves in both simulations evolve towards a circularly polarized non-propagating magnetic structure. Its current and magnetic field are aligned and the structure is in a force-free state. We examine how a background magnetic field B 0, which is parallel to the simulation direction, affects the waves in the pair plasma. A weak B 0 cannot inhibit the growth of the aperiodically growing instability but it prevents it from reaching the force-free stable state. The mode collapses and seeds a pair Alfvén waves. An intermediate B 0 couples the thermal anisotropy to the pair Alfvén mode and propagating magnetowaves grow. The phase speed of the pair of Alfvén waves is increased by the thermal anisotropy. Its growth is suppressed when B 0 is set to the value that stabilizes the mirror mode.
27.	Dieckmann, Mark Eric, et al. (författare) Simulation study of the formation of a non-relativistic pair shock 2017 Ingår i: Journal of Plasma Physics. - 0022-3778 .- 1469-7807. ; 83, s. 1-19 Tidskriftsartikel (refereegranskat)abstract We examine with a particle-in-cell (PIC) simulation the collision of two equally dense clouds of cold pair plasma. The clouds interpenetrate until instabilities set in, which heat up the plasma and trigger the formation of a pair of shocks. The fastest-growing waves at the collision speed $c/5$, where $c$ is the speed of light in vacuum, and low temperature are the electrostatic two-stream mode and the quasi-electrostatic oblique mode. Both waves grow and saturate via the formation of phase space vortices. The strong electric fields of these nonlinear plasma structures provide an efficient means of heating up and compressing the inflowing upstream leptons. The interaction of the hot leptons, which leak back into the upstream region, with the inflowing cool upstream leptons continuously drives electrostatic waves that mediate the shock. These waves heat up the inflowing upstream leptons primarily along the shock normal, which results in an anisotropic velocity distribution in the post-shock region. This distribution gives rise to the Weibel instability. Our simulation shows that even if the shock is mediated by quasi-electrostatic waves, strong magnetowaves will still develop in its downstream region.
28.	Marcowith, Alexandre, et al. (författare) The microphysics of collisionless shock waves 2016 Ingår i: Reports on progress in physics (Print). - : Institute of Physics Publishing (IOPP). - 0034-4885 .- 1361-6633. ; 79:4 Forskningsöversikt (refereegranskat)abstract Collisionless shocks, that is shocks mediated by electromagnetic processes, are customary in space physics and in astrophysics. They are to be found in a great variety of objects and environments: magnetospheric and heliospheric shocks, supernova remnants, pulsar winds and their nebulæ, active galactic nuclei, gamma-ray bursts and clusters of galaxies shock waves. Collisionless shock microphysics enters at different stages of shock formation, shock dynamics and particle energization and/or acceleration. It turns out that the shock phenomenon is a multi-scale non-linear problem in time and space. It is complexified by the impact due to high-energy cosmic rays in astrophysical environments. This review adresses the physics of shock formation, shock dynamics and particle acceleration based on a close examination of available multi-wavelength or in situ observations, analytical and numerical developments. A particular emphasis is made on the different instabilities triggered during the shock formation and in association with particle acceleration processes with regards to the properties of the background upstream medium. It appears that among the most important parameters the background magnetic field through the magnetization and its obliquity is the dominant one. The shock velocity that can reach relativistic speeds has also a strong impact over the development of the micro-instabilities and the fate of particle acceleration. Recent developments of laboratory shock experiments has started to bring some new insights in the physics of space plasma and astrophysical shock waves. A special section is dedicated to new laser plasma experiments probing shock physics.
29.	Murphy, GC, et al. (författare) Magnetic field amplification and electron acceleration to near-energy equipartition with ions by a mildly relativistic quasi-parallel plasma protoshock 2010 Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 524, s. A84- Tidskriftsartikel (refereegranskat)abstract Context. The prompt emissions of gamma-ray bursts (GRBs) are seeded by radiating ultrarelativistic electrons. Kinetic energy dominated internal shocks propagating through a jet launched by a stellar implosion, are expected to dually amplify the magnetic field and accelerate electrons.Aims. We explore the effects of density asymmetry and of a quasi-parallel magnetic field on the collision of two plasma clouds.Methods. A two-dimensional relativistic particle-in-cell (PIC) simulation models the collision with 0.9c of two plasma clouds, in the presence of a quasi-parallel magnetic field. The cloud density ratio is 10. The densities of ions and electrons and the temperature of 131 keV are equal in each cloud, and the mass ratio is 250. The peak Lorentz factor of the electrons is determined, along with the orientation and the strength of the magnetic field at the cloud collision boundary.Results. The magnetic field component orthogonal to the initial plasma flow direction is amplified 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, caused by a current sheet which develops in response to the differing deflection of the upstream electrons and ions incident on the magnetised shock transition layer. The electron deflection implies a charge separation of the upstream electrons and ions; the resulting electric field drags the electrons through the magnetic field, whereupon they acquire a relativistic mass comparable to that of the ions. We demonstrate how a magnetic field structure resembling the cross section of a flux tube grows self-consistently in the current sheet of the shock transition layer. Plasma filamentation develops behind the shock front, as well as signatures of orthogonal magnetic field striping, indicative of the filamentation instability. These magnetic fields convect away from the shock boundary and their energy density exceeds by far the thermal pressure of the plasma. Localized magnetic bubbles form.Conclusions. Energy equipartition between the ion, electron and magnetic energy is obtained at the shock transition layer. The electronic radiation can provide a seed photon population that can be energized by secondary processes (e.g. inverse Compton).
30.	Sarri, Gianluca, et al. (författare) Two-dimensional particle-in-cell simulation of the expansion of a plasma into a rarefied medium 2011 Ingår i: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 13:7, s. 073023-1-073023-23 Tidskriftsartikel (refereegranskat)abstract The expansion of a dense plasma through a more rarefied ionized medium has been studied by means of two-dimensional particle-in-cell simulations. The initial conditions involve a density jump by a factor of 100, located in the middle of an otherwise equally dense electron-proton plasma with uniform proton and electron temperatures of 10 eV and 1keV, respectively. Simulations show the creation of a purely electrostatic collisionless shock together with an ion-acoustic soliton tied to its downstream region. The shock front is seen to evolve in filamentary structures consistently with the onset of the ion-ion instability. Meanwhile, an un-magnetized drift instability is triggered in the core part of the dense plasma. Such results explain recent laser-plasma experiments, carried out in similar conditions, and are of intrinsic relevance to non-relativistic shock scenarios in the solar and astrophysical systems.

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