PIC Simulations of the Temperature Anisotropy-Driven Weibel Instability: Analyzing the perpendicular mode

An instability driven by the thermal anisotropy of a single electron species is investigated in a 2D particle-in-cell (PIC) simulation. This instability is the one considered by Weibel and it differs from the beam driven filamentation instability. A comparison of the simulation results with analytic theory provides similar exponential growth rates of the magnetic field during the linear growth phase of the instability. We observe in accordance with previous works the growth of electric fields during the saturation phase of the instability. Some components of this electric field are not accounted for by the linearized theory. A single-fluid-based theory is used to determine the source of this nonlinear electric field. It is demonstrated that the magnetic stress tensor, which vanishes in a 1D geometry, is more important in this 2-dimensional model used here. The electric field grows to an amplitude, which yields a force on the electrons that is comparable to the magnetic one. The peak energy density of each magnetic field component in the simulation plane agrees with previous estimates. Eddy currents develop, which let the amplitude of the third magnetic field component grow, which is not observed in a 1D simulation.Comment: accepted by Plasma Physics and Controlled Fusio

The filamentation instability driven by warm electron beams: Statistics and electric field generation

The filamentation instability of counterpropagating symmetric beams of electrons is examined with 1D and 2D particle-in-cell (PIC) simulations, which are oriented orthogonally to the beam velocity vector. The beams are uniform, warm and their relative speed is mildly relativistic. The dynamics of the filaments is examined in 2D and it is confirmed that their characteristic size increases linearly in time. Currents orthogonal to the beam velocity vector are driven through the magnetic and electric fields in the simulation plane. The fields are tied to the filament boundaries and the scale size of the flow-aligned and the perpendicular currents are thus equal. It is confirmed that the electrostatic and the magnetic forces are equally important, when the filamentation instability saturates in 1D. Their balance is apparently the saturation mechanism of the filamentation instability for our initial conditions. The electric force is relatively weaker but not negligible in the 2D simulation, where the electron temperature is set higher to reduce the computational cost. The magnetic pressure gradient is the principal source of the electrostatic field, when and after the instability saturates in the 1D simulation and in the 2D simulation.Comment: 10 pages, 6 figures, accepted by the Plasma Physics and Controlled Fusion (Special Issue EPS 2009

Surfatron and stochastic acceleration of electrons in astrophysical plasmas

Electron acceleration by large amplitude electrostatic waves in astrophysical plasmas is studied using particle-in-cell (PIC) simulations. The waves are excited initially at the electron plasma frequency $\omega_{\rm pe}$ by a Buneman instability driven by ion beams: the parameters of the ion beams are appropriate for high Mach number astrophysical shocks, such as those associated with supernova remnants (SNRs). If $\omega_{\rm pe}$ is much higher than the electron cyclotron frequency $\Omega_{\rm e}$, the linear phase of the instability does not depend on the magnitude of the magnetic field. However, the subsequent time evolution of particles and waves depends on both $\omega_{\rm pe}/\Omega_{\rm e}$ and the size of the simulation box $L$. If $L$ is equal to one wavelength, $\lambda_0$, of the Buneman-unstable mode, electrons trapped by the waves undergo acceleration via the surfatron mechanism across the wave front. This occurs most efficiently when $\omega_{\rm pe}/\Omega_{\rm e} \simeq 100$: in this case electrons are accelerated to speeds of up $c/2$ where $c$ is the speed of light. In a simulation with $L=4\lambda_0$ and $\omega_{\rm pe}/\Omega_{\rm e} = 100$, it is found that sideband instabilities give rise to a broad spectrum of wavenumbers, with a power law tail. Some stochastic electron acceleration is observed in this case, but not the surfatron process. Direct integration of the electron equations of motion, using parameters approximating to those of the wave modes observed in the simulations, suggests that the surfatron is compatible with the presence of a broad wave spectrum if $\omega_{\rm pe}/\Omega_{\rm e}> 100$. It is concluded that a combination of stochastic and surfatron acceleration could provide an efficient generator of mildly relativistic electrons at SNR shocks

Prognostic factors in seminomas with special respect to HCG: Results of a prospective multicenter study

Objective: In a prospective multicenter trial, it was our intention to elucidate clinical prognostic factors of seminomas with special reference to the importance of human chorionic gonadotropin (HCG) elevations in histologically pure seminomas. Methods: Together with 96 participating urological departments in Germany, Austria, and Switzerland, we recruited 803 seminoma patients between 1986 and 1991. Out of 726 evaluable cases, 378 had elevated, while 348 had normal HCG values in the cubital vein. Histology was reviewed by two reference pathologists. HCG levels were determined in local laboratories and in a study laboratory. Standard therapy was defined as radiotherapy in stages I (30 Gy) and IIA/B (36 Gy) to the paraaortal and the ispilateral (stage I) and bilateral (stage IIA/B) iliac lymph nodes; higher stages received polychemotherapy and surgery in case of residual tumor masses. Statistics included chi-square tests, linear Cox regression, and log-rank test. Results: The HCG elevation is associated with a larger tumor mass (primary tumor and/or metastases). HCG-positive and HCG-negative seminomas had no different prognostic outcome after standard therapy. The overall relapse rate of 6% and the survival rate of 98% after 36 months (median) indicate an excellent prognosis. The calculation of the relative risk of developing a relapse discovered only stage of the disease and elevation of the lactate dehydrogenase concentration and its prolonged marker decay as independent prognostic factors for seminomas. A more detailed analysis of the prognostic significance of the stage revealed that the high relapse rate in stage IIB seminomas after radiotherapy (24%) is responsible for this result. Conclusions: We conclude that HCG-positive seminomas do not represent a special entity. Provided standard therapy is applied, HCG has no influence on the prognosis. Patients with stage IIB disease should be treated with chemotherapy because of the demonstrated higher relapse rate outside the retroperitoneum. Copyright (C) 1999 S. Karger AG. Basel

Strategy bifurcation and spatial inhomogeneity in a simple model of competing sellers

We present a simple one-parameter model for spatially localised evolving agents competing for spatially localised resources. The model considers selling agents able to evolve their pricing strategy in competition for a fixed market. Despite its simplicity, the model displays extraordinarily rich behavior. In addition to ``cheap'' sellers pricing to cover their costs, ``expensive'' sellers spontaneously appear to exploit short-term favorable situations. These expensive sellers ``speciate'' into discrete price bands. As well as variety in pricing strategy, the ``cheap'' sellers evolve a strongly correlated spatial structure, which in turn creates niches for their expensive competitors. Thus an entire ecosystem of coexisting, discrete, symmetry-breaking strategies arises.Comment: 6 pages, 6 figures, epl2; 1 new figure, include nash equilibrium analysis, typo fixe

One-dimensional thermal pressure-driven expansion of a pair cloud into an electron-proton plasma

Recently a filamentation instability was observed when a laser-generated pair cloud interacted with an ambient plasma. The magnetic field it drove was strong enough to magnetize and accelerate the ambient electrons. It is of interest to determine if and how pair cloud-driven instabilities can accelerate ions in the laboratory or in astrophysical plasma. For this purpose, the expansion of a localized pair cloud with the temperature 400 keV into a cooler ambient electron-proton plasma is studied by means of one-dimensional particle-in-cell (PIC) simulations. The cloud's expansion triggers the formation of electron phase space holes that accelerate some protons to MeV energies. Forthcoming lasers might provide the energy needed to create a cloud that can accelerate protons.Comment: 5 pages 4 figures, accepted for publication in Physics of Plasma

Two-dimensional PIC simulations of ion-beam instabilities in Supernova-driven plasma flows

Supernova remnant (SNR) blast shells can reach the flow speed $v_s = 0.1 c$ and shocks form at its front. Instabilities driven by shock-reflected ion beams heat the plasma in the foreshock, which may inject particles into diffusive acceleration. The ion beams can have the speed $v_b \approx v_s$. For $v_b \ll v_s$ the Buneman or upper-hybrid instabilities dominate, while for $v_b \gg v_s$ the filamentation and mixed modes grow faster. Here the relevant waves for $v_b \approx v_s$ are examined and how they interact nonlinearly with the particles. The collision of two plasma clouds at the speed $v_s$ is modelled with particle-in-cell (PIC) simulations, which convect with them magnetic fields oriented perpendicular to their flow velocity vector. One simulation models equally dense clouds and the other one uses a density ratio of 2. Both simulations show upper-hybrid waves that are planar over large spatial intervals and that accelerate electrons to $\sim$ 10 keV. The symmetric collision yields only short oscillatory wave pulses, while the asymmetric collision also produces large-scale electric fields, probably through a magnetic pressure gradient. The large-scale fields destroy the electron phase space holes and they accelerate the ions, which facilitates the formation of a precursor shock.Comment: 15 pages, 11 figures, accepted for publication in Plasma Physics and Controlled Fusio

On the Nature of MeV-blazars

Broad-band spectra of the FSRQ (flat-spectrum-radio quasars) detected in the high energy gamma-ray band imply that there may be two types of such objects: those with steep gamma-ray spectra, hereafter called MeV-blazars, and those with flat gamma-ray spectra, GeV-blazars. We demonstrate that this difference can be explained in the context of the ERC (external-radiation-Compton) model using the same electron injection function. A satisfactory unification is reachable, provided that: (a) spectra of GeV-blazars are produced by internal shocks formed at the distances where cooling of relativistic electrons in a jet is dominated by Comptonization of broad emission lines, whereas spectra of MeV-blazars are produced at the distances where cooling of relativistic electrons is dominated by Comptonization of near-IR radiation from hot dust; (b) electrons are accelerated via a two step process and their injection function takes the form of a double power-law, with the break corresponding to the threshold energy for the diffusive shock acceleration. Direct predictions of our model are that, on average, variability time scales of the MeV-blazars should be longer than variability time scales of the GeV-blazars, and that both types of the blazar phenomenon can appear in the same object.Comment: Accepted for publication in the Astrophysical Journa