Theoretical modeling of radiation-driven plasma turbulence in an unmagnetized plasma

The radiation-driven plasma-turbulence problem is in essence an application problem of electrodynamics. In electrodynamics, electromagnetic fields at any point are determined by all charges and currents in the underlying physical system, the fields' history and physical constraints. Starting from this standpoint, we have proved that radiation-driven electromagnetic turbulence in a plasma can be studied in the same way we study the electrostatic turbulence excited by electromagnetic waves in a plasma by means of a two-fluid approximation, a two-timescale technique, and a two-spacescale technique. The main difference between electromagnetic turbulence model equations and the Zakharov equations governing electrostatic turbulence is that a driving term appears in the former. The physical origin of this driving term is the current that emits the radiation which supplies the free energy source that gives rise to both electromagnetic and electrostatic turbulences. Simulated electromagnetic emissions, large scale density perturbation and anomalous absorption can be calculated quantitatively based on the electromagnetic turbulence model equations.Published from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 1, pp. 108–120, January, 1996.     

Charges and Fluxes in Maxwell Theory on Compact Manifolds with Boundary

We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of force emanating from brane sources, thus allowing non-zero net electric charges, but it also introduces new types of electric and magnetic flux. The resulting structure of currents, charges, and fluxes is studied and expressed in the language of relative homology and de Rham cohomology and the corresponding abelian groups. These can be organised in terms of a pair of exact sequences related by the Poincaré-Lefschetz isomorphism and by a weaker flip symmetry exchanging the ends of the sequences. It is shown how all this structure is brought into play by the imposition of the appropriately generalised Maxwell’s equations. The requirement that these equations be integrable restricts the world-volume of a permitted brane (assumed closed) to be homologous to a cycle on the boundary of space-time. All electric charges and magnetic fluxes are quantised and satisfy the Dirac quantisation condition. But through some boundary cycles there may be unquantised electric fluxes associated with quantised magnetic fluxes and so dyonic in nature.     

The Hamilton Cartan formalism for rth-order Lagrangians and the integrability of the KdV and modified KdV equations

The Hamilton Cartan formalism for rth order Lagrangians is presented in a form suited to dealing with higher-order conserved currents. Noether's Theorem and its converse are stated and Poisson brackets are defined for conserved charges. An isomorphism between the Lie algebra of conserved currents and a Lie algebra of infinitesimal symmetries of the Cartan form is established. This isomorphism, together with the commutativity of the Bäcklund transformations for the KdV and modified KdV equations, allows a simple geometric proof that the infinite collections of conserved charges for these equations are in involution with respect to the Poisson bracket determined by their Lagrangians. Thus, the formal complete integrability of these equations appears as a consequence of the properties of their Bäcklund transformations.It is noted that the Hamilton Cartan formalism determines a symplectic structure on the space of functionals determined by conserved charges and that, in the case of the KdV equation, the structure is the same as that given by Miura et al. [5].     

Group analysis of the nonlinear electrodynamics equations

The symmetry of the Maxwell equations is investiated in this paper in a nonlinear isotropic medium without currents and charges. A group-theoretic classification is given of the material equations and partially invariant solutions. Exact solutions of the Maxwell equations are found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 27–31, July, 1990.     

Flat Currents and Solutions of Sigma Model on Supercoset Targets with Z2m Grading

We find one parameter fiat currents of the sigma model on supercoset targets with Z2m grading given by Young satisfaction equations of motion and the Virasoro constraint. This means that one can generate a series of classical solutions from the original one. For these new solutions one can also construct fiat currents and conserved charges, which form the same set with the original one.     

New full-wave theory for scattering from rough metal surfaces—the correction current method: the TE-polarization case

A new full-wave theory of scattering from metal surfaces with one-dimensional roughness profiles is presented. A primary field and a complete system of modal functions (radiation modes) are defined to be relatively simple in structure (plane-wave-type fields) and to satisfy the boundary conditions at the rough surface, individually and rigorously. These fields will not necessarily satisfy Maxwell's equations. But compliance with these equations is enforced by the introduction of fictitious current distributions, associated with each of these fields, and chosen such that these 'passive' currents compensate for any field errors. In addition, each radiation mode is assumed to include an 'active' current distribution in the form of a current sheet which generates this mode. The composite field, formulated as a superposition of the primary field and the radiation modes, must be source free. It cannot involve any active or passive currents; and this zero-current requirement is then used to solve the scatter problem by an iterative procedure which, in a step-by-step fashion, eliminates the passive currents of the primary field and radiation modes by the active currents of the radiation modes. The result is a composite field that satisfies all requirements (Maxwell's equations, boundary conditions and radiation condition) while all fictitious current distributions are eliminated by mutual compensation. This composite field is therefore the solution of the scatter problem. This new theory—involving fictitious current distributions—is unconventional. But after definition of the primary field and the radiation modes, it is straightforward and conceptually transparent. The first-order scatter pattern is reciprocal and bridges the gap between the small-perturbation method and the physical optics method. Since the passive currents quantify the field errors, the theory allows the establishment of an error criterion which indicates when field errors can be expected to be small. The results are compared with those of existing theories. The present paper presents the TE case; the TM case, which is more complex, will be described in a follow-on paper.

(Some figures in this article are in colour only in the electronic version)     

Earthquakes and global electrical circuit

Based on recent experimental and theoretical model results, the role of earthquakes and processes of their preparation as electricity sources in the global electric circuit (GEC) is discussed. In addition to the traditional elements of the GEC, such as thunderstorm currents, ionosphere currents, fair weather currents, and telluric currents, hypothetical seismogenic currents flowing between the faults and the ionosphere are considered. The ionization sources for these currents are presumably the radiation of radioactive gases and the ionization by the electric field of so-called “positive holes” created by the compression of tectonic plates, whereas transportation of electric charges between the Earth and the ionosphere occurs under the action of electric fields and turbulent diffusion (for heavy charged species). Seismogenic currents deliver electric charges into the ionosphere, which give rise to electric fields in it and in the magnetically conjugated region. The drift of magnetized plasma in the ionosphere F2-region and plasmasphere plasma under the action of these fields causes disturbances in the electron density and total electron content (TEC) of the ionosphere, which are observed by GPS satellites before strong earthquakes. The typical features of these disturbances (magnitudes, dimensions, stability, nighttime predominance of the relative TEC disturbances, geomagnetic conjugacy) are well reproduced in theoretical model calculations based on the solution of the equation for the electric ionosphere potential with specified seismogenic electric current at the lower boundary of the ionosphere if this current is strong enough (comparable with thunderstorm currents). The feasibility of such seismogenic currents is discussed. It is argued that the TEC disturbances observed before strong earthquakes cannot be explained by neutral atmosphere disturbances. These TEC disturbances can be treated as ionospheric earthquake precursors created by seismogenic GEC disturbances.     

Remarks on A 2 Toda theory

We study the Toda field theory with finite Lie algebras using an extension of the Goulian-Li technique. In this way, we show that, after integrating over the zero mode in the correlation functions of the exponential fields, the resulting correlation function resembles that of a free theory. Furthermore, it is shown that for some ratios of the charges of the exponential fields the four-point correlation functions which contain a degenerate field satisfy the Riemann ordinary differential equation. Using this fact and the crossing symmetry, we derive a set of functional equations for the structure constants of the A ₂ Toda field theory.     

Effects of the electric field shape on nano-scale oxidation

An axisymmetric continuum model for oxide growth by the scanned probe oxidation technique is presented. The model includes equations describing the electric fields, hydroxyl and hydrogen ion concentrations, and oxide free boundaries defining the system. The governing system of partial differential equations tracks ion transport in the liquid and oxide layers and includes reactions at the substrate/oxide interface. Further, space charge effects are considered near the substrate/oxide interface. Two liquid configurations, semi-infinite layer and hemispherical drop of liquid, are examined to determine the potential in the liquid region. The AFM tip is modeled as either a point or a ring source of charges. The asymptotic limit of a small aspect ratio (height to width) oxide feature is used to reduce the governing equations to a quasi-one-dimensional system to determine the ion transport. The solution of the reduced system leads to an evolution equation for the oxide thickness and radius. Numerical simulations of the evolution equation predict oxide features that qualitatively agree with experimental observations. A parametric study is conducted to determine the influence of key operating and material parameters on the thickness and radius of the oxide, and the electric and ion concentration fields in the system.     

Wave equation for vectons and magnetic charges

Based on the wave equation for spin-one particles (vectons) proposed earlier by the author, we select an interaction operator and then in the limit go to field variables and the Maxwell equations of classical electrodynamics. Additional terms arising in this case are interpreted as magnetic charges and currents. We discuss the consequences. We conclude that it is possible to find magnetic charges in matter and present some characteristics of such materials. We logically derive free magnetic charges and their currents. We construct an electrodynamics taking into account material media.Karachaevsk State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 49–54, September, 1994.     

The universal C*-algebra of the electromagnetic field II. Topological charges and spacelike linear fields

Conditions for the appearance of topological charges are studied in the framework of the universal C*-algebra of the electromagnetic field, which is represented in any theory describing electromagnetism. It is shown that non-trivial topological charges, described by pairs of fields localised in certain topologically non-trivial spacelike separated regions, can appear in regular representations of the algebra only if the fields depend non-linearly on the mollifying test functions. On the other hand, examples of regular vacuum representations with non-trivial topological charges are constructed, where the underlying field still satisfies a weakened form of “spacelike linearity”. Such representations also appear in the presence of electric currents. The status of topological charges in theories with several types of electromagnetic fields, which appear in the short distance (scaling) limit of asymptotically free non-abelian gauge theories, is also briefly discussed.     

Electromagnetic Field Theory Without Divergence Problems 1. The Born Legacy

Born's quest for the elusive divergence problem-free quantum theory of electromagnetism led to the important discovery of the nonlinear Maxwell–Born–Infeld equations for the classical electromagnetic fields, the sources of which are classical point charges in motion. The law of motion for these point charges has however been missing, because the Lorentz self-force in the relativistic Newtonian (formal) law of motion is ill-defined in magnitude and direction. In the present paper it is shown that a relativistic Hamilton–Jacobi type law of point charge motion can be consistently coupled with the nonlinear Maxwell–Born–Infeld field equations to obtain a well-defined relativistic classical electrodynamics with point charges. Curiously, while the point charges are spinless, the Pauli principle for bosons can be incorporated. Born's reasoning for calculating the value of his aether constant is re-assessed and found to be inconclusive.     

Quantum Effects of Mesoscopic Inductance and Capacity Coupling Circuits

Using the quantum theory for a mesoscopic circuit based on the discretenes of electric charges, the finite-difference Schrödinger equation of the non-dissipative mesoscopic inductance and capacity coupling circuit is achieved. The Coulomb blockade effect, which is caused by the discreteness of electric charges, is studied. Appropriately choose the components in the circuits, the finite-difference Schrödinger equation can be divided into two Mathieu equations in \hat p representation. With the WKBJ method, the currents quantum fluctuations in the ground states of the two circuits are calculated. The results show that the currents quantum zero-point fluctuations of the two circuits are exist and correlated.     

Can the macroscopic Maxwell equations be obtained from the microscopic Maxwell-Lorentz equations by performing averages?

It is shown that the usual procedures of obtaining the macroscopic Maxwell equations from the microscopic Maxwell-Lorentz equations by performing averages contain an arbitrary choice of gauge. By a suitable different choice of the gauge the so-obtained Maxwell equations can be cast back to the form of the starting Maxwell-Lorentz equations. Therefore one cannot consider the Maxwell equations to be obtainable from the Maxwell-Lorentz equations by simply performing averages. The implication of this result is that besides the electromagnetic fields produced by the moving electric charges, as given by the Maxwell-Lorentz equations, there may be some other agents that cannot be identified as some kind of motion of the electric charges and that participate in the production of the electromagnetic fields.     

A refined integro-surface energy-based model for vibration of magnetically actuated double-nanowire-systems carrying electric current

A novel surface energy-based model is developed to examine more precisely vibrations of current-carrying double-nanowire-systems immersed in a longitudinal magnetic field. Using Biot-Savart and Lorentz laws, a more refined version of interwire interactional magnetic forces is presented. By employing Rayleigh beam theory, the equations of motion are derived. In fact, these are coupled integro-differential equations which are more accurate with respect to those of the previously developed models. For simply supported and clamped nanosystems, governing equations are analyzed via assumed mode method. The effects of interwire distance, slenderness ratio, electric current, magnetic field strength, and surface effect on the fundamental frequency are addressed carefully. The obtained results display the importance of exploiting the refined model for vibration analysis of nanosystems with low interwire distance, high electric current, and high magnetic field strength.     

Recent improvements in the numerical scheme of estimatingfield-aligned current systems from ground magnetometer records

The capability of ground-based magnetometer data of estimating field-aligned current system is discussed. Starting with some basic equations governing electrodynamic parameters in the ionosphere, the author describes both the advantages and limitations of the algorithms known as magnetogram-inversion techniques. It is pointed out that the proposed numerical scheme has been considerably improved so that simultaneous measurements of electric fields, conductivities, and field-aligned currents by satellites and radars can be incorporated in a consistent manner. One of the advantages of the magnetogram-inversion technique is that, since the technique deduces the global distribution of various electrodynamic quantities in the ionosphere with a time resolution of several minutes, it is possible to compare their spatial distributions with each other, especially for the auroral region. Results on important characteristics of auroral electrojets are presented     

Electrodynamics of Balanced Charges

We introduce here a new “neoclassical” electromagnetic (EM) theory in which elementary charges are represented by wave functions and individual EM fields to account for their EM interactions. We call so defined charges balanced or “b-charges”. We construct the EM theory of b-charges (BEM) based on a relativistic field Lagrangian and show that: (i) the elementary EM fields satisfy the Maxwell equations; (ii) the Newton equations with the Lorentz forces hold approximately when b-charges are well separated and move with non-relativistic velocities. When the BEM theory is applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the Schrodinger model with desired accuracy. An important feature of the theory is a mechanism of elementary EM energy absorption established for retarded potentials.     

On the Equivalence of Sources of Electromagnetic Fields Excited in an Isotropic Chiral Medium

The possibilities of exciting equal electromagnetic fields in an isotropic chiral medium by external monochromatic electric and magnetic sources are discussed. The possibility of exciting fields that differ in a specified way is also considered. The equivalence relationships for currents and charges are determined.