Correction to “Particle-in-cell simulations of the lunar wake with high phase space resolution”

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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Cooling of Sr to high phase-space density by laser and sympathetic cooling in isotopic mixtures

Physical Review A ◽

10.1103/physreva.73.023408 ◽

2006 ◽

Vol 73 (2) ◽

Cited By ~ 24

Author(s):

G. Ferrari ◽

R. E. Drullinger ◽

N. Poli ◽

F. Sorrentino ◽

G. M. Tino

Keyword(s):

Phase Space ◽

Phase Space Density ◽

Sympathetic Cooling ◽

Space Density ◽

High Phase

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Method for obtaining high phase space density in a surface-mounted atom trap

Applied Physics B ◽

10.1007/s00340-004-1556-9 ◽

2004 ◽

Vol 79 (3) ◽

pp. 367-370 ◽

Cited By ~ 2

Author(s):

A. Shevchenko ◽

A. Jaakkola ◽

T. Lindvall ◽

I. Tittonen ◽

M. Kaivola

Keyword(s):

Phase Space ◽

Phase Space Density ◽

Space Density ◽

Atom Trap ◽

High Phase

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

Nonlinear Processes in Geophysics ◽

10.5194/npg-15-831-2008 ◽

2008 ◽

Vol 15 (6) ◽

pp. 831-846 ◽

Cited By ~ 8

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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Electron phase-space hole transverse instability at high magnetic field

Journal of Plasma Physics ◽

10.1017/s0022377819000564 ◽

2019 ◽

Vol 85 (5) ◽

Cited By ~ 1

Author(s):

I. H. Hutchinson

Keyword(s):

Phase Space ◽

Low Frequency ◽

Force Balance ◽

Complex Frequency ◽

Electron Hole ◽

Particle In Cell ◽

Planar Electron ◽

Wave Phenomena ◽

Slow Growing ◽

Infinite Particle

Analytic treatment is presented of the electrostatic instability of an initially planar electron hole in a plasma of effectively infinite particle magnetization. It is shown that there is an unstable mode consisting of a rigid shift of the hole in the trapping direction. Its low frequency is determined by the real part of the force balance between the Maxwell stress arising from the transverse wavenumber $k$ and the kinematic jetting from the hole’s acceleration. The very low growth rate arises from a delicate balance in the imaginary part of the force between the passing-particle jetting, which is destabilizing, and the resonant response of the trapped particles, which is stabilizing. Nearly universal scalings of the complex frequency and $k$ with hole depth are derived. Particle in cell simulations show that the slow-growing instabilities previously investigated as coupled hole–wave phenomena occur at the predicted frequency, but with growth rates 2 to 4 times greater than the analytic prediction. This higher rate may be caused by a reduced resonant stabilization because of numerical phase-space diffusion in the simulations.

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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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