IDENTIFICATION OF COMPLEX PROCESSES BASED ON ANALYSIS OF PHASE SPACE STRUCTURES

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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ANOMALOUS TRANSPORT AND PHASE SPACE STRUCTURES

Chaos, Complexity And Transport ◽

10.1142/9789814405645_0006 ◽

2012 ◽

pp. 58-66

Author(s):

B. MEZIANI ◽

O. OURRAD ◽

X. LEONCINI

Keyword(s):

Phase Space ◽

Anomalous Transport ◽

Space Structures

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Tilting and Squeezing: Phase Space Geometry of Hamiltonian Saddle-Node Bifurcation and its Influence on Chemical Reaction Dynamics

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420300086 ◽

2020 ◽

Vol 30 (04) ◽

pp. 2030008 ◽

Cited By ~ 6

Author(s):

Víctor J. García-Garrido ◽

Shibabrat Naik ◽

Stephen Wiggins

Keyword(s):

Phase Space ◽

Hamiltonian System ◽

Potential Energy ◽

Invariant Manifolds ◽

Reaction Dynamics ◽

Potential Energy Function ◽

Space Structures ◽

Stable And Unstable Manifolds ◽

Saddle Node Bifurcation ◽

Saddle Node

In this article, we present the influence of a Hamiltonian saddle-node bifurcation on the high-dimensional phase space structures that mediate reaction dynamics. To achieve this goal, we identify the phase space invariant manifolds using Lagrangian descriptors, which is a trajectory-based diagnostic suitable for the construction of a complete “phase space tomography” by means of analyzing dynamics on low-dimensional slices. First, we build a Hamiltonian system with one degree-of-freedom (DoF) that models reaction, and study the effect of adding a parameter to the potential energy function that controls the depth of the well. Then, we extend this framework to a saddle-node bifurcation for a two DoF Hamiltonian, constructed by coupling a harmonic oscillator, i.e. a bath mode, to the other reactive DoF in the system. For this problem, we describe the phase space structures associated with the rank-1 saddle equilibrium point in the bottleneck region, which is a Normally Hyperbolic Invariant Manifold (NHIM) and its stable and unstable manifolds. Finally, we address the qualitative changes in the reaction dynamics of the Hamiltonian system due to changes in the well depth of the potential energy surface that gives rise to the saddle-node bifurcation.

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Phase space structures generated by absorbing obstacles in streaming plasmas

Annales Geophysicae ◽

10.5194/angeo-23-853-2005 ◽

2005 ◽

Vol 23 (3) ◽

pp. 853-865 ◽

Cited By ~ 16

Author(s):

P. Guio ◽

H. L. Pécseli

Keyword(s):

Phase Space ◽

Collisionless Plasma ◽

Flow Characteristics ◽

Plasma Potential ◽

Velocity Shear ◽

Space Structures ◽

Space Plasmas ◽

Physical Parameters ◽

Particle In Cell ◽

Cell Simulation

Abstract. The dynamic behavior of a collisionless plasma flowing around an obstacle is investigated by numerical methods. In the present studies, the obstacle is formed by an absorbing cylinder, and a 2-D electrostatic particle-in-cell simulation is used to study the flow characteristics, with extensions to a fully 3-D generalization of the problem demonstrated as well. The formation of irregular filamented density depletions, oblique to the flow, is observed. The structures form behind the obstacle, in a region with a strong velocity shear, but also other instability mechanisms can be identified. The dynamics of these structures is highly dependent on the physical parameters of the plasma, and they can either be quasi-stationary or undergo a dynamic evolution. The structures are found to be associated with phase-space vortices, observed especially in the phase space spanned by the velocity direction perpendicular to the flow and the spatial coordinate in the same direction. The bias of the obstacle with respect to the plasma potential is found to be an important parameter for the dynamics of the structures, but seemingly not for their formation as such. The results can be of interest in the interpretation of structures in space plasmas as observed by instrumented spacecrafts.

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