A Self-Similar Solution for the Propagation of a Relativistic Shock in an Exponential Atmosphere

We derive a fully relativistic, self-similar solution to describe the propagation of a shock along an exponentially decreasing atmosphere, in the limit of very large Lorentz factor. We solve the problem in planar symmetry and compute the acceleration of the shock in terms of the density gradient crossed during its evolution. We apply our solution to the acceleration of shocks within the atmosphere of a HyperNova, and show that velocities consistent with the requirements of GRB models can be achieved with exponential atmospheres spanning a wide density range.Comment: ApJL in pres

On the stability of accelerating relativistic shock waves

We consider the corrugation instability of the self-similar flow with an accelerating shock in the highly relativistic regime. We derive the correct dispersion relation for the proper modes in the self-similar regime, and conclude that this solution is unstable.Comment: 25 pages, 10 figures. Accepted for publication in the Astrophysical Journa

Moving boundary approximation for curved streamer ionization fronts: Solvability analysis

The minimal density model for negative streamer ionization fronts is investigated. An earlier moving boundary approximation for this model consisted of a "kinetic undercooling" type boundary condition in a Laplacian growth problem of Hele-Shaw type. Here we derive a curvature correction to the moving boundary approximation that resembles surface tension. The calculation is based on solvability analysis with unconventional features, namely, there are three relevant zero modes of the adjoint operator, one of them diverging; furthermore, the inner/outer matching ahead of the front has to be performed on a line rather than on an extended region; and the whole calculation can be performed analytically. The analysis reveals a relation between the fields ahead and behind a slowly evolving curved front, the curvature and the generated conductivity. This relation forces us to give up the ideal conductivity approximation, and we suggest to replace it by a constant conductivity approximation. This implies that the electric potential in the streamer interior is no longer constant but solves a Laplace equation; this leads to a Muskat-type problem.Comment: 22 pages, 6 figure

Moving boundary approximation for curved streamer ionization fronts: Numerical tests

Recently a moving boundary approximation for the minimal model for negative streamer ionization fronts was extended with effects due to front curvature; this was done through a systematic solvability analysis. A central prediction of this analysis is the existence of a nonvanishing electric field in the streamer interior, whose value is proportional to the front curvature. In this paper we compare this result and other predictions of the solvability analysis with numerical simulations of the minimal model.Comment: 8 pages, 8 figure

Breakdown in hydrogen and deuterium gases in static and radio-frequency fields

We report the results of a combined experimental and modeling study of the electrical breakdown of hydrogen and deuterium in static (DC) and radio-frequency (RF) (13.56 MHz) electric fields. For the simulations of the breakdown events, simplified models are used and only electrons are traced by Monte Carlo simulation. The experimental DC Paschen curve of hydrogen is used for the determination of the effective secondary electron emission coefficient. A very good agreement between the experimental and the calculated RF breakdown characteristics for hydrogen is found. For deuterium, on the other hand, presently available cross section sets do not allow a reproduction of RF breakdown characteristics

Giant magnetoresistance in semiconductor / granular film heterostructures with cobalt nanoparticles

We have studied the electron transport in SiO${}_2$(Co)/GaAs and SiO${}_2$(Co)/Si heterostructures, where the SiO${}_2$(Co) structure is the granular SiO${}_2$ film with Co nanoparticles. In SiO${}_2$(Co)/GaAs heterostructures giant magnetoresistance effect is observed. The effect has positive values, is expressed, when electrons are injected from the granular film into the GaAs semiconductor, and has the temperature-peak type character. The temperature location of the effect depends on the Co concentration and can be shifted by the applied electrical field. For the SiO${}_2$(Co)/GaAs heterostructure with 71 at.% Co the magnetoresistance reaches 1000 ($10^5$ %) at room temperature. On the contrary, for SiO${}_2$(Co)/Si heterostructures magnetoresistance values are very small (4%) and for SiO${}_2$(Co) films the magnetoresistance has an opposite value. High values of the magnetoresistance effect in SiO${}_2$(Co)/GaAs heterostructures have been explained by magnetic-field-controlled process of impact ionization in the vicinity of the spin-dependent potential barrier formed in the semiconductor near the interface. Kinetic energy of electrons, which pass through the barrier and trigger the avalanche process, is reduced by the applied magnetic field. This electron energy suppression postpones the onset of the impact ionization to higher electric fields and results in the giant magnetoresistance. The spin-dependent potential barrier is due to the exchange interaction between electrons in the accumulation electron layer in the semiconductor and $d$-electrons of Co.Comment: 25 pages, 16 figure

Spontaneous Branching of Anode-Directed Streamers between Planar Electrodes

Non-ionized media subject to strong fields can become locally ionized by penetration of finger-shaped streamers. We study negative streamers between planar electrodes in a simple deterministic continuum approximation. We observe that for sufficiently large fields, the streamer tip can split. This happens close to Firsov's limit of `ideal conductivity'. Qualitatively the tip splitting is due to a Laplacian instability quite like in viscous fingering. For future quantitative analytical progress, our stability analysis of planar fronts identifies the screening length as a regularization mechanism.Comment: 4 pages, 6 figures, submitted to PRL on Nov. 16, 2001, revised version of March 10, 200

The moving boundary problem in the presence of a dipole magnetic field

An exact analytic solution is obtained for a uniformly expanding, neutral, infinitely conducting plasma sphere in an external dipole magnetic field. The electrodynamical aspects related to the radiation and transformation of energy were considered as well. The results obtained can be used in analyzing the recent experimental and simulation data.Comment: 17 pages, 1 figure, Submitted to J. Phys. A, Math. and Genera

Investigation of initiation of gigantic jets connecting thunderclouds to the ionosphere

The initiation of giant electrical discharges called as "gigantic jets" connecting thunderclouds to the ionosphere is investigated by numerical simulation method in this paper. Using similarity relations, the triggering conditions of streamer formation in laboratory situations are extended to form a criterion of initiation of gigantic jets. The energy source causing a gigantic jet is considered due to the quasi-electrostatic field generated by thunderclouds. The electron dynamics from ionization threshold to streamer initiation are simulated by the Monte Carlo technique. It is found that gigantic jets are initiated at a height of ~18-24 km. This is in agreement with the observations. The method presented in this paper could be also applied to the analysis of the initiation of other discharges such as blue jets and red sprites.Comment: 12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France