Root locus diagrams by digital computer

Adaptation of root locus method to programming on IBM 7074 digital compute

Gamma-Ray Burst Afterglow: Polarization and Analytic Light Curves

GRB afterglow polarization is discussed. We find an observable, up to 10%, polarization, if the magnetic field coherence length grows at about the speed of light after the field is generated at the shock front. Detection of a polarized afterglow would show that collisionless ultrarelativistic shocks can generate strong large scale magnetic fields and confirm the synchrotron afterglow model. Non-detection, at a 1% level, would imply that either the synchrotron emission model is incorrect, or that strong magnetic fields, after they are generated in the shock, somehow manage to stay un-dissipated at ``microscopic'', skin depth, scales. Analytic lightcurves of synchrotron emission from an ultrarelativistic self-similar blast wave are obtained for an arbitrary electron distribution function, taking into account the effects of synchrotron cooling. The peak synchrotron flux and the flux at frequencies much smaller than the peak frequency are insensitive to the details of the electron distribution function; hence their observational determination would provide strong constraints on blast wave parameters.Comment: 19 pages, submitted to Ap

Attracted Diffusion-Limited Aggregation

In this paper, we present results of extensive Monte Carlo simulations of diffusion-limited aggregation (DLA) with a seed placed on an attractive plane as a simple model in connection with the electrical double layers. We compute the fractal dimension of the aggregated patterns as a function of the attraction strength \alpha. For the patterns grown in both two and three dimensions, the fractal dimension shows a significant dependence on the attraction strength for small values of \alpha, and approaches to that of the ordinary two-dimensional (2D) DLA in the limit of large \alpha. For non-attracting case with \alpha=1, our results in three dimensions reproduce the patterns of 3D ordinary DLA, while in two dimensions our model leads to formation of a compact cluster with dimension two. For intermediate \alpha, the 3D clusters have quasi-2D structure with a fractal dimension very close to that of the ordinary 2D-DLA. This allows one to control morphology of a growing cluster by tuning a single external parameter \alpha.Comment: 6 pages, 6 figures, to appear in Phys. Rev. E (2012

Self-consistent nonlinear kinetic simulations of the anomalous Doppler instability of suprathermal electrons in plasmas

Suprathermal tails in the distributions of electron velocities parallel to the magnetic field are found in many areas of plasma physics, from magnetic confinement fusion to solar system plasmas. Parallel electron kinetic energy can be transferred into plasma waves and perpendicular gyration energy of particles through the anomalous Doppler instability (ADI), provided that energetic electrons with parallel velocities v ≥ (ω + Ωce )/k are present; here Ωce denotes electron cyclotron frequency, ω the wave angular frequency and k the component of wavenumber parallel to the magnetic field. This phenomenon is widely observed in tokamak plasmas. Here we present the first fully self-consistent relativistic particle-in-cell simulations of the ADI, spanning the linear and nonlinear regimes of the ADI. We test the robustness of the analytical theory in the linear regime and follow the ADI through to the steady state. By directly evaluating the parallel and perpendicular dynamical contributions to j · E in the simulations, we follow the energy transfer between the excited waves and the bulk and tail electron populations for the first time. We find that the ratio Ωce /(ωpe + Ωce ) of energy transfer between parallel and perpendicular, obtained from linear analysis, does not apply when damping is fully included, when we find it to be ωpe /(ωpe + Ωce ); here ωpe denotes the electron plasma frequency. We also find that the ADI can arise beyond the previously expected range of plasma parameters, in particular when Ωce > ωpe . The simulations also exhibit a spectral feature which may correspond to observations of suprathermal narrowband emission at ωpe detected from low density tokamak plasmas

Nonlinear Electron Oscillations in a Viscous and Resistive Plasma

New non-linear, spatially periodic, long wavelength electrostatic modes of an electron fluid oscillating against a motionless ion fluid (Langmuir waves) are given, with viscous and resistive effects included. The cold plasma approximation is adopted, which requires the wavelength to be sufficiently large. The pertinent requirement valid for large amplitude waves is determined. The general non-linear solution of the continuity and momentum transfer equations for the electron fluid along with Poisson's equation is obtained in simple parametric form. It is shown that in all typical hydrogen plasmas, the influence of plasma resistivity on the modes in question is negligible. Within the limitations of the solution found, the non-linear time evolution of any (periodic) initial electron number density profile n_e(x, t=0) can be determined (examples). For the modes in question, an idealized model of a strictly cold and collisionless plasma is shown to be applicable to any real plasma, provided that the wavelength lambda >> lambda_{min}(n_0,T_e), where n_0 = const and T_e are the equilibrium values of the electron number density and electron temperature. Within this idealized model, the minimum of the initial electron density n_e(x_{min}, t=0) must be larger than half its equilibrium value, n_0/2. Otherwise, the corresponding maximum n_e(x_{max},t=tau_p/2), obtained after half a period of the plasma oscillation blows up. Relaxation of this restriction on n_e(x, t=0) as one decreases lambda, due to the increase of the electron viscosity effects, is examined in detail. Strong plasma viscosity is shown to change considerably the density profile during the time evolution, e.g., by splitting the largest maximum in two.Comment: 16 one column pages, 11 figures, Abstract and Sec. I, extended, Sec. VIII modified, Phys. Rev. E in pres

A Coronal Hole's Effects on CME Shock Morphology in the Inner Heliosphere

We use STEREO imagery to study the morphology of a shock driven by a fast coronal mass ejection (CME) launched from the Sun on 2011 March 7. The source region of the CME is located just to the east of a coronal hole. The CME ejecta is deflected away from the hole, in contrast with the shock, which readily expands into the fast outflow from the coronal hole. The result is a CME with ejecta not well centered within the shock surrounding it. The shock shape inferred from the imaging is compared with in situ data at 1 AU, where the shock is observed near Earth by the Wind spacecraft, and at STEREO-A. Shock normals computed from the in situ data are consistent with the shock morphology inferred from imaging.Comment: to appear in The Astrophysical Journa

Parameter dependence of magnetized CMB observables

Pre-decoupling magnetic fields affect the scalar modes of the geometry and produce observable effects which can be constrained also through the use of current (as opposed to forthcoming) data stemming from the Cosmic Microwave Background observations. The dependence of the temperature and polarization angular power spectra upon the parameters of an ambient magnetic field is encoded in the scaling properties of a set of basic integrals whose derivation is simplified in the limit of small angular scales. The magnetically-induced distortions patterns of the relevant observables can be computed analytically by employing scaling considerations which are corroborated by numerical results.Comment: 48 pages, 11 figures; corrected minor typos; discussions added; to appear in Physical Revie

An Arbitrary Curvilinear Coordinate Method for Particle-In-Cell Modeling

A new approach to the kinetic simulation of plasmas in complex geometries, based on the Particle-in- Cell (PIC) simulation method, is explored. In the two dimensional (2d) electrostatic version of our method, called the Arbitrary Curvilinear Coordinate PIC (ACC-PIC) method, all essential PIC operations are carried out in 2d on a uniform grid on the unit square logical domain, and mapped to a nonuniform boundary-fitted grid on the physical domain. As the resulting logical grid equations of motion are not separable, we have developed an extension of the semi-implicit Modified Leapfrog (ML) integration technique to preserve the symplectic nature of the logical grid particle mover. A generalized, curvilinear coordinate formulation of Poisson's equations to solve for the electrostatic fields on the uniform logical grid is also developed. By our formulation, we compute the plasma charge density on the logical grid based on the particles' positions on the logical domain. That is, the plasma particles are weighted to the uniform logical grid and the self-consistent mean electrostatic fields obtained from the solution of the logical grid Poisson equation are interpolated to the particle positions on the logical grid. This process eliminates the complexity associated with the weighting and interpolation processes on the nonuniform physical grid and allows us to run the PIC method on arbitrary boundary-fitted meshes.Comment: Submitted to Computational Science & Discovery December 201