Electron Phase Space Distribution Research Articles

Driven phase space holes and synchronized Bernstein, Greene, and Kruskal modes

The excitation of synchronized Bernstein, Greene, and Kruskal (BGK) modes in a pure electron plasma confined in Malmberg–Penning trap is studied. The modes are excited by controlling the frequency of an oscillating external potential. Initially, the drive resonates with, and phase-locks to, a group of axially bouncing electrons in the trap. These initially phase-locked electrons remain phase-locked (in “autoresonance”) during a subsequent downward chirp of the external potential’s oscillation frequency. Only a few new particles are added to the resonant group as the frequency, and, hence, the resonance, moves to lower velocities in phase space. Consequently, the downward chirp creates a charge density perturbation (a hole) in the electron phase space distribution. The hole oscillates in space, and its associated induced electric field constitutes a BGK mode synchronized with the drive. The size of the hole in phase space, and thus the amplitude of the mode, are largely controlled by only two external parameters: the driving frequency and amplitude. A simplified kinetic theory of this excitation process is developed. The dependence of the excited BGK mode amplitude on the driving frequency chirp rate and other plasma parameters is discussed and theoretical predictions are compared with recent experiments and computer simulations.

Simulated expansion of an ultra-cold, neutral plasma

The details of recent calculations of the expansion of ultra-cold, neutral plasmas are given. The calculations are performed at several levels. The simplest level assumes an ansatz for the form of the electron and ion density; the result is a simple, ordinary differential equation which can be easily solved. The medium level of sophistication assumes the electrons are in thermal equilibrium but does not assume a particular form for the ion density; the result is a partial differential equation which is solved numerically. For the highest level of sophistication, a Monte Carlo technique is used to solve for the electron phase space distribution and solve for the ion motion in the resulting mean field. All levels of simulation include three body recombination and electron-Rydberg scattering. This paper contains the results of our simulations and compares them to measurements made on ultra-cold plasmas. Three body recombination is found to be important at very low temperatures since it is a heating mechanism for the electron gas. The collisions between cold electrons and Rydberg atoms are another important source of electron heating and de-excitation of atoms formed in the plasma. The evolution of the distribution of atoms in the plasma is simulated and several counter-intuitive effects that have been observed can be explained. Our simulations show that the plasma coupling constant does not become larger than ∼1/5 for the reported experiments. The behavior of plasma processes are investigated, e.g., ion acoustic waves, spike formation, and electron evaporation. The evolution of a cold Rydberg gas into a plasma is also simulated but certain properties of our simulation do not agree with measurements.

Three-dimensional visualization of electron acceleration in a magnetized plasma

We examine wave-particle interactions in a magnetized plasma. We present snapshots of an animation of the three-dimensional electron phase space distribution produced by an electrostatic wave propagating across a magnetic field. The distribution function has been evolved by a particle in cell simulation. The electron phase space has been visualized by distributing the simulation electrons over an array representing phase space density and by volume rendering this array. The results are, due to the choice of initial plasma and wave parameters, of relevance for electron acceleration at astrophysical shocks.

Start-up noise in 3-D self-amplified spontaneous emission

We discuss the effective start-up noise in Self-Amplified Spontaneous Emission (SASE), taking into account the finite angular spread as well as the size of the electron beam. The results obtained here generalize those obtained previously in the case of parallel beams, and clarify the role of the electron phase space distribution in the SASE start-up.

Discussion 2: On the convection and velocity filter

During conditions of northward interplanetary magnetic field (IMF), the near-tail plasma sheet is known to become denser and cooler, and is described as the cold-dense plasma sheet (CDPS). While its source is likely the solar wind, the prominent penetration mechanisms are less clear. The two main candidates are solar wind direct capture via double high-latitude reconnection on the dayside and Kelvin–Helmholtz/diffusive processes at the flank magnetopause. This paper presents a case study on the formation of the CDPS utilizing a wide variety of space- and ground-based observations, but primarily from the Double Star and Polar spacecraft on December 5th, 2004. The pertinent observations can be summarized as follows: TC-1 observes quasi-periodic (∼2 min period) cold-dense boundary layer (compared to a hot-tenuous plasma sheet) signatures interspersed with magnetosheath plasma at the dusk flank magnetopause near the dawn-dusk terminator. Analysis of this region suggests the boundary to be Kelvin–Helmholtz unstable and that plasma transport is ongoing across the boundary. At the same time, IMAGE spacecraft and ground based SuperDARN measurements provide evidence of high-latitude reconnection in both hemispheres. The Polar spacecraft, located in the southern hemisphere afternoon sector, sunward of TC-1, observes a persistent boundary layer with no obvious signature of boundary waves. The plasma is of a similar appearance to that observed by TC-1 inside the boundary layer further down the dusk flank, and by TC-2 in the near-Earth magnetotail. We present comparisons of electron phase space distributions between the spacecraft. Although the dayside boundary layer at Polar is most likely formed via double high-altitude reconnection, and is somewhat comparable to the flank boundary layer at Double Star, some differences argue in favour of additional transport that augment solar wind plasma entry into the tail regions.

Solitary structures in the magnetospheric plasma observed by Viking

The Viking low frequency wave experiment, with unique two point measurements of plasma density fluctuations and measurements of potential fluctuations, provided detailed diagnostics of small scale, large amplitude solitary structures in the auroral acceleration region. The structures have a spatial scale of the order of 100 m, density depletions up to 50%, negative potentials up to about 5V, and propagate upwards along the magnetic field lines with velocities from about 5 to more than 50 km s−1. Some structures have a net potential drop of up to a few volts, in general directed upwards. The structures are characterized as solitary waves (no net potential drop) and weak double layers (a net potential drop comparable to kTe/e), or holes in the thermal ion (and electron) phase space distribution. Their occurrence is correlated with that of beams of upward flowing energetic ions, dominated by protons, and electrostatic ion cyclotron waves. The field-aligned currents seem to be relatively weak. A great number of structures with a net potential may account for a large scale potential drop along the geomagnetic field lines and the observed acceleration of auroral particles up to kilovolt energies.

Nonlinear interactions during magnetic field-line reconnection in plasmas

Stimulated by important dynamic processes in space and fusion plasmas, the reconnection of magnetic fields in plasmas is investigated. A well-controlled large laboratory plasma is established, and direct observations of magnetic fields and particle distributions are performed. High speed computers are interfaced with the experiment so as to permit the analysis of multidimensional functions. These include the average magnetic field topology 〈 B ( r , t)〈 and the tensor correlation function 〈 B 1 B 2〉 ω, k of magnetic fluctuations, as well as the electron phase space distribution function ƒ( v , r , t). The observations show that the characteristic field topology of a neutral sheet is subject to a high level of magnetic turbulence consisting of low frequency whistler waves. These are excited by anisotropies in the electron distribution functions inside the current sheet, in particular by energetic electrons which run away in the electric field along the separator. The observed microinstabilities and kinetic processes cannot be described by classical fluid theories or MHD simulations but are important in determining the effective resistivity and reconnection rate.

General Spherical Harmonics Formulation of Plasma Boltzmann Equation

The Boltzmann equation for the phase space distribution of electrons in the presence of ions is reduced to an infinite set of differential equations which do not involve angle variables. The usual method of expanding the electron phase space distribution function in terms of spherical harmonics is employed and it is assumed, in analyzing the scattering process, that the ion velocities can be neglected in comparison with the electron velocities. The expansion includes both polar and azimuthal angles obviating the assumption of symmetry about a polar axis made in previous work. The differential equation for the general component of the spherical harmonics expansion is derived and explicit equations for the first few components are presented. The component equations are seen to be considerably more tractable for cases which involve electric and/or magnetic fields along a single axis.