H. Thiemann

Simulations of auroral plasma processes: Electric fields, waves and particles

Abstract Satellite and rocket observations have revealed a host of auroral plasma processes, including large dc perpendicular electric fields ( E ⊥ ) associated with electrostatic shocks, relatively weak parallel electric fields ( E ∥ ) associated with double layers, upflowing ions in the form of beams and conics, downflowing and upflowing accelerated electron beams, several wave modes such as the elctrostatic ion-cyclotron (EIC), lower hybrid (LH), VLH, ELF and high frequency waves and associated non-linear phenomena. We have attempted to simulate these various processes using a two-dimensional particle-in-cell code. In these simulations the plasma is driven by current sheets (carrying upward currents) of a finite thicknesses. Striking similarities between the observed auroral plasma processes and those seen in the simulations are found. Large perpendicular electric fields ( E ⊥ e ) develop near the edges of the current sheets, which have features similar to electrostatic shocks. Double layer formation occurs inside the current sheets and also outside the sheet where downward current flows. The polarities of the parallel electric fields of the double layers inside and outside the current sheet are found to be mainly upward and downward, respectively. The double layer electric field strength ( E ∥ ) is found to be highly variable, depending on the plasma parameters. However, it is generally found that E ⊥ m ⪢ and E ∥ m where, E ⊥ m and E ∥ m are respectively, the maximum strengths of E ⊥ and E ∥ seen in the simulations irrespective of their relative locations. Normally, the electric field strength of double layers in larger than the parallel electric fields occurring at the locations where E ⊥ e maximizes. The non-linear phenomenon associated with the waves near the electron plasma frequency is found to cause a low frequency relaxation-type of oscillition in the potential structure. The low frequency waves seen in the simulations range from below the ion-cyclotron frequency to above the lower hybrid frequency. In some simulations, spiky ion-cyclotron waves are seen. Ion beam formation with a positive slope in the parallel velocity distribution function is seen only in a narrow currentsheet with a thickness l ∼ p i , where p i is an appropriate ion Larmor radius. In wide sheets l ⪢ p i ; the upflowing ions are found to be considerably heated. The most energetic ions seen in the simulations have pitch angles near 90°, implying perpendicular ion acceleration, which is the main mechanism for the generation of ion conics. The inverted-V feature in the horizontal distribution of the downflowing accelerated electrons is seen. However, the accelerated electrons are found to be neither monoenergetic nor perfectly field-aligned. Double layers in the current sheets are found to be the triggering mechanism for the plasma processes which shape the distribution function of the accelerated electrons. Counterstreaming accelerated electrons are also seen. Upward electron beams in the downward current regions are found to be nearly a permanent feature of the simulations with wide sheets. On the other hand, in simulations with narrow sheets such beams are transient.

Studies on Counterstreaming Plasma Expansion

Counterstreaming plasma expansion occurs in a variety of physical situations ranging from laboratory devices to plasmas in space. In such situations, the counterstreaming plasma streams consisting of accelerated ions, collide with each other. Upon this collision, the interaction of the ion streams can lead to a variety of plasma physical phenomena such as the excitation of waves and instabilities and formations of shocks. In order to study these phenomena, several types of numerical simulations were carried out. One-dimensional Vlasov simulations with Boltzmann electrons showed that the H+ streams produced by the counterstreaming expansion of an O+ - H+ ion plasma in which H+ is minor, do not couple with each other. The H+ streams pass through each other without exciting any instability which turns out to be in agreement with the linear stability of the plasma. Thus, the streams do not thermalize in the expansion region and penetrate the source plasmas, where they slow down and interact with the ambient plasmas exciting relatively strong oscillations. In order to remove the limitations on the above type of simulations, such as the plasma being one dimensional and the electrons obeying the Boltzmann law, two-dimensional particle simulations, in which electrons and ions were treated like particles, were carried out. Despite the limitations imposed by computer resources, the 2-D simulations brought out some interesting results as follows. The ion streams were seen to mix together via the ion-ion instability when Te/Ti 3, where Te and Ti are the electron and ion temperatures in the source plasmas. For Te/Ti 5, the collisions of the ion streams produced a pair of electrostatic shocks propagating in opposite directions. On the other hand, for smaller temperature ratio (5 < Te/Ti 3), the instability resulted into short wavelength waves, which evolved into highly structured nearly stationary waveforms giving spiky electric fields. Since the small scale Vlasov or particle simulations are limited in their spatial extent, their applicability to large scale counterstreaming plasma expansions in space cannot be easily appreciated. This led to the studies on counterstreaming ionospheric plasma expansion along the closed geomagnetic flux tubes in the outer region of the terrestrial plasmasphere. In such studies the hydrodynamic equations were solved. The formation of a shock pair, upon the collision of the ion streams, was always seen, irrespective of the electron-ion temperature ratio, as expected from hydrodynamic calculations. The refilling of the flux tube occurs by the downward propagation of the shocks. The refilling rates derived from the hydrodynamic calculations are found to be in fair agreement with satellite observations. The kinetic aspects of the shock formations as derived from the small-scale simulations are discussed.

Comparison of macroscopic particle-in-cell and semikinetic models of the polar wind

The outflow of the polar wind along diverging geomagnetic field lines has been the subject of many modeling studies for the past 25 years. As the plasma drifts up and out of the topside ionosphere, it undergoes several transitions; for instance, its velocity changes from subsonic to supersonic and its velocity distribution changes from Maxwellian to non-Maxwellian. The complexity of the flow led to the development of several modeling approaches, such as the generalized moment, the kinetic, and the semikinetic models. Recently, a macroscopic particle-in-cell (PIC) model was adopted to study the polar wind. However, because one is always restricted to a finite number of particles, the validity of the approach must be established when it is applied to macroscopic flows. In this study the polar wind predictions obtained from a macroscopic PIC simulation were compared to those obtained from the more rigorous semikinetic model for steady state conditions. The study also shows the sensitivity of the PIC simulation to the adopted modeling parameters for both time-dependent and steady state conditions, including the number of simulation particles, the time step, the spatial bin size, etc. The study indicates that (1) the PIC model can be a powerful simulation tool if special attention is given to its potential pitfalls; (2) because of the finite number of particles the PIC technique is subject to a considerable amount of noise; (3) the noise level is higher for the higher-order moments, such as heat flow, and for the velocity distribution function; (4) the use of a time step that is too large leads to a modulation of the results; (5) an insufficient number of spatial bins yields a poor spatial resolution, while too many spatial bins leads to more noise; (6) the noise level can be reduced by averaging over time and/or space, but this affects the spatial and/or temporal resolution; (7) the bin size in velocity space must be carefully chosen to balance numerical noise and velocity space resolution; (8) in the steady state the PIC technique can achieve the same accuracy as the semikinetic model if all of the PIC modeling parameters are optimized; and (9) a few hundred thousand simulation particles, as used in some previous studies, are not adequate to resolve the tail of the velocity distribution, even in the steady state when time averaging is possible. For 10 6 particles the noise in the tail is still appreciable; and (10) when poor spatial resolution is used, important features can be missed, as was the case in some previous studies.

Particle-in-cell simulations of sheath formation around biased interconnectors in a low-earth-orbit plasma

The interaction between satellite solar arrays and the LEO plasma is presently studied with particle-in-cell simulations in which an electrical potential was suddenly applied to the solar cell interconnector. The consequent temporal response was followed for the real O(+)-electron mass ratio in the cases of 100- and 250-V solar cells, various solar cell thicknesses, and solar cells with secondary electron emission. Larger applied potentials and thinner solar cells lead to greater initial polarization surface charges, and therefore longer discharging and shielding times. When secondary electron emission from the cover glass is brought to bear, however, the potential structure is nearly planar, allowing constant interaction between plasma electrons and cover glass; a large fraction of the resulting secondary electrons is collected by the interconnector, constituting an order-of-magnitude increase in collected current.

Electric fields and double layers in plasmas

Various mechanisms for driving double layers in plasmas are briefly described, including applied potential drops, currents, contact potentials, and plasma expansions. Some dynamic features of the double layers are discussed. These features, as seen in simulations, laboratory experiments and theory, indicate that double layers and the currents through them undergo slow oscillations, which are determined by the ion transit time across an effective length of the system in which the double layers form. It is shown that a localized potential dip forms at the low potential end of a double layer, which interrupts the electron current through it according to the Langmuir criterion, whenever the ion flux into the double is disrupted. The generation of electric fields perpendicular to the ambient magnetic field by contact potentials is also discussed. Two different situations have been considered; in one, a low-density hot plasma is sandwiched between high-density cold plasmas, while in the other a high-density current sheet permeates a low-density background plasma. Perpendicular electric fields develop near the contact surfaces. In the case of the current sheet, the creation of parallel electric fields and the formation of double layers are also discussed when the current sheet thickness is varied. Finally, the generation of electric fields (parallel to an ambient magnetic field) and double layers in an expanding plasma are discussed.

Some features of auroral electric fields as seen in 2D numerical simulations

Abstract Results of 2D plasma simulations, which show the formation of V-shaped double layers with larger perpendicular than parallel electric field amplitudes, the excitation of electrostatic ion-cyclotron waves and the occurrence of return currents, are presented and related to auroral observations.

Numerical simulations of double layers and auroral electric fields

Recent numerical simulations on double layers (DL) are reviewed and discussed in the light of relevant space observations in the auroral plasma. Two-dimensional (2-d) DLs driven by current sheets of a finite thickness l show different characteristics depending on whether l 100 μA/m2) and the excitation of Buneman double layers.

Shocks in the polar wind

The occurrence of shock waves in the terrestrial polar wind was predicted many years ago by a time-dependent three-dimensional model based on hydrodynamic equations. These shocks were seen to occur for counterstreaming ion populations and for cases when a convecting flux tube entered a region of sharply increasing electron temperature, such as the dayside cusp. Other studies conducted at about the same time showed that the shocks induced by counterstreaming ion populations may simply be artifacts of the adopted hydrodynamic model. The validity of shocks induced by electron temperature enhancements has remained an open question. Using a macroscopic particle-in-cell (PIC) code, we have verified the hydrodynamic prediction that sudden electron temperature enhancements can launch shock waves in a convecting flux tube of plasma. Our simulation follows a flux tube as it convects antisunward across the dayside auroral oval, the polar cap, and the nightside auroral oval. The electron temperature at 2000 km altitude is assumed to be relatively low (3000 K) in the subauroral ionosphere and in the polar cap but much higher (7000 K) in the dayside and nightside auroral oval. As the flux tube enters the auroral oval, either on the dayside or the nightside, forward and reverse shock pairs in the H+ component of the plasma are created at the bottom of the flux tube and propagate upward until they exit the simulation region at the top. The forward and reverse shock fronts propagate at speeds greater than and less than the drift speed of the H+ gas, respectively.

High-voltage solar cell modules in simulated low-earth-orbit plasma

The behavior of solar cell modules at high voltages in a surrounding simulated LEO plasma has been characterized over an applied voltage range from -700 to +500 V. Measurements were obtained in a large chamber under high vacuum using argon ions from a Kaufman source to generate a high-density plasma of up to 10 to the 6th/cu cm. The results suggest that secondary electrons contribute to the anomalous current increase noted at positive module voltages above 300 V. The surface potential on the coverglasses of the solar cells was shown to increase to high values only in the vicinity of the interconnectors. 27 references.

High-latitude ionospheric model

A set of regional maps of peak electron density in the northern polar cap was deduced from aeronomical computations for southward IMF executed at Utah State University (USU) /1/. Each of the 12 maps holds for invariant latitudes greater than 50° N, covering 24h both in magnetic local time and in UT. The maps for two parameters are analyzed in terms of Empirical Orthogonal Functions (EOF). The dependence on other parameters is described by continuous functions. In the northern polar cap, these maps might be used as a partially substituting supplement of the world wide maps recommended by the CCIR/2/.