Phase Space Holes Research Articles

Electron Preacceleration Mechanisms in the Foot Region of High Alfvenic Mach Number Shocks

High Mach number, collisionless perpendicular shocks are known to accelerate electrons to strongly relativistic energies by diffusive shock acceleration. This presupposes the existence of mildly relativistic electrons, whose preacceleration mechanism from lower ambient energies (the injection problem) remains an open question. Here a particle in cell simulation is used to investigate the preacceleration mechanism. Depending on the parameters of the upstream plasma and the shock velocity, the growth rate of instabilities in the foot of the shock can be significant, leading to the existence of nonlinear modes and the formation of electron phase space holes. It is found that these are associated with electron preacceleration, which can be divided into three phases. In the initial phase electrons are accelerated in the shock foot by the surfatron mechanism, which involves particle trapping in nonlinear wave modes. This mechanism is strongly linked to the existence of solitary electron phase space holes. The second phase is characterized by fluctuations in the magnetic field strength together with μ-conserving motion of the electrons. Finally, in the third phase the magnetic moment μ is no longer conserved, perhaps due to turbulent scattering processes. Energies up to Lorentz factors of 6 are achieved, for simulations in which the inflow kinetic energy of upstream electrons is 3.5 keV.

Characteristics of parallel electric fields in the downward current region of the aurora

Direct measurements of parallel electric fields suggest that they are, in part, self-consistently supported as strong double layers in the auroral downward current region. The observed parallel electric fields have amplitudes reaching nearly 1 V/m and are confined to a thin layer of approximately 10 Debye lengths. The structures are moving at roughly the ion acoustic speed in the direction of the accelerated electrons, i.e., anti-earthward. On the high-potential side of the parallel electric field there is a clear signature of an accelerated electron beam which rapidly plateaus within a few hundred Debye lengths from the parallel electric field. Strong wave turbulence is observed in the vicinity of the plateaued electron distribution. Fast solitary waves, identified as a signature of electron phase-space holes, are seen farther away from the parallel electric field on the high-potential side. The observed ion distributions also indicate the presence of the parallel electric field. On the low-potential side of the double layer an ion beam is observed moving in the opposite direction of the electron beam and ion conics appear to be trapped between their mirror point and the moving double layer.

BGK electron solitary waves: 1D and 3D

Abstract. This paper presents new results for 1D BGK electron solitary wave (phase-space electron hole) solutions and, based on the new results, extends the solutions to include the 3D electrical interaction (E ~ 1/r 2) of charged particles. Our approach for extending to 3D is to solve the nonlinear 3D Poisson and 1D Vlasov equations based on a key feature of 1D electron hole (EH) solutions; the positive core of an EH is screened by electrons trapped inside the potential energy trough. This feature has not been considered in previous studies. We illustrate this key feature using an analytical model and argue that the feature is independent of any specific model. We then construct azimuthally symmetric EH solutions under conditions where electrons are highly field-aligned and ions form a uniform background along the magnetic field. Our results indicate that, for a single humped electric potential, the parallel cut of the perpendicular component of the electric field (E⊥) is unipolar and that of the parallel component (E||) bipolar, reproducing the multi-dimensional features of the solitary waves observed by the FAST satellite. Our analytical solutions presented in this article capture the 3D electric interaction and the observed features of (E|| ) and E⊥. The solutions predict a dependence of the parallel width-amplitude relation on the perpendicular size of EHs. This dependence can be used in conjunction with experimental data to yield an estimate of the typical perpendicular size of observed EHs; this provides important information on the perpendicular span of the source region as well as on how much electrostatic energy is transported by the solitary waves.

Evidence for correlated double layers, bipolar structures, and very-low-frequency saucer generation in the auroral ionosphere

Recent observations by the Fast Auroral SnapshoT satellite have provided high-time-resolution measurements of three interrelated phenomena in the downward current region of the auroral ionosphere: Intense parallel electric fields (double layers) localized to tens of Debye lengths; drifting localized bipolar field structures interpreted in terms of electron phase-space holes; and intense quasi-electrostatic whistler emissions (very-low-frequency saucers) originating on the same field lines as the bipolar structures. Numerical simulations and theoretical modeling suggest how these observations may be related.

Numerical simulation of phase-space flows in the Collisionless Terrella experiment

Non-Maxwellian plasmas confined in a magnetic dipole can become unstable to hot electron interchange (HEI) instability, which saturates nonlinearly exciting drift-resonant fluctuations with complex time-varying frequency spectrum. A fully self-consistent nonlinear model, which includes /spl mu/, J preserving guiding center drift Hamiltonian dynamics of hot electrons, reproduces the frequency sweeping observed experimentally, and suggests spontaneous formation and consequent inward propagation of phase-space holes- coherent structures in phase-space, that can cause particle radial transport. We present the results of the numerical simulation showing the time evolution of the phase-space.

Fast evolving spatial structure of auroral parallel electric fields

We use a new nonlinear guiding center particle in cell code to investigate the role of Alfvén waves in the auroral particle acceleration. The propagation of an Alfvén wave in an inhomogeneous auroral plasma, described by a density cavity, is considered. Parallel electric fields are generated on the edges of the cavity, leading to an efficient electron acceleration and to the formation of electron beams. A beam‐plasma instability takes place. It evolves nonlinearly, and small‐scale electrostatic structures are created and propagate at a velocity close to the Alfvén velocity. A first category of these structures could be assimilated to weak double layers, whereas a second may be related to electron phase space holes. This study demonstrates the potential importance of Alfvén waves in the auroral acceleration and the coupling between large‐scale electromagnetic and small‐scale electrostatic phenomena.

An overview of observations by the Cassini radio and plasma wave investigation at Earth

On August 18, 1999, the Cassini spacecraft flew by Earth at an altitude of 1186 km on its way to Saturn. Although the flyby was performed exclusively to provide the spacecraft with sufficient velocity to get to Saturn, the radio and plasma wave science (RPWS) instrument, along with several others, was operated to gain valuable calibration data and to validate the operation of a number of capabilities. In addition, an opportunity to study the terrestrial radio and plasma wave environment with a highly capable instrument on a swift fly‐through of the magnetosphere was afforded by the encounter. This paper provides an overview of the RPWS observations at Earth, including the identification of a number of magnetospheric plasma wave modes, an accurate measurement of the plasma density over a significant portion of the trajectory using the natural wave spectrum in addition to a relaxation sounder and Langmuir probe, the detection of natural and human‐produced radio emissions, and the validation of the capability to measure the wave normal angle and Poynting flux of whistler‐mode chorus emissions. The results include the observation of a double‐banded structure at closest approach including a band of Cerenkov emission bounded by electron plasma and upper hybrid frequencies and an electron cyclotron harmonic band just above the second harmonic of the electron cyclotron frequency. In the near‐Earth plasma sheet, evidence for electron phase space holes is observed, similar to those first reported by Geotail in the magnetotail. The wave normal analysis confirms the Polar result that chorus is generated very close to the magnetic equator and propagates to higher latitudes. The integrated power flux of auroral kilometric radiation is also used to identify a series of substorms observed during the outbound passage through the magnetotail.

Formation of double layers and electron holes in a current-driven space plasma.

Kinetic 1D simulations reveal that a weak density depression in a current-carrying plasma can lead to the formation of a strong potential ramp (double layer). The ramp and plasma turbulence it creates share many features with recent particle and field measurements in the auroral ionosphere. An electron beam accelerated by the ramp produces a series of propagating electron phase-space holes via a spatial two-stream instability. Electron heating associated with the formation and merging of these holes is found to influence the subsequent evolution of the potential ramp.

Detailed structure and dynamics in particle-in-cell simulations of the lunar wake

The solar wind plasma from the Sun interacts with the Moon, generating a wake structure behind it, since the Moon is to a good approximation an insulator, has no intrinsic magnetic field and a very thin atmosphere. The lunar wake in simplified geometry has been simulated via a 112D electromagnetic particle-in-cell code, with high resolution in order to resolve the full phase space dynamics of both electrons and ions. The simulation begins immediately downstream of the moon, before the solar wind has infilled the wake region, then evolves in the solar wind rest frame. An ambipolar electric field and a potential well are generated by the electrons, which subsequently create a counter-streaming beam distribution, causing a two-stream instability which confines the electrons. This also creates a number of electron phase space holes. Ion beams are accelerated into the wake by the ambipolar electric field, generating a two-stream distribution with phase space mixing that is strongly influenced by the potentials created by the electron two-stream instability. The simulations compare favorably with WIND observations.

Electron heating and phase space signatures at supercritical, fast mode shocks

We investigate the effect of the nonmonotonic features of the macroscopic magnetic field B(chi;) and the deHoffmann‐Teller frame electrostatic potential ΦHT(chi;) on the electron distribution functions within collisionless, fast mode shocks. The signatures of electron distribution functions are explored by using Liouville's theorem in the adiabatic approximation to map model upstream and downstream boundary electron velocity distribution functions to regions inside model shocks with monotonic and nonmonotonic magnetic fields under the empirically motivated approximation that δΦHT ∝ δB. In the case of shocks with monotonically increasing magnetic fields, we show that there are no “exclusion” regions and that the electron distribution function at all pitch angles and hence the electron temperature increase can be explained by the reversible behavior of magnetized electrons in the shock macroscopic electric and magnetic fields. However, at shocks with nonmonotonic magnetic fields, there exist regions of inaccessibility which are outside the domain of the one‐Dimensional (1‐D), steady state Vlasov‐Liouville (V‐L) approach as defined by the upstream and downstream boundaries. Such regions, if occupied, may be filled by electrons scattered into these regions by waves, or perhaps by reversible processes such as the adiabatic convection of electrons into these regions of a curved bow shock, or by coherent nonadiabatic access. As a further test, the V‐L method is employed to study, for the first time, the detailed signatures of full 3‐D electron velocity distribution functions observed by the Wind spacecraft through the resolved layer of a supercritical, fast mode Earth bow shock crossing. We demonstrate that much of the complex structure of the observed electron distribution function within the shock layer can be explained by the motion of adiabatic electrons in the non‐monotonic shock macroscopic magnetic and electric fields. However, a significant portion of electron phase space appears to be the remnants of electron phase space holes. The mechanisms responsible for allowing electrons to gain access to the exclusion regions are not well understood and may have important implications on the thermodynamic properties of collisionless shocks.

Direct observation of localized parallel electric fields in a space plasma.

We report direct measurements of parallel electric fields related to particle acceleration in a collisionless space plasma. The electric field is that of a monotonic potential ramp localized to approximately 10 debye lengths along the magnetic field. Electrons accelerated by the parallel electric field are accompanied by intense electrostatic waves and nonlinear structures interpreted as electron phase-space holes.

Evolution of electron phase‐space holes in 3D

Electron phase‐space holes are regions of depleted electron density commonly generated during the nonlinear stage of the two‐stream instability. Recently, bipolar electric field structures—a signature of electron holes —have been identified in the acceleration region of the auroral ionosphere. This paper compares the evolution of electron holes in 2‐D and 3‐D using massively‐parallel PIC simulations. In 2‐D, the holes decay after hundreds of plasma periods while emitting electrostatic whistler waves. In the 3‐D simulations, electron holes also go unstable and generate whistlers but, due to physical processes not present in 2‐D, energy flows out of the whistlers and into highly perpendicular lower hybrid modes. As a result of this difference, 3‐D holes do not decay as far as 2‐D holes. The differences between 2‐D and 3‐D evolution may have important implications for hole longevity and wave generation in the auroral ionosphere.

Electrostatic mode excitation in electron holes due to wave bounce resonances.

A kinetic theory of resonant interaction between electrostatic waves and the bounce motion of electrostatically trapped electrons is developed. Precise criteria are derived for the stability of electrostatic potential structures which trap electrons in a highly magnetized plasma. The theory explains the energy transfer from electron phase space holes to waves observed in simulations. It may also account for the destabilization of electrostatic waves propagating obliquely to the geomagnetic field and some characteristics of the holes as observed in the auroral ionosphere.

Dynamics and instability of electron phase-space tubes.

Two-dimensional simulations of beam-driven turbulence in the auroral ionosphere have shown the formation and instability of phase-space tubes. These tubes are a generalization of electron phase-space holes in a one-dimensional plasma. In a strongly magnetized plasma, such tubes vibrate at frequencies below the bounce frequency of the trapping potential. A theory for these vibrations yields quantitative agreement with kinetic simulations. Furthermore, the theory predicts that the vibrations can become unstable when resonantly coupled to electrostatic whistlers-also in agreement with simulations.

Electron Acceleration in the Heliosphere

We review the evidence for electron acceleration in the heliosphere putting emphasis on the acceleration processes. There are essentially four classes of such processes: shock acceleration, reconnection, wave particle interaction, and direct acceleration by electric fields. We believe that only shock and electric field acceleration can in principle accelerate electrons to very high energies. The shocks known in the heliosphere are coronal shocks, traveling interplanetary shocks, CME shocks related to solar type II radio bursts, planetary bow shocks, and the termination shock of the heliosphere. Even in shocks the acceleration of electrons requires the action of wave particle resonances of which beam driven whistlers are the most probable. Other mechanisms of acceleration make use of current driven instabilities which lead to electron and ion hole formation. In reconnection acceleration is in the current sheet itself where the particles perform Speiser orbits. Otherwise, acceleration takes place in the slow shocks which are generated in the reconnection process and emanate from the diffusion region in the Petschek reconnection model and its variants. Electric field acceleration is found in the auroral zones of the planetary magnetospheres and may also exist on the sun and other stars including neutron stars. The electric potentials are caused by field aligned currents and are concentrated in narrow double layers which physically are phase space holes in the ion and electron distributions. Many of them add up to a large scale electric field in which the electrons may be impulsively accelerated to high energies and heated to large temperatures.

Phase Space, Density Matrices, Energy Densities, and Exchange Holes

In the general case, quantum-mechanical quantities are represented by operators in position- or momentum-space representations, but in phase space they are represented by functions. The correspondence between classical mechanics and quantum mechanics is non-unique as a consequence of [

Strong Electron Acceleration at High Mach Number Shock Waves: Simulation Study of Electron Dynamics

Electron-ion dynamics in a perpendicular magnetosonic shock wave in a high Mach number regime is studied by using the particle-in-cell simulation. It is shown that in the shock transition layer nonlinear evolution of two-stream instabilities plays an important role on the electron rapid heating and acceleration. As the shock Mach number greatly exceeds the critical Mach number, a series of large-amplitude, coherent electrostatic waves with the electron holes in phase space are excited by the two-stream instability between the reflected ions and the incident electrons in the shock transition layer. As the incident electrons are decelerated by the instability, other electrostatic waves grow in time by another two-stream instability between the incident ions and the decelerated incident electrons. The dynamic timescale of these instabilities is of the order of ω, where ωpe is the plasma frequency. The nonlinear interaction of these waves leads to the strong electron heating as well as the nonthermal high-energy electron acceleration in the shock transition layer.

Electron beam generated solitary structures in a nonuniform plasma system

Recent observations by the FAST satellite have identified numerous occurrences in the downward auroral current region of fast solitary structures with a characteristic size of a few local Debye lengths. We utilize a 2.5D electrostatic particle‐in‐cell code to investigate the generation of such structures by the interaction of narrow energetic electron beams with a gravitationally‐bound exponential atmosphere. Cold, narrow electron beams are injected from both the high‐altitude and low‐altitude edges of the simulation domain. Both upward and downward‐going beams experience a strong beam‐plasma instability yielding net positive potential structures. These structures, seen to be holes in electron phase space, then accelerate or decelerate along the density gradient. For the up‐going beams, the potential structures escape from the initial region of intense interaction, after which they propagate surprisingly far. The down‐going structures accelerate but become degraded and break up due to the finer scales present in the increased density region. The gradient‐dependent acceleration therefore selects upward‐going structures as likely to be more robust in the auroral region.

Transverse instability of magnetized electron holes

We study a transverse instability of the nonlinear equilibria known as electron phase-space holes in the presence of a magnetic field. The instability is intrinsically two dimensional and is determined by the dynamics of the trapped electrons. It depends on hole amplitudes, ambient magnetic fields, and the perpendicular velocity spread. The long-standing hole stability problem in multiple dimensions can be characterized by the gyro-to-bounce frequency ratio. A low ratio associated with a small perpendicular velocity spread results in a disintegration of the positive potential spikes.

Spaced measurements and progress in understanding space plasma waves

Measuring plasma wave properties with spatially separated antennae observes wavelength, propagation speed, and direction as well as frequency. This approach has been pivotal to progress in understanding three phenomena in space plasmas. The first is lower hybrid solitary waves, which are waves with cylindrical symmetry propagating inside a density cavity. The second is electron phase-space holes, which are propagating vortices in phase space. The third is called broadband ELF (extra low frequency) electric fields and is an important but poorly understood wave process essential to transverse ion acceleration.