A Bayesian k-vector estimation method for electromagnetic waves in magnetized cold plasma

1.1 Historical perspective Interaction between electromagnetic waves and plasmas has been explored for several decades in various fields, such as ionosphere layers and outer space (Ginzburg, 1964), fusion plasmas (Stix, 1962; Swanson, 1989; Nishikawa & Wakatani, 1990), and plasma materialprocessing reactors (Lieberman & Lichtenberg, 1994). When an electromagnetic wave is launched in or near a non-magnetized plasma whose size is much larger than the wavelength, it is transmitted, reflected, or absorbed; these features are determined by a set of the electromagnetic wave frequency, the electron plasma frequency, and the electron elastic collision frequency. These three parameters determine real and imaginary parts of permittivity. In other words, plasmas equivalently behave as conductors or dielectric materials for electromagnetic waves, and these behaviours are controllable by changing complex permittivity, or electron density and gas pressure, which is associated with the electron plasma frequency and the electron elastic collision frequency; this controllability and the time-varying manner for permittivity distinguish plasmas from other electromagnetic media. First of all, in this section, we briefly review the historical perspective of the electromagnetic waves in plasmas, and we point out the reasons why the concept of electromagnetic media composed of plasmas and their discontinuities is focused on in this chapter. Electromagnetic waves in magnetized plasmas have been well investigated for more than half century, aiming at ultimate goals of controlled fusion plasmas for energy production and space plasmas for launching human beings using spacecrafts. In a magnetized plasma, various kinds of wave branches are present from low to high frequency ranges, and change of the external magnetic field induces “walk” on the dispersion curves in a “zoo” of plasma waves. Sometimes a branch leads to another totally-different branch; that is called mode conversion (Stix, 1962; Swanson, 1989). These waves can be launched from the outer side of the plasma, but there are also many inherent waves found as magnetohydrodynamic and micro instabilities (Swanson, 1989; Nishikawa & Wakatani, 1990). Other characteristic features of plasma waves are their nonlinearity; shock waves, solitons, and nonlinear mode conversion originate from the aspects of high-energy-state substance (Swanson 1989). The main focus in this chapter is different from such conventional scientific interests. Before we start our description, one more comment about plasma production for industry should be addressed (Lieberman & Lichtenberg, 1994). Plasma production in fabrication

Professor Vitaly D Shafranov is widely known as one of the acknowledged leaders of the world's scientific community in plasma physics and controlled fusion. His theoretical research on plasma equilibrium and stability made an outstanding contribution to the physics of magnetically confined toroidal plasmas which plays a decisive role for the problem of magnetic fusion.

Formulations describing the propagation of electromagnetic waves in a cold plasma in the presence of a constant magnetic field H0 become particularly simple in a limit case that corresponds to a high longitudinal conductivity component (component parallel to H0) and negligible transverse conductivity components. In this case, perfect guidance along the magnetic force lines is found for one propagation mode and propagation independent of direction for the other, characteristics known to appear in hydromagnetic waves. In the present case, however, no ion effects need be taken into consideration and the phase velocity is high, equaling vacuum velocity. Propagation of plane waves is treated and a wave-theoretical formulation is derived, valid for any wave field under the assumed conditions with a uniform magnetic field. A section on propagation in force line tubes includes some physical discussion. Comparisons are made between our limit case and other limit cases of waves in plasmas, which have been thoroughly studied previously—hydromagnetic waves (without compressional forces) and ionospheric whistlers.

There are various analysis methods for CT perfusion (CTP). Although the advantages of Bayesian estimation algorithms have been newly suggested, comparisons with other analysis methods on clinical data are still limited. In this study, we compared the Bayesian estimation method with the singular value decomposition (SVD) method in the evaluation of patients with acute cerebral infarction and examined its usefulness. CTP data from 13 patients with acute stroke were analyzed using the SVD and Bayesian estimation methods implemented in Vitrea. Evaluation of visual clarity of the ischemic area and quantitative values of the healthy side-affected side ratio using the mean values of the left and right region of interest (ROI) on the images were compared using the SVD and Bayesian estimation methods. In visual evaluation, there were significant differences in CBV in four cases, and in CBF, MTT, and TTP in many cases. The healthy side-affected side ratio of the SVD and Bayesian estimation methods were as follows: CBF 1.19, 1.84; CBV 1.09, 1.02; MTT 1.12, 1.79; and TTP 1.48, 1.19. For CBF and MTT, the Bayesian estimation method had a larger ratio of the healthy side to the affected side, and for TTP, the SVD method had a larger ratio of the test side to the affected side. We suggest that the Bayesian estimation method is more useful than the SVD method for assessing CBF and MTT in CTP analysis of patients with acute stroke.

Starting from kinetic models of cold magnetized collisionless plasmas, we provide a complete description of the characteristic variety sustaining electromagnetic wave propagation. As in [ 4 , 13 , 17 ], the analysis is based on some asymptotic calculus exploiting the presence at the level of dimensionless relativistic Vlasov-Maxwell equations of a large parameter: the electron gyrofrequency. The method is inspired from geometric optics [ 29 , 33 ]. It allows to unify all the preceding results [ 8 , 12 , 38 , 31 , 37 , 40 ], while incorporating new aspects. Specifically, the non trivial effects [ 5 , 9 , 10 , 24 ] of the spatial variations of the background density, temperature and magnetic field are exhibited. In this way, a comprehensive overview of the dispersion relations becomes available, with important possible applications in plasma physics [ 7 , 28 , 30 ].

This article is a survey of theoretical work performed with respect to the structure of a shock wave in plasma in the absence of collisions; under these conditions motion of the medium is laminar. The magnetic field is taken to be non-zero. For the case when the magnetic field equals zero, the formulation of the problem for the structure of a shock wave in the absence of collisions is incorrect. The thermal energy behind the shock wave is concentrated in ion-acoustic waves appearing at the fron of the shock wave due to reversed Landau damping. Non–linear interaction of the waves leads to disordered, that is, thermal, oscillations. In the survey, non-linear waves in cold plasma that move at an acute or at a right angle with the magnetic field, shock waves for rare collisions, unsteady shock waves in a cold plasma without collisions and dissipation resulting from instabilities are discussed. Plasma heating has been investigated in an isolated wave for the case when the square of the thermal velocity can be neglected. The case of arbitrary temperature has shown that in a kinetic study, the structure of the shock wave is of an ergodic nature. This means that infinitesimal fluctuations of hydromagnetic values in front of the shock wave increase exponentially at first and then pulsate randomly without returning to the initial state. If one averages over these pulsations one obtains the effective heating. It is shown that this process leads to an increase of the course of thermonuclear reactions. The relaxation length is equal to the Debye radius. The question of the difference between electron and ion temperatures and also anisotropy of the pressure tensor behind the shock wave are discussed.

Self-action of electromagnetic wave in plasma under parametric instability

The three-dimensional instability of two coupled electromagnetic waves in an unmagnetized plasma is investigated theoretically and numerically. In the regime of two-plasmon decay, where one pump wave frequency is approximately twice the electron plasma frequency, we find that the coupled pump waves give rise to enhanced instability with wavevectors between those of the two beams. In the case of ion parametric decay instability, where the pump wave decays into one Langmuir wave and one ion acoustic wave, the instability regions are added with no distinct amplification. Our investigation can be useful in interpreting laser-plasma as well as ionospheric heating experiments.

A 3-D global Earth-ionosphere finite-difference time-domain (FDTD) model is introduced that includes for the first time an anisotropic magnetized cold plasma ionosphere. All previous global FDTD Earth-ionosphere models to date have employed an isotropic conductivity profile. To generate the new model, a previously validated and published 3-D Cartesian magnetized cold plasma algorithm is adapted to the global latitude-longitude FDTD mesh that involves trapezoidal cells, merging of cells in the Polar regions, and triangular cells at the Poles. The global geomagnetic field, ionospheric particle densities and collision frequencies, as well as the Earth's topographic and bathymetric data are all mapped onto the global space grid. After a local high-resolution validation that demonstrates correct calculations of electromagnetic propagation in magnetized plasma, another numerical study is performed to validate the model on a global scale. This new model opens doors to a wide variety of advanced modeling for higher frequency and higher altitude electromagnetic phenomena and represents a paradigm shift from the commonly used ray-tracing codes. It also provides the opportunity to couple FDTD Earth-ionosphere models to other geophysical models, such as the Naval Research Lab's SAMI3, to yield a multiphysics simulator.

This paper studies modulational instabilities of intensely propagating, circularly polarized, plane electromagnetic plasma waves in the presence of an external magnetic field pointing exactly in the direction of propagation. By ‘intense propagation’, we mean that eEo/mw (where Eo is the amplitude of the wave's transverse electric field) is comparable to unity, so that the problem is fully nonlinear and cannot be solved by regular perturbation methods. The positive component may consists of either positrons or singly charged ions. The plasma is assumed to be fully ionized and cold. Modulated intensely propagating electromagnetic waves couple (in general) to longitudinal motions via the ponderomotive force. For given wavenumber, the frequency of the wave depends on the amplitude not only via the obvious mechanism of relativistic mass increase but also via the density inhomogeneities induced by the ponderomotive force. This coupling effectively involves derivatives of the envelope, and the effect of longitudinal motions is comparable to that of relativistic nonlinearities. For this reason, a proper expansion procedure requires verification that one has obtained a self-consistent solution of all the field equations up to the appropriate order, including the longitudinal equations. This is best accomplished using the well-known two-timing approach. Modulational instability arises in the case of an ion-electron plasma with relativistic electrons but non-relativistic ions. However, for parameter values appropriate to pulsar magnetospheres, where the electron-cyclotron frequency is much larger than the frequency of the wave, there is no instability on the time scale of a micropulse.

The amplitude modulation of magnetic field-aligned circularly polarized electromagnetic (CPEM) waves in a magnetized pair plasma is reexamined. The nonlinear frequency shifts include the effects of the radiation pressure driven density and compressional magnetic field perturbations as well as relativistic particle mass variations. The dynamics of the modulated CPEM wave packets is governed by a nonlinear Schrödinger equation, which has attractive and repulsive interaction potentials for fast and slow CPEM waves. The modulational stability of a constant amplitude CPEM wave is studied by deriving a nonlinear dispersion from the cubic Schrödinger equation. The fast (slow) CPEM mode is modulationally unstable (stable). Possible stationary amplitude solutions of the modulated fast (slow) CPEM mode can be represented in the form of bright and dark/gray envelope electromagnetic soliton structures. Localized envelope excitations can be associated with the microstructures in pulsar magnetospheres and in laboratory pair magnetoplasmas.

This is the second part of a three part article examining methods for Bayesian estimation and tracking. In the first part we presented the general theory of Bayesian estimation where we showed that Bayesian estimation methods can be divided into two very general classes: a class where the observation conditioned posterior densities are propagated in time through a predictor/corrector method; and a second class where the first two moments are propagated in time, with state and observation moment prediction steps followed by state moment update steps that use the latest observations. In this second part, we make the assumption that all densities are Gaussian and, after applying an affine transformation and approximating all nonlinear functions by interpolating polynomials, we recover the sigma‐point class of Kalman filters, including the unscented, spherical simplex, and Gauss‐Hermite Kalman filters. In part 3, we will show that approximating a density by a set of Monte Carlo samples leads to particle filter methods, where the posterior density is propagated in time and moment integrals are approximated by sample moments. WIREs Comput Stat 2012 doi: 10.1002/wics.1215This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory

New exact analytical solutions describing the non-stationary propagation of non-sine electromagnetic waves in plasma are obtained by direct solution of Maxwell equations without the traditional Fourier transformations. Unlike the usual travelling monochromatic waves the fields discussed are distinguished by unequal periods of electric and magnetic oscillations, fast oscillative diffusion of the envelope and collisionless damping of peak amplitudes due to strong plasma dispersion. The transformation of these non-sine fields to the trains of quasimonochromatic waves in the depth of plasma is considered for both isotropic and magnetized plasmas.

This letter focuses on the propagation characteristics of the electromagnetic wave in the plasma under high-power microwave (HPM) illumination. A multiphysical method coupling the electromagnetic field and plasma fluid field is proposed as the dynamic Drude model. The differences between the method based on dynamic Drude model and traditional static Drude model are discussed theoretically for the first time. Unlike the static Drude model, the dynamic Drude model fully considers the motion of electrons in plasma driven by electromagnetic field. Numerical examples demonstrate that both the dynamic Drude model-based and static Drude model-based method are consistent with each other under low power microwave illumination, where the plasma can be considered as a static media. While under HPM illumination, electrons gradually gather together to hinder the propagation of electromagnetic waves. Hence, the proposed dynamic Drude model is more logical to analyze the characteristics of electromagnetic wave in plasma than the traditional static Drude model under HPM illumination.

The dispersion characteristics of electromagnetic waves in a relativistic plasma having a one-dimensional distribution function established through radiation losses in a strong magnetic field are studied. It is shown that the longitudinal waves in such a plasma exist in a certain frequency interval near the plasma frequency, they propagate at small angles to the external magnetic field, and their phase velocities exceed the velocity of light, as a consequence of which the longitudinal waves do not have clear advantages over other types of waves in terms of generation (their ''Cherenkov'' generation is impossible). The dispersion properties of the electromagnetic waves in the low-frequency intervals of ..omega../sub Hi/ less than ..omega.. less than ..omega../sub He/ and ..omega.. much less than ..omega../sub Hi/ in the ''quasivacuum'' approximation (parallel bar n/sup 2/ -- 1 parallel bar much less than 1) are analogous to the properties of normal waves in a cold plasma in the corresponding frequency intervals. A distinguishing feature of a relativistic plasma is the attenuation of the waves caused by the presence in it of a continuous spectrum of gyrofrequencies and strong spatial dispersion. The instability increments of Alfven and fast magnetosonic waves, connected with the one-dimensionality of the distribution function,more » are found for quasilongitudinal propagation.« less