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

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

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

Probing background ionization: Positive streamers with varying pulse repetition rate and with a radioactive admixture

Positive streamers need a source of free electrons ahead of them to propagate. A streamer can supply these electrons by itself through photo-ionization, or the electrons can be present due to external background ionization. Here we investigate the effects of background ionization on streamer propagation and morphology by changing the gas composition and the repetition rate of the voltage pulses, and by adding a small amount of radioactive Krypton 85. We find that the general morphology of a positive streamer discharge in high purity nitrogen depends on background ionization: at lower background ionization levels the streamers branch more and have a more feather-like appearance. This is observed both when varying the repetition rate and when adding Krypton 85, though side branches are longer with the radioactive admixture. But velocities and minimal diameters of streamers are virtually independent of the background ionization level. In air, the inception cloud breaks up into streamers at a smaller radius when the repetition rate and therefore the background ionization level is higher. When measuring the effects of the pulse repetition rate and of the radioactive admixture on the discharge morphology, we found that our estimates of background ionization levels are consistent with these observations; this gives confidence in the estimates. Streamer channels generally do not follow the paths of previous discharge channels for repetition rates of up to 10 Hz. We estimate the effect of recombination and diffusion of ions and free electrons from the previous discharge and conclude that the old trail has largely disappeared at the moment of the next voltage pulse; therefore the next streamers indeed cannot follow the old trail.Comment: 30 pages, 13 figure

Pressurized rf cavities in ionizing beams

A muon collider or Higgs factory requires significant reduction of the six dimensional emittance of the beam prior to acceleration. One method to accomplish this involves building a cooling channel using high pressure gas filled radio frequency cavities. The performance of such a cavity when subjected to an intense particle beam must be investigated before this technology can be validated. To this end, a high pressure gas filled radio frequency (rf) test cell was built and placed in a 400 MeV beam line from the Fermilab linac to study the plasma evolution and its effect on the cavity. Hydrogen, deuterium, helium and nitrogen gases were studied. Additionally, sulfur hexafluoride and dry air were used as dopants to aid in the removal of plasma electrons. Measurements were made using a variety of beam intensities, gas pressures, dopant concentrations, and cavity rf electric fields, both with and without a 3 T external solenoidal magnetic field. Energy dissipation per electron-ion pair, electron-ion recombination rates, ion-ion recombination rates, and electron attachment times to SF6 and O-2 were measured.ope