Coherent phase space structures in a 1D electrostatic plasma using particle-in-cell and Vlasov simulations: A comparative study

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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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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Formation and interaction of multiple coherent phase space structures in plasma

Physics of Plasmas ◽

10.1063/1.4986109 ◽

2017 ◽

Vol 24 (6) ◽

pp. 060704 ◽

Cited By ~ 10

Author(s):

Amar Kakad ◽

Bharati Kakad ◽

Yoshiharu Omura

Keyword(s):

Phase Space ◽

Space Structures ◽

Coherent Phase

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Ion phase-space vortices in 2.5-dimensional simulations

Journal of Plasma Physics ◽

10.1017/s0022377801008947 ◽

2001 ◽

Vol 65 (2) ◽

pp. 107-129 ◽

Cited By ~ 8

Author(s):

STEINAR BØRVE ◽

HANS L. PÉCSELI ◽

JAN TRULSEN

Keyword(s):

Magnetic Field ◽

Phase Space ◽

Ion Beam ◽

Plasma Boundary ◽

Space Structures ◽

Beam Diameter ◽

Particle In Cell ◽

Spatial Dimensions ◽

Cell Simulation ◽

Transverse Modulation

The formation and propagation of ion phase-space vortices are observed in a numerical particle-in-cell simulation in two spatial dimensions and with three velocity components. The code allows for an externally applied magnetic field. The electrons are assumed to be isothermally Boltzmann-distributed at all times, implying that Poisson's equation becomes nonlinear for the present problem. Ion phase-space vortices are formed by the nonlinear saturation of the ion-ion two-stream instability, excited by injecting an ion beam at the plasma boundary. We consider the effect of a finite beam diameter and a magnetic field, in particular. A vortex instability is observed, appearing as a transverse modulation, which slowly increases with time and ultimately breaks up the vortex. When many vortices are present at the same time, we find that it is their interaction that eventually leads to a gradual filling-up of the phase-space structures. The ion phase-space vortices have a finite lifetime, which is noticeably shorter than that found in one-dimensional simulations. An externally imposed magnetic field can increase this lifetime considerably. For high injected beam velocities in magnetized plasmas, we observe the excitation of electrostatic ion-cyclotron instabilities, but see no associated formation of ion phase-space vortices. The results are relevant, for instance, for the interpretation of observations by instrumented spacecraft in the Earth's ionosphere and magnetosphere.

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Nonlinear instabilities driven by coherent phase-space structures

Physical Review E ◽

10.1103/physreve.87.031101 ◽

2013 ◽

Vol 87 (3) ◽

Cited By ~ 25

Author(s):

M. Lesur ◽

P. H. Diamond

Keyword(s):

Phase Space ◽

Space Structures ◽

Coherent Phase

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Geometric particle-in-cell methods for the Vlasov–Maxwell equations with spin effects

Journal of Plasma Physics ◽

10.1017/s0022377821000532 ◽

2021 ◽

Vol 87 (3) ◽

Author(s):

Nicolas Crouseilles ◽

Paul-Antoine Hervieux ◽

Yingzhe Li ◽

Giovanni Manfredi ◽

Yajuan Sun

Keyword(s):

Phase Space ◽

Maxwell Equations ◽

Stimulated Raman Scattering ◽

Extended Phase ◽

Five Dimensions ◽

Particle In Cell ◽

Spin Effects ◽

Dimensional Phase Space ◽

Spin Polarized ◽

Underdense Plasma

We propose a numerical scheme to solve the semiclassical Vlasov–Maxwell equations for electrons with spin. The electron gas is described by a distribution function $f(t,{\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ that evolves in an extended 9-dimensional phase space $({\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ , where $\boldsymbol s$ represents the spin vector. Using suitable approximations and symmetries, the extended phase space can be reduced to five dimensions: $(x,{{p_x}}, {\boldsymbol s})$ . It can be shown that the spin Vlasov–Maxwell equations enjoy a Hamiltonian structure that motivates the use of the recently developed geometric particle-in-cell (PIC) methods. Here, the geometric PIC approach is generalized to the case of electrons with spin. Total energy conservation is very well satisfied, with a relative error below $0.05\,\%$ . As a relevant example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, where the electrons are partially or fully spin polarized. It is shown that the Raman instability is very effective in destroying the electron polarization.

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