KINETIC SIMULATIONS OF THE CURRENT-DRIVEN INSTABILITY IN COSMIC RAY MODIFIED RELATIVISTIC SHOCKS

2008 ◽  
Vol 17 (10) ◽  
pp. 1803-1809 ◽  
Author(s):  
M. A. RIQUELME ◽  
A. SPITKOVSKY
Keyword(s):  
Cosmic Ray ◽  
Back Reaction ◽  
Speed Of Light ◽  
One Dimensional ◽  
Particle In Cell ◽  
Nonlinear Properties ◽  
Relativistic Shock ◽  
Relativistic Shocks ◽  
Viable Mechanism ◽  
Alfven Velocity

We study the current-driven instability predicted by Bell (2004) using particle-in-cell simulations. We use one-dimensional simulations to test the dispersion relation and the nonlinear properties of the instability for the case of a relativistic shock front under idealized conditions. We find that if the cosmic rays (CR) are energetic enough to not get deflected by the generated magnetic field, the instability can grow exponentially until the Alfvén velocity of the plasma becomes comparable to the speed of light. We also use one- and two-dimensional simulations to study the effect of the back reaction of the instability on CR. We find that the deflection and filamentation of CR and background plasma play an important role in the saturation of the instability. The current-driven instability is a viable mechanism for the amplification of magnetic fields in both non-relativistic and relativistic shock environments.

Formation of an inverted sheath in a one-dimensional bounded plasma system studied by particle-in-cell simulation

2021 ◽  
Vol 28 (12) ◽  
pp. 123507
Author(s):  
T. Gyergyek ◽  
S. Costea ◽  
K. Bajt ◽  
A. Valič ◽  
J. Kovačič
Keyword(s):  
Plasma System ◽  
One Dimensional ◽  
Particle In Cell ◽  
Bounded Plasma ◽  
Cell Simulation

scholarly journals The influence of resistivity gradients on shock conditions for a Petschek reconnection geometry

2016 ◽  
Vol 34 (4) ◽  
pp. 421-425
Author(s):  
Christian Nabert ◽  
Karl-Heinz Glassmeier
Keyword(s):  
Magnetic Field ◽  
Necessary Conditions ◽  
The Other ◽  
Diffusion Region ◽  
Two Dimensional ◽  
Characteristic Velocity ◽  
Magnetohydrodynamic Equations ◽  
One Dimensional ◽  
The Magnetic Field ◽  
Alfven Velocity

Abstract. Shock waves can strongly influence magnetic reconnection as seen by the slow shocks attached to the diffusion region in Petschek reconnection. We derive necessary conditions for such shocks in a nonuniform resistive magnetohydrodynamic plasma and discuss them with respect to the slow shocks in Petschek reconnection. Expressions for the spatial variation of the velocity and the magnetic field are derived by rearranging terms of the resistive magnetohydrodynamic equations without solving them. These expressions contain removable singularities if the flow velocity of the plasma equals a certain characteristic velocity depending on the other flow quantities. Such a singularity can be related to the strong spatial variations across a shock. In contrast to the analysis of Rankine–Hugoniot relations, the investigation of these singularities allows us to take the finite resistivity into account. Starting from considering perpendicular shocks in a simplified one-dimensional geometry to introduce the approach, shock conditions for a more general two-dimensional situation are derived. Then the latter relations are limited to an incompressible plasma to consider the subcritical slow shocks of Petschek reconnection. A gradient of the resistivity significantly modifies the characteristic velocity of wave propagation. The corresponding relations show that a gradient of the resistivity can lower the characteristic Alfvén velocity to an effective Alfvén velocity. This can strongly impact the conditions for shocks in a Petschek reconnection geometry.

Peculiarities of linear wave interaction with nonlinear media interface

2018 ◽  
Vol 32 (30) ◽  
pp. 1850371 ◽  
Author(s):  
S. E. Savotchenko
Keyword(s):  
Guided Waves ◽  
Mathematical Formulation ◽  
Wave Interaction ◽  
Linear Wave ◽  
Stationary Waves ◽  
One Dimensional ◽  
Nonlinear Properties ◽  
Dimensional Boundary ◽  
Nonlinear Interface ◽  
Plane Defect

We analyze guided waves in the linear media separated nonlinear interface. The mathematical formulation of the model is a one-dimensional boundary value problem for the nonlinear Schrödinger equation. The Kerr type nonlinearity in the equation is taken into account only inside the waveguide. We show that the existence of nonlinear stationary waves of three types is possible in defined frequency ranges. We derive the frequency of obtained stationary states in explicit form and find the conditions of its existence. We show that it is possible to obtain the total wave transition through a plane defect. We determine the condition for realizing of such a resonance. We obtain the reflection and transition coefficients in the vicinity of the resonance. We establish that complete wave propagation with nonzero defect parameters can occur only when the nonlinear properties of the defect are taken into account.

scholarly journals CALCULATION OF A JET ENGINE IN A COMPLEX PLANE USING A ONE-DIMENSIONAL SOLUTION OF THE NAVIER-STOKES EQUATION

2021 ◽  
Vol 7 (1(37)) ◽  
pp. 9-22
Author(s):  
E.G. Yakubovsky
Keyword(s):  
Speed Of Sound ◽  
Added Mass ◽  
Navier Stokes ◽  
Speed Of Light ◽  
Attached Mass ◽  
Additional Mass ◽  
Navier Stokes Equation ◽  
Dimensional Solution ◽  
Jet Engine ◽  
One Dimensional

This article proposes an algorithm to describe the motion of a body in the atmosphere using the added mass. Attached mass is the property of a medium to form additional mass, as I assume with a relativistic denominator at the speed of sound instead of the speed of light. Newton’s second law for added mass assumes two terms with the same speed, one is relativistic at the speed of light, and the other is attached mass with a relativistic denominator at the speed of sound. The use of a relativistic denominator with the speed of sound is a new idea that allows, according to well-known formulas with added mass, which is valid at low speeds of a body, to describe

Expansion of hot plasma with Kappa distribution in coronal flare sources

2021 ◽  
Author(s):  
Jan Benáček ◽  
Marian Karlický
Keyword(s):  
Langmuir Wave ◽  
Maxwellian Distribution ◽  
Double Layers ◽  
Kappa Distribution ◽  
One Dimensional ◽  
X Ray ◽  
Particle In Cell ◽  
Hot Plasma ◽  
The Difference ◽  
Field Lines

<p>We study how hot plasma that is released during a solar flare can be confined in its source and interact with surrounding colder plasma. The X-ray emission of coronal flare sources is well explained using Kappa velocity distribution. Therefore, we compare the difference in the confinement of plasma with Kappa and Maxwellian distribution. We use a 3D Particle-in-Cell code, which is large along magnetic field lines, effectively one-dimensional, but contains all electromagnetic effects. In the case with Kappa distribution, contrary to Maxwellian distribution, we found formation of several thermal fronts associated with double-layers that suppress particle fluxes. As the Kappa distribution of electrons forms an extended tail, more electrons are not confined by the first front and cause formation of multiple fronts. A beam of electrons from the hot part is formed at each front; it generates return current, Langmuir wave density depressions, and a double layer with a higher potential step than in the Maxwellian case. We compare the Kappa and Maxwellian cases and discuss how these processes could be observed.</p>

scholarly journals Regular and Stochastic Dynamics of Relativistic Particles in Alfvén Waves

1990 ◽  
Vol 140 ◽  
pp. 155-156
Author(s):  
S. M. Carioli ◽  
V. N. Fedorenko
Keyword(s):  
Stochastic Dynamics ◽  
Interplanetary Medium ◽  
Cosmic Ray ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
One Dimensional ◽  
Test Particles ◽  
Particle Propagation ◽  
Space Dynamics ◽  
Relativistic Particles

We study the exact phase space dynamics of relativistic test particles propagating in static one-dimensional Alfvén waves, modelling cosmic ray propagation in the interplanetary medium and in the interstellar medium. The result shows that the conventional approach should not be considered adequate to explain important features of particle propagation in Alfvén waves.

scholarly journals The formation of relativistic plasma structures and their potential role in the generation of cosmic ray electrons

2008 ◽  
Vol 15 (6) ◽  
pp. 831-846 ◽  
Author(s):  
M. E. Dieckmann
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Magnetic Energy ◽  
Ion Beam ◽  
Cosmic Ray ◽  
Compact Objects ◽  
Space Structures ◽  
Magnetic Field Generation ◽  
Particle In Cell ◽  
Field Generation

Abstract. Recent particle-in-cell (PIC) simulation studies have addressed particle acceleration and magnetic field generation in relativistic astrophysical flows by plasma phase space structures. We discuss the astrophysical environments such as the jets of compact objects, and we give an overview of the global PIC simulations of shocks. These reveal several types of phase space structures, which are relevant for the energy dissipation. These structures are typically coupled in shocks, but we choose to consider them here in an isolated form. Three structures are reviewed. (1) Simulations of interpenetrating or colliding plasma clouds can trigger filamentation instabilities, while simulations of thermally anisotropic plasmas observe the Weibel instability. Both transform a spatially uniform plasma into current filaments. These filament structures cause the growth of the magnetic fields. (2) The development of a modified two-stream instability is discussed. It saturates first by the formation of electron phase space holes. The relativistic electron clouds modulate the ion beam and a secondary, spatially localized electrostatic instability grows, which saturates by forming a relativistic ion phase space hole. It accelerates electrons to ultra-relativistic speeds. (3) A simulation is also revised, in which two clouds of an electron-ion plasma collide at the speed 0.9c. The inequal densities of both clouds and a magnetic field that is oblique to the collision velocity vector result in waves with a mixed electrostatic and electromagnetic polarity. The waves give rise to growing corkscrew distributions in the electrons and ions that establish an equipartition between the electron, the ion and the magnetic energy. The filament-, phase space hole- and corkscrew structures are discussed with respect to electron acceleration and magnetic field generation.

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