scholarly journals Theory of the formation of a collisionless Weibel shock: pair vs. electron/proton plasmas

2016 ◽  
Vol 34 (2) ◽  
pp. 362-367 ◽  
Author(s):  
A. Bret ◽  
A. Stockem Novo ◽  
R. Narayan ◽  
C. Ruyer ◽  
M. E. Dieckmann ◽  
...  
Keyword(s):  
Mean Free Path ◽  
Particle Accelerators ◽  
Incoming Flow ◽  
Collisionless Shock ◽  
Collisionless Shocks ◽  
Trapping Time ◽  
Particle In Cell ◽  
The Mean ◽  
The One ◽  
Overlapping Region

AbstractCollisionless 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.

scholarly journals Ion-acoustic shocks with reflected ions: modelling and particle-in-cell simulations

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
T. V. Liseykina ◽  
G. I. Dudnikova ◽  
V. A. Vshivkov ◽  
M. A. Malkov
Keyword(s):  
Particle Accelerators ◽  
Collisionless Shock ◽  
Astrophysical Plasmas ◽  
Particle In Cell ◽  
Electrons And Ions ◽  
Ion Acoustic ◽  
Main Driver ◽  
Real Mass ◽  
Astrophysical Shocks ◽  
The One

Non-relativistic collisionless shock waves are widespread in space and astrophysical plasmas and are known as efficient particle accelerators. However, our understanding of collisionless shocks, including their structure and the mechanisms whereby they accelerate particles, remains incomplete. We present here the results of numerical modelling of an ion-acoustic collisionless shock based on the one-dimensional kinetic approximation for both electrons and ions with a real mass ratio. Special emphasis is paid to the shock-reflected ions as the main driver of shock dissipation. The reflection efficiency, the velocity distribution of reflected particles and the shock electrostatic structure are studied in terms of the shock parameters. Applications to particle acceleration in geophysical and astrophysical shocks are discussed.

scholarly journals Adaptation of the de Hoffmann–Teller frame for quasi-perpendicular collisionless shocks

2015 ◽  
Vol 33 (3) ◽  
pp. 345-350 ◽  
Author(s):  
H. Comişel ◽  
Y. Narita ◽  
U. Motschmann
Keyword(s):  
Shock Wave ◽  
Electric Field ◽  
Shock Layer ◽  
Local Magnetic Field ◽  
Sliding Velocity ◽  
Collisionless Shock ◽  
Collisionless Shocks ◽  
Particle In Cell ◽  
Cell Simulation ◽  
High Mach

Abstract. The concept of the de Hoffmann–Teller frame is revisited for a high Mach-number quasi-perpendicular collisionless shock wave. Particle-in-cell simulation shows that the local magnetic field oscillations in the shock layer introduce a residual motional electric field in the de Hoffmann–Teller frame, which is misleading in that one may interpret that electrons were not accelerated but decelerated in the shock layer. We propose the concept of the adaptive de Hoffmann–Teller (AHT) frame in which the residual convective field is canceled by modulating the sliding velocity of the de Hoffmann–Teller frame. The electrostatic potential evaluated by Liouville mapping supports the potential profile obtained by electric field in this adaptive frame, offering a wide variety of applications in shock wave studies.

Transport processes in dilute gases over the whole range of Knudsen numbers. Part 1. General theory

1979 ◽  
Vol 93 (3) ◽  
pp. 585-607 ◽  
Author(s):  
L. C. Woods
Keyword(s):  
Free Path ◽  
Mean Free Path ◽  
Transport Processes ◽  
Burnett Equations ◽  
Flux Vector ◽  
Dilute Gases ◽  
Knudsen Numbers ◽  
Heat Flux Vector ◽  
The Mean ◽  
The One

The mean-free-path approach to kinetic theory, initiated by Maxwell, and largely abandoned after the Chapman-Enskog success with Boltzmann's equation, is revised and considerably extended in order to find expressions for the heat flux vector q and pressure tensor p, valid (it is hoped) for all Knudsen numbers, K. These expressions (equations (2.24) and (2.26)) are integrals taken over the whole volume of the fluid plus surface integrals taken over the solid boundaries. The one phenomenological element is the mean free path λ, which takes different values according to whether it is mass, momentum or energy that is transported by the molecules. The need for such an approach is evidenced by the existence of critical values of K, above which the Chapman-Enskog expansion in powers of K, truncated after a finite number of terms, fails to yield a solution. For example with the Burnett equations, which are correct to O(K2), the critical K in a shock wave is only 0·2 based upon the upstream λ.

DSMC Simulation of Supersonic Gas Flow in Microchannel

2011 ◽  
Author(s):  
Mohamad M. Joneidipour ◽  
Reza Kamali
Keyword(s):  
Gas Flow ◽  
Characteristic Length ◽  
Flow Characteristics ◽  
Mean Free Path ◽  
Incoming Flow ◽  
Characteristic Length Scale ◽  
Flow Pressure ◽  
Supersonic Gas Flow ◽  
The Mean ◽  
Gas Molecules

The present study is concerned with the flow characteristics of a microchannel supersonic gas flow. The direct simulation Monte Carlo (DSMC) method is employed for predicting the density, velocity and temperature distributions. For gas flows in micro systems, the continuum hypothesis, which underpins the Navier-Stokes equations, may be inappropriate. This is because the mean free path of the gas molecules may be comparable to the characteristic length scale of the device. The Knudsen number, Kn, which is the ratio of the mean free path of the gas molecules to the characteristic length scale of the device, is a convenient measure of the degree of rarefaction of the flow. In this paper, the effect of Knudsen number on supersonic microchannel flow characteristics is studied by varying the incoming flow pressure or the microchannel height. In addition, the microchannel height and the incoming flow pressure are varied simultaneously to investigate their effects on the flow characteristics. Meanwhile, the results show that until the diffuse reflection model is used throughout the microchannel, the temperature and the Mach number in the microchannel entrance may not be equal to free-stream values and therefore a discontinuity appear in the flow field.

scholarly journals Bridging the gap between collisional and collisionless shock waves

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Antoine Bret ◽  
Asaf Pe'er
Keyword(s):  
Mach Number ◽  
Free Path ◽  
Plasma Parameter ◽  
Strong Shock ◽  
Mean Free Path ◽  
Collisionless Shock ◽  
Strongly Coupled ◽  
Collisionless Regime ◽  
The Mean ◽  
High Mach

While the front of a fluid shock is a few mean-free-paths thick, the front of a collisionless shock can be orders of magnitude thinner. By bridging between a collisional and a collisionless formalism, we assess the transition between these two regimes. We consider non-relativistic, non-magnetized, planar shocks in electron–ion plasmas. In addition, our treatment of the collisionless regime is restricted to high-Mach-number electrostatic shocks. We find that the transition can be parameterized by the upstream plasma parameter $\varLambda$ which measures the coupling of the upstream medium. For $\varLambda \lesssim 1.12$ , the upstream is collisional, i.e. strongly coupled, and the strong shock front is about $\mathcal {M}_1 \lambda _{\mathrm {mfp},1}$ thick, where $\lambda _{\mathrm {mfp},1}$ and $\mathcal {M}_1$ are the upstream mean free path and Mach number, respectively. A transition occurs for $\varLambda \sim 1.12$ beyond which the front is $\sim \mathcal {M}_1\lambda _{\mathrm {mfp},1}\ln \varLambda /\varLambda$ thick for $\varLambda \gtrsim 1.12$ . Considering that $\varLambda$ can reach billions in astrophysical settings, this allows an understanding of how the front of a collisionless shock can be orders of magnitude smaller than the mean free path, and how physics transitions continuously between these two extremes.

Ion dynamics in a perpendicular collisionless shock

1977 ◽  
Vol 17 (2) ◽  
pp. 265-279 ◽  
Author(s):  
D. Sherwell ◽  
R. A. Cairns
Keyword(s):  
Magnetic Field ◽  
Shock Waves ◽  
Dissipative Process ◽  
Ion Dynamics ◽  
Collisionless Shock ◽  
Collisionless Shocks ◽  
Ion Heating ◽  
Potential Jump ◽  
Electric And Magnetic Fields ◽  
The Mean

Some properties of perpendicular collisionless shocks are investigated, using a model in which the ion orbits in the shock are assumed to be determined by the average electric and magnetic fields in the shock. These fields are modelled, with the jump in magnetic field across the shock being determined by the conservation relations, and the potential jump determined self-consistently within the model, using the fact that the mean ion velocity downstream of the shock is determined by the conservation relations. Extensive numerical calculations of ion orbits show that effective ion heating can occur in the absence of any dissipative process, with the energy residing in non-Maxwellian velocity distributions in the downstream regions. Results on this and on a number of other features of shock waves, agree well with experiments.

scholarly journals Departure from MHD prescriptions in shock formation over a guiding magnetic field

2017 ◽  
Vol 35 (3) ◽  
pp. 513-519 ◽  
Author(s):  
A. Bret ◽  
A. Pe'er ◽  
L. Sironi ◽  
M.E. Dieckmann ◽  
R. Narayan
Keyword(s):  
Magnetic Field ◽  
Free Path ◽  
Mean Free Path ◽  
Distribution Functions ◽  
Shock Formation ◽  
Physical Analysis ◽  
Particle In Cell ◽  
The Mean ◽  
Collective Plasma ◽  
Aligned Magnetic Field

AbstractIn 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 by 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 magnetohydrodynamics 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.

Relativistic collisionless shocks formation in pair plasmas

2013 ◽  
Vol 79 (4) ◽  
pp. 367-370 ◽  
Author(s):  
ANTOINE BRET ◽  
A. STOCKEM ◽  
F. FIUZA ◽  
C. RUYER ◽  
L. GREMILLET ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Reasonable Agreement ◽  
Collisionless Plasma ◽  
The Other ◽  
Shock Formation ◽  
Linear Phase ◽  
Collisionless Shocks ◽  
Seed Field ◽  
The One ◽  
Overlapping Region

AbstractCollisionless shocks are ubiquitous in astrophysics and in the laboratory. Recent numerical simulations and experiments have shown how these can arise from the encounter of two collisionless plasma shells. When the shells interpenetrate, the overlapping region turns unstable, triggering the shock formation. As a first step toward a microscopic understanding of the process, we here analyze in detail the initial instability phase. On the one hand, 2D relativistic PIC simulations are performed where two unmagnetized, symmetric, and initially cold pair plasmas collide. On the other hand, the instabilities at work are analyzed, as well as the field at saturation and the seed field which gets amplified. For mildly relativistic motions and onward, Weibel modes with ω=0+iδ govern the linear phase. We derive an expression for the duration of the linear phase in reasonable agreement with the simulations.

scholarly journals On the Brownian displacements and thermal diffusion of grains suspended in a non-uniform fluid

1928 ◽  
Vol 119 (781) ◽  
pp. 34-54 ◽  
Keyword(s):  
Distribution Function ◽  
Equilibrium Distribution ◽  
Mean Free Path ◽  
Physical Analysis ◽  
Brownian Particles ◽  
Uniform Case ◽  
The Mean ◽  
The One ◽  
Coefficient Of Diffusion ◽  
Uniform Fluid

1. In two famous papers on the Brownian motion of grains suspended in a stationary uniform fluid (liquid or gaseous) Einstein obtained, inter alia , the distribution function for the displacements of the grains during any interval t = 0 to t = τ from their positions at time t = 0. The object of this paper is to determine the distribution function for the more general case of a non-uniform fluid. The non-uniformity may refer to temperature, composition, or any other property which affects the coefficient of diffusion (D) of the grains in the fluid. The distribution function is given in 8, where it is shown how its accuracy might be experimentally tested. It contains terms additional to the one given by Einstein for the uniform case; certain of these are definitely determined, but another important term contains a coefficient that cannot be evaluated by considerations of the kind used in this paper (which depend purely on the conservation of the number of grains), but requires more detailed physical analysis; it is surmised that this coefficient vanishes in the case of Brownian particles which are large compared with the mean free path of the surrounding molecules. The main results of the paper refer to the rate of diffusion of the grains due to the non-uniformity of the fluid (9), and to the equilibrium distribution of the grains (10, 11). It is found that if their density is the same as that of the fluid, so that there is no tendency for them to settle in the lower strata, their steady distribution when the fluid is non-uniform is such that the concentration n (or number per unit volume of the fluid) is inversely proportional to D; a solution is also given for the case when the densities are not equal.

scholarly journals Electron Energization Dynamics in Interaction of Self-Generated Magnetic Vortices in Upstream of Collisionless Electron/Ion Shocks

2021 ◽  
Author(s):  
N. Naseri ◽  
S. G. Bochkarev ◽  
V. Y. Bychenkov ◽  
V. Khudik ◽  
G. Shvets
Keyword(s):  
Synergetic Effect ◽  
Upstream Region ◽  
Incoming Flow ◽  
Two Dimensional ◽  
Collisionless Shocks ◽  
Fast Electrons ◽  
Particle In Cell ◽  
Magnetic Vortices ◽  
Particle Energization ◽  
Front Region

Abstract Relativistic collisionless shocks are considered responsible for particle energization mechanisms leading to particle acceleration. While electron energization in shock front region of electron/ion collisionless shocks are the most commonly studied, the mechanism of electron energization in interaction with self-generated magnetic vortices (MVs) in upstream region is still unclear. We investigate electron energization mechanism in upstream region of electron/ion relativistic collisionless shocks, using two dimensional particle-in-cell (PIC) simulations. We discuss mechanism of electron energization which takes place in upstream region of the shock, where the counter stream particles interact with incoming flow. The energy gain of electrons happens during their interaction with evolving fields of self-generated magnetic vortices in this region. Three Fermi-like electron energization scenarios are discussed. Stochastic acceleration of electrons in interaction with fields of MV leads to anisotropic heating of fast electrons due to diffusion in the momentum space of electrons and, finally, synergetic effect of evolving fields of MVs leads to the formation of a power-law tail of supra-thermal particles.

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