Efficient electron heating in relativistic shocks and gamma ray burst afterglow

Electrons in shocks are efficiently energized due to the cross-shock potential, which develops because of differential deflection of electrons and ions by the magnetic field in the shock front. The electron energization is necessarily accompanied by scattering and thermalization. The mechanism is efficient in both magnetized and non-magnetized relativistic electron-ion shocks. It is proposed that the synchrotron emission from the heated electrons in a layer of strongly enhanced magnetic field is responsible for gamma ray burst afterglows.Comment: revtex

Analysis of the geomagnetic activity of the D(st) index and self-affine fractals using wavelet transforms

The geomagnetic activity of the D(st) index is analyzed using wavelet transforms and it is shown that the D(st) index possesses properties associated with self-affine fractals. For example, the power spectral density obeys a power-law dependence on frequency, and therefore the D(st) index can be viewed as a self-affine fractal dynamic process. In fact, the behaviour of the D(st) index, with a Hurst exponent H≈0.5 (power-law exponent β≈2) at high frequency, is similar to that of Brownian motion. Therefore, the dynamical invariants of the D(st) index may be described by a potential Brownian motion model. Characterization of the geomagnetic activity has been studied by analysing the geomagnetic field using a wavelet covariance technique. The wavelet covariance exponent provides a direct effective measure of the strength of persistence of the D(st) index. One of the advantages of wavelet analysis is that many inherent problems encountered in Fourier transform methods, such as windowing and detrending, are not necessary

Multiscale time series modelling with an application to the relativistic electron intensity at the geosynchronous orbit

In this paper, a Bayesian system identification approach to multiscale time series modelling is proposed, where multiscale means that the output of the system is observed at one(coarse) resolution while the input of the system is observed at another (One) resolution. The proposed method identifies linear models at different levels of resolution where the link between the two resolutions is realised via non-overlapping averaging process. This averaged time series at the coarse level of resolution is assumed to be a set of observations from an implied process so that the implied process and the output of the system result in an errors-in-variables ARMAX model at the coarse level of resolution. By using a Bayesian inference and Markov Chain Monte Carlo (MCMC) method, such a modelling framework results in different dynamical models at different levels of resolution at the same time. The new method is also shown to have the ability to combine information across different levels of resolution. An application to the analysis of the relativistic electron intensity at the geosynchronous orbit is used to illustrate the new method

Mirror modes: Nonmaxwellian distributions

We perform direct analysis of mirror mode instabilities from the general dielectric tensor for several model distributions, in the longwavelength limit. The growth rate at the instability threshold depends on the derivative of the distribution for zero parallel energy. The maximum growth rate is always $\sim k_\parallel v_{T\parallel}$ and the instability is of nonresonant kind. The instability growth rate and its dependence on the propagation angle depend on the shape of the ion and electron distribution functions.Comment: 18 pages, 15 figures, revtex4, amsmath, amssymb,amsfonts,times, graphicx, float,verbatim,psfra

Nonzero electron temperature effects in nonlinear mirror modes

The nonlinear theory of the magnetic mirror instability (MI) accounting for nonzero electron temperature effects is developed. Based on our previous low-frequency approach to the analysis of this instability and including nonzero electron temperature effects a set of equations describing nonlinear dynamics of mirror modes is derived. In the linear limit a Fourier transform of these equations recovers the linear MI growth rate in which the finite ion Larmor radius and nonzero electron temperature effects are taken into account. When the electron temperature T-e becomes of the same order as the parallel ion temperature T the growth rate of the MI is reduced by the presence of a parallel electric field. The latter arises because the electrons are dragged by nonresonant ions which are mirror accelerated from regions of high to low parallel magnetic flux. The nonzero electron temperature effect also substantially modifies the mirror mode nonlinear dynamics. When T-e similar or equal to T the transition from the linear to nonlinear regime occurred for wave amplitudes that are only half that which was inherent to the cold electron temperature limit. Further nonlinear dynamics developed with the explosive formation of magnetic holes, ending with a saturated state in the form of solitary structures or cnoidal waves. This shows that the incorporation of nonzero temperature results in a weak decrease in their spatial dimensions of the holes and increase in their depth

Single-event upsets in the Cluster and Double Star Digital Wave Processor instruments

Radiation-induced upsets are an important issue for electronic circuits operating in space. Upsets due to solar protons, trapped protons, and galactic cosmic rays are frequently observed. Modeling the expected frequency of upsets is a necessary part of the design process for space hardware. The Cluster and Double Star spacecraft were respectively European and Chinese missions dedicated to the study of the wave and particle environment in the Earth's magnetosphere. All four Cluster spacecraft and one Double Star spacecraft included a Digital Wave Processor (DWP) instrument. The primary purpose of this instrument was as the central controller of the Wave Experiment Consortium. This paper investigates the occurrence of radiation-induced single-event upsets in these DWP instruments. The memory devices used in the DWP were not specifically radiation-hardened parts and so are relatively sensitive to single-event effects. We present the experience gained during the first 11 years of operation of the Cluster mission and the nearly 4 year lifetime of the Double Star TC-1 spacecraft and compare with models of the radiation environment

Collisionless shocks in the heliosphere: Foot width revisited

For single-point measurements of quasi-perpendicular shocks, analytical measurements of the foot width are often used to evaluate the velocity of the shock relative to the satellite. This velocity is of crucial importance for in situ observations because it enables the identification of the spatial scale of other regions of the shock front such as a magnetic ramp for which the comprehensive understanding of their formation is not yet achieved. Knowledge of the spatial scale is one of the key parameters for the validation of theoretical models that are developed to explain the formation of these regions. Previously available estimates of the foot width for a quasi-perpendicular shock are based on several simplifications such as zero upstream ion temperature and specular ion reflection by the cross-shock electrostatic potential. The occurrence of specular reflection implies high values of the cross-shock electrostatic potential that significantly exceed the values obtained from in situ measurements. In this paper the effects of nonzero ion temperature and nonspecular ion reflection on the foot width are investigated. It is shown that in the case of nonspecular reflection the foot width can be as small as half of the size of the standard widely used estimate. Results presented here enable more reliable identification of the shock velocity from single-point observations

Kinetic description of avalanching systems

Avalanching systems are treated analytically using the renormalization group (in the self-organized-criticality regime) or mean-field approximation, respectively. The latter describes the state in terms of the mean number of active and passive sites, without addressing the inhomogeneity in their distribution. This paper goes one step further by proposing a kinetic description of avalanching systems making use of the distribution function for clusters of active sites. We illustrate application of the kinetic formalism to a model proposed for the description of the avalanching processes in the reconnecting current sheet of the Earth magnetosphere.Comment: 9 page

Width dependent collisionless electron dynamics in the static fields of the shock ramp, 1, Single particle behavior and implications for downstream distribution

International audienceWe study the collisionless dynamics of electrons in the shock ramp using the numerical trajectory analysis in the model electric and magnetic fields of the shock. Even with very modest assumptions about the cross-shock potential the electron trajectories are very sensitive to the width of the ramp. The character of electron motion changes from the fully adiabatic (with conservation of v2 /B) when the ramp is wide, to the nonadiabatic one, when the ramp becomes sufficiently narrow. The downstream electron distribution also changes drastically, although this change depends on the initial electron temperature

Relativistic filamentary equilibria

Plasma filamentation is often encountered in collisionless shocks and inertial confinement fusion. We develop a general analytical description of the two-dimensional relativistic filamentary equilibrium and derive the conditions for existence of potential-free equilibria. A pseudopotential equation for the vector-potential is constructed for cold and relativistic Maxwellian distributions. The role of counter-streaming is explained. We present single current sheet and periodic current sheet solutions, and analyze the equilibria with electric potential. These solutions can be used to study linear and nonlinear evolution of the relativistic filamentation instabilit