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(Color online) The thin shell at the time t = 68: (a) shows n p (x,y). (b) shows (E 2 x + E 2 y ) 1/2 .
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The thin-shell instability has been named as one process, which can generate
entangled structures in astrophysical plasma on collisional (fluid) scales. It
is driven by a spatially varying imbalance between the ram pressure of the
inflowing upstream plasma and the downstream's thermal pressure at a non-planar
shock. Here we show by means of a parti...
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Context 1
... impact of this secondary ambipolar electric field on the protons in the thin shell is evidenced by Fig. 5, which corresponds to the simulation time t = 68. Figure 5(a) reveals a complicated proton density distribution within the thin shell. Most protons are still located behind the concave shocks at (x,y) = (20,250), (x,y) = (115,250), (x,y) = (70,350), and (x,y) = (160,350). New proton density maxima have appeared, which are centered at ...
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... impact of this secondary ambipolar electric field on the protons in the thin shell is evidenced by Fig. 5, which corresponds to the simulation time t = 68. Figure 5(a) reveals a complicated proton density distribution within the thin shell. Most protons are still located behind the concave shocks at (x,y) = (20,250), (x,y) = (115,250), (x,y) = (70,350), and (x,y) = (160,350). ...
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... at the positions x ≈ 300 and y = 0, 45, 90 and 135. These y coordinates correspond to those locations where the initial contact boundary x B (y) = 0 and where the density of the thin shell was lowest in Fig. 3(a). The density decreases from 3 to about 1.8 near these maxima. These density jumps give rise to the strongest electric fields in Fig. 5(b). The localized proton density depletions inside of the thin shell and their associated electric fields appear to be stable and they convect with the thin shell. This is evidenced by movie 3 [29], which animates in time (E 2 x + E 2 y ) 1/2 . Figure 6 demonstrates that two electrostatic shocks, which separate the downstream region at x ...
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Citations
... Following the work of Goicoechea et al. (2016), it is possible that the force imbalance between thermal (isotropic) and ram pressure (parallel to the flow) is what causes the instability known as the "thin shell" (see also Garcia-Segura & Franco 1996;Williams 2003). One can also expect entangled structures in astrophysical plasma on collisional (fluid) scales in the "thin-shell" instability (Dieckmann et al. 2015). Therefore, the intertwined/entangled substructures seem to be caused by the "thin-shell" instability. ...
We report the discovery of intertwined/entangled substructures toward the bubble wall of NGC 3324 below a physical scale of 4500 au, which is the sharp edge/ionization front/elongated structure traced at the interface between the H ii region and the molecular cloud. The sharp edge appears wavy in the Spitzer 3.6–8.0 μ m images (resolution ∼2″). Star formation signatures have mostly been traced on one side of the ionization front, which lies on the molecular cloud’s boundary. The James Webb Space Telescope’s (JWST) near- and mid-infrared images (resolution ∼0.″07—0.″7) are employed to resolve the sharp edge, which has a curvature facing the exciting O-type stars. The elongated structures are associated with the 3.3 μ m polycyclic aromatic hydrocarbon (PAH) emission, the 4.05 μ m ionized emission, and the 4.693 μ m H 2 emission. However, the PAH-emitting structures are depicted between the other two. The H 2 emission reveals numerous intertwined substructures that are not prominently traced in the 3.3 μ m PAH emission. The separation between two substructures in the H 2 emission is ∼1.″1 or 2420 au. The intertwined substructures are traced in the spatial areas associated with the neutral to H 2 transition zone, suggesting the origin of these structures by “thin-shell” instability. Furthermore, an arc-like feature traced in the Spitzer 3.6–8.0 μ m images is investigated as a bipolar H ii region (extent ∼0.35 pc) at T d ∼25–28 K using the JWST images. A massive-star candidate VPHAS-OB1 #03518 seems to be responsible for the bipolar H ii region.
... They have identified the proton-proton beam instability as the process that limits the lifetime of the thin shell. This instability is known to destroy planar double layers and electrostatic shocks (Karimabadi et al. 1991;Kato and Takabe 2010;Dieckmann et al. 2015) and it also affects the non-planar ones. ...
... The collisionless NTSI drove bending modes and breathing modes, which is also the case for the hydrodynamic one. The breathing modes involved large electric fields if the wavelength of the seed perturbation was short and they recovered here the complex spatial plasma density distribution from Dieckmann et al. (2015). These structures could not develop in the case of the large initial seed wavelength due to the weaker electric field and a slower growth and they obtained the final proton density distribution from (Dieckmann et al. 2015;Ahmed et al. 2017). ...
... The breathing modes involved large electric fields if the wavelength of the seed perturbation was short and they recovered here the complex spatial plasma density distribution from Dieckmann et al. (2015). These structures could not develop in the case of the large initial seed wavelength due to the weaker electric field and a slower growth and they obtained the final proton density distribution from (Dieckmann et al. 2015;Ahmed et al. 2017). ...
The Particle-In-Cell (PIC) method has been developed by Oscar Buneman, Charles Birdsall, Roger W. Hockney, and John Dawson in the 1950s and, with the advances of computing power, has been further developed for several fields such as astrophysical, magnetospheric as well as solar plasmas and recently also for atmospheric and laser-plasma physics. Currently more than 15 semi-public PIC codes are available which we discuss in this review. Its applications have grown extensively with increasing computing power available on high performance computing facilities around the world. These systems allow the study of various topics of astrophysical plasmas, such as magnetic reconnection, pulsars and black hole magnetosphere, non-relativistic and relativistic shocks, relativistic jets, and laser-plasma physics. We review a plethora of astrophysical phenomena such as relativistic jets, instabilities, magnetic reconnection, pulsars, as well as PIC simulations of laser-plasma physics (until 2021) emphasizing the physics involved in the simulations. Finally, we give an outlook of the future simulations of jets associated to neutron stars, black holes and their merging and discuss the future of PIC simulations in the light of petascale and exascale computing.
... They accumulate where the piston is convex relative to the positrons. Those parts of the piston where protons accumulate offer more resistance to the expansion of the pair cloud and this increased inertia amplifies the boundary oscillation triggering a thin shell instability.25 The piston is strong enough to confine most of the protons. ...
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.
... Particle-in-cell (PIC) simulations [20,21] and an experiment [19] suggest that the NTSI can also develop in collisionless plasma. Section 2 summarises the PIC simula- tion technique, it discusses electrostatic shocks and the mechanism that is responsible for the collisionless NTSI. ...
... This instability was examined with numerical simulations using MHD and hydrodynamic codes [14,15] and it was observed in a recent laser-plasma experiment [19], where it deformed a thin shell of collisionless plasma. The PIC simulations in [19][20][21] have shown that a collisionless analogue of the NTSI exists. A thin-shell, which is bounded by two solitary waves that are growing into electrostatic shocks [24], is destabilised by a spatial displacement of its central curve along the plasma flow direction that varies as a function of the orthogonal direction. ...
... The collisionless NTSI drove bending modes and breathing modes, which is also the case for the hydrodynamic one. The breathing modes involved large electric fields if the wavelength of the seed perturbation was short and we recovered here the complex spatial plasma density distribu- tion from [20]. These structures could not develop in the case of the large initial seed wavelength due to the weaker electric field and a slower growth and we obtained the final proton density distribution from [19,20]. ...
Contemporary lasers allow us to create shocks in the laboratory that propagate at a speed that matches that of energetic astrophysical shocks like those that ensheath supernova blast shells. The rapid growth time of the shocks and the spatio-temporal resolution, with which they can be sampled, allow us to identify the processes that are involved in their formation and evolution. Some laser-generated unmagnetized shocks are mediated by collective electrostatic forces and effects caused by binary collisions between particles can be neglected. Hydrodynamic models, which are valid for many large-scale astrophysical shocks, assume that collisions enforce a local thermodynamic equilibrium in the medium; laser-generated shocks are thus not always representative for astrophysical shocks. Laboratory studies of shocks can improve the understanding of their astrophysical counterparts if we can identify processes that affect electrostatic shocks and hydrodynamic shocks alike. An example is the nonlinear thin-shell instability (NTSI). We show that the NTSI destabilises collisionless and collisional shocks by the same physical mechanism.
... The lack of experimental observations so far is presumably tied to the difficulty with creating a thin rippled shell of fluid or plasma that is confined by a shock on either side. Recently, Dieckmann et al. (2015) showed that the hydrodynamic NTSI has an analog in collisionless plasma. The shocks are substituted by ambipolar electric fields but the instability mechanism is the same in both cases. ...
... The proton distribution in Figure 3(a) is not uniform along y and the accumulation of protons at the concave parts of the boundary at » x y , 50,50 ( ) ( ) and at » x y , 150, 40 ( ) ( ) is evidence for a developing TSI ( Dieckmann et al. 2015). The density of the thin shell has increased to values » n 3.3 0 at the time 165 ps and it is no longer sinusoidal in Figure 3(b). ...
... The density of the thin shell has increased to values » n 3.3 0 at the time 165 ps and it is no longer sinusoidal in Figure 3(b). The piecewise linear shape of the shell resembles the one in Dieckmann et al. (2015) after the thin-shell instability had saturated. Figure 3(c) shows that the oscillation amplitude has increased to over 11 mm. ...
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.
... On the other hand, for large bulk flows V > V A , where V A = B( γ −1 b /μ 0 N mΓ ) 1/2 = V A0 ( γ −1 b /Γ ) 1/2 is the relativistic Alfvén velocity-with Γ = (1+ P 2 /m 2 c 2 ) 1/2 , and γ b = [1 + (P + p) 2 /m 2 c 2 ] 1/2 the total relativistic factor including the bulk flow momentum P and the single particle momentum p, the argument of the momentum space distribution F(p)-relativistic reconnection necessarily couples to shock waves. The reader is referred to Dieckmann et al. (2015) for the evolution of shocks and magnetisation in high-speed interaction of non-magnetic plasmas. In both cases, one obtains a mix of reconnection effects with relativistic shock effects, and reconnection becomes more complicated than either in non-relativistic and/or in pair plasmas. ...
... This value is readily exceeded by any flow bulk velocity for almost all reasonable densities. One hence expects shock waves to be generated, and the conditions for reconnection are substantially modified and superseded by the shock properties (see also Dieckmann et al. 2015). Under those conditions, one, in fact, expects the evolution of turbulence and decay of the large-scale current sheet into many small-scale turbulent current filaments, a case the discussion of which we will discuss later. ...
... The resulting flow becomes the famous "reconnection jets" of slow Alfvénic speed (Hoshino and Higashimori 2015) that are observed in near-Earth space, where they emanate that at large distances from the X point reconnection sites. Retardation of the fast lepton-exhaust jet does, in principle, imply the possibility that a leptonic shock wave may form (Dieckmann et al. 2015) at this location, a process that has not been investigated so far. This might result in the signature of a leptonic whistler soliton since nucleons are involved only via charge coupling. ...
The present review concerns the relevance of collisionless reconnection in the astrophysical context. Emphasis is put on recent developments in theory obtained from collisionless numerical simulations in two and three dimensions. It is stressed that magnetic reconnection is a universal process of particular importance under collisionless conditions, when both collisional and anomalous dissipation are irrelevant. While collisional (resistive) reconnection is a slow, diffusive process, collisionless reconnection is spontaneous. On any astrophysical time scale, it is explosive. It sets on when electric current widths become comparable to the leptonic inertial length in the so-called lepton (electron/positron) "diffusion region", where leptons de-magnetise. Here, the magnetic field contacts its oppositely directed partner and annihilates. Spontaneous reconnection breaks the original magnetic symmetry, violently releases the stored free energy of the electric current, and causes plasma heating and particle acceleration. Ultimately, the released energy is provided by mechanical motion of either the two colliding magnetised plasmas that generate the current sheet or the internal turbulence cascading down to lepton-scale current filaments. Spontaneous reconnection in such extended current sheets that separate two colliding plasmas results in the generation of many reconnection sites (tearing modes) distributed over the current surface, each consisting of lepton exhausts and jets which are separated by plasmoids. Volume-filling factors of reconnection sites are estimated to be as large as per current sheet. Lepton currents inside exhausts may be strong enough to excite Buneman and, for large thermal pressure anisotropy, also Weibel instabilities. They bifurcate and break off into many small-scale current filaments and magnetic flux ropes exhibiting turbulent magnetic power spectra of very flat power-law shape in wavenumber k with power becoming as low as . Spontaneous reconnection generates small-scale turbulence. Imposed external turbulence tends to temporarily increase the reconnection rate. Reconnecting ultra-relativistic current sheets decay into large numbers of magnetic flux ropes composed of chains of plasmoids and lepton exhausts. They form highly structured current surfaces, "current carpets". By including synchrotron radiation losses, one favours tearing-mode reconnection over the drift-kink deformation of the current sheet. Lepton acceleration occurs in the reconnection-electric field in multiple encounters with the exhausts and plasmoids. This is a Fermi-like process. It results in power-law tails on the lepton energy distribution. This effect becomes pronounced in ultra-relativistic reconnection where it yields extremely hard lepton power-law energy spectra approaching , with the lepton energy. The synchrotron radiation limit becomes substantially exceeded. Relativistic reconnection is a probable generator of current and magnetic turbulence, and a mechanism that produces high-energy radiation. It is also identified as the ultimate dissipation mechanism of the mechanical energy in collisionless magnetohydrodynamic turbulent cascades via lepton-inertial-scale turbulent current filaments. In this case, the volume-filling factor is large. Magnetic turbulence causes strong plasma heating of the entire turbulent volume and violent acceleration via spontaneous lepton-scale reconnection. This may lead to high-energy particle populations filling the whole volume. In this case, it causes non-thermal radiation spectra that span the entire interval from radio waves to gamma rays.
The expansion of a radial blast shell into an ambient plasma is modeled with a particle-in-cell (PIC) 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 radially 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 slows down the blast shell protons and brings the post-shock plasma closer to an equilibrium.
Thin, magnetically aligned striations of relatively moderate contrast with the background are commonly observed in both atomic and molecular clouds. They are also prominent in MHD simulations with turbulent converging shocks. The simulated striations develop within a dense, stagnated sheet in the mid plane of the post-shock region where magnetically-induced converging flows collide. We show analytically that the secondary flows are an inevitable consequence of the jump conditions of oblique MHD shocks. They produce the stagnated, sheet-like sub-layer through a secondary shock when, roughly speaking, the Alfv\'enic speed in the primary converging flows is supersonic, a condition that is relatively easy to satisfy in interstellar clouds. The dense sub-layer is naturally threaded by a strong magnetic field that lies close to the plane of the sub-layer. The substantial magnetic field makes the sheet highly anisotropic, which is the key to the striation formation. Specifically, perturbations of the primary inflow that vary spatially perpendicular to the magnetic field can easily roll up the sheet around the field lines without bending them, creating corrugations that appear as magnetically-aligned striations in column density maps. On the other hand, perturbations that vary spatially along the field lines curve the sub-layer and alter its orientation relative to the magnetic field locally, seeding special locations that become slanted overdense filaments and prestellar cores through enhanced mass accumulation along field lines. In our scenario, the dense sub-layer unique to magnetized oblique shocks is the birthplace for both magnetically-aligned diffuse striations and massive star-forming structures.
