Fatih Erden

Temporal Cavity Oscillations Caused by a Wide-Band Waveform

Excitation of the electromagnetic fields by a wide-band current surge, which has a beginning in time, is studied in a cavity bounded by a closed perfectly conducting surface. The cavity is filled with Debye or Lorentz dispersive medium. The fields are presented as the modal expansion in terms of the solenoidal and irrotational cavity modes with the time-dependent modal amplitudes, which should be found. Completeness of this form of solution has been proved earlier. The systems of ordinary differential equations with time derivative for the modal amplitudes are derived and solved explicitly under the initial conditions and in compliance with the causality principle. The solutions are obtained in the form of simple convolution (with respect to time variable) integrals. Numerical examples are exhibited as well.

Analytical approach for studying a time-domain cavity problem

A time-domain cavity problem for the system of Maxwells equations with time derivative and dynamic constitutive relation for a dielectric with temporal dispersion is solved within the framework of the evolutionary approach. The field vectors and polarization vector for the dielectric are presented as the modal expansions in terms of the solenoidal and irrotational modal basis vectors. The modal amplitudes are scalar and time-dependent herein. Cauchy problems are obtained for the modal amplitudes. Every Cauchy problem exhibits how the process progresses in time (i.e., evolves, shortly) starting from a given initial state up to the state at a time of observation. That is why we call our approach as evolutionary.

Temporal evolution of the irrotational and solenoidal cavity modes

An outline of the evolutionary approach to time-domain electromagnetics is presented in a compact form available for practical using. A cavity is loaded with a given source of transient signal. The cavity field is presented via expansions in terms of the solenoidal and irrotational modes having time-dependent modal amplitudes. The differential equations with time derivative are derived from Maxwells equations for the amplitudes jointly with appropriate initial conditions. The frequency-domain theory usually interprets the irrotational modes as some static fields. Graphical results illustrating the time dependence of the irrotational and solenoidal modes will be exhibited in the presentation.

Evolution equations for the oscillations in a cavity filled with a dynamic medium

Development of the time-harmonic electromagnetic theory dates back to the end of 19th century stating that all the electromagnetic field quantities vary harmonically in time. This assumption, being formalised in the system of Maxwells equations (ME) with time derivative, changes the hyperbolic type of the partial differential equation into the elliptic type. Therefore, the time-harmonic solutions to the ME of elliptic type do not satisfy the causality principle and have difficulties with the relativistic transformations. Progress of the time-domain field theory has started via the development of computational electromagnetics in the second part of the 20th century. Numerical techniques are capable of providing huge volumes of numerical data; however, a deep physical insight to the data can be achieved under the presence of analytical results. Nevertheless, analytical theory of time-domain electromagnetics goes through an initial step of its development.

Time-domain forced oscillations in a cavity filled with a plasma driven by the dynamic ohm's law

Statement of the problem involves the system of Maxwells equations (with the time derivative) and the motion equation for a nonmagnetic quasi-neutral homogeneous plasma simultaneously. The motion equation governs the behavior of the charged particles that is conditioned by their interactions in the plasma with the electromagnetic field, which is governed by the Maxwells equations, in turn. These processes are considered in a cylindrical cavity bounded by the closed surface of perfect electric conductivity. Within the cavity, an input item is placed that is meant for excitation of the forced oscillations by a given signal applied to that one. The signal has a beginning and an end. The time-domain problem is solved within the framework of the Evolutionary Approach to Electrodynamics (EAE). The EAE was recognized recently as an alternative to the classical time-harmonic field method: (O. A. Tretyakov and F. Erden, “Evolutionary approach to Electromagnetics as an alternative to the time-harmonic field method,” IEEE International Symposium on Antennas and Propagation and USNC-URSI National Radio Sci. Meeting, 8–14 July, Chicago, US, 2012).

Properties of the time-domain waveguide modes

The time-domain problem is solved within the framework of the evolutionary approach to electrodynamics. The procedure is decomposed onto solving two autonomous problems. The first one is standard solving a boundary-eigenvalue problem for transverse Laplacian what yields a configurational basis in the waveguide cross section. Elements of this basis depend on transverse coordinates only. At the last step, we extract from Maxwells equations with ∂t a system of the evolutionary equations for the modal amplitudes dependent on axial coordinate, 2, and time, t. Klein-Gordon equation (KGE) plays the main role herein. Solving KGE yields an evolutionary basis for analysis of the modal amplitudes in Minkowski plane (2, ct).

Time-domain energetic properties of the TM-modes in a lossy waveguide

The amplitudes and energetic properties of the TM-modal fields for a lossy waveguide are solved analytically in time-domain. Solving the boundary-eigenvalue for transverse Laplacian problem results a basis in the waveguide cross section. Elements of this basis depend on transverse coordinates, r, and the modal amplitudes depend on the longitudinal coordinate, z, and time, t. Exact solutions are derived and presented graphically.

Analytical study of the TE-waveguide modes in time domain

The problem of propagation is solved for circular waveguide TE-modal waveforms within the framework of the evolutionary approach to electrodynamics (EAE). Physical dimensions of the electric and magnetic intensity vectors, volt per meter and ampere per meter, ingressed in Maxwells equations are factorized in SI units. Then a system of evolutionary equations for the modal amplitudes dependent on axial coordinate and time are obtained from the Maxwells equations supplemented with the boundary conditions for perfect electric conductor surfaces. Solutions for the waveguide modal fields and for the energetic field characteristics are presented graphically.

Evolution of the quadratic functions of the time-domain waveguide fields

The quadratic field characteristics are derived in the class of real-valued functions of time for the circular waveguide. The evolutionary approach to electrodynamics is applied for the field analysis where Klein-Gordon equation plays a central role.

Evolution of the solenoidal and irrotational modal fields in a cavity excited by a signal

In this study; first, an outline of the evolutionary approach to electromagnetics (EAE) is presented in a compact form, and secondly, electromagnetic oscillations in a cavity excited by a casual time-dependent signal (e.g. a sinusoid) is studied in the time domain within the frame of the EAE. The signal exciting the field is installed in Maxwells equations via electric current density given as a function of coordinates and time. The signal may be an arbitrary integrable function of time. Modal field expansions with time-dependent modal amplitudes are derived. The modal amplitudes are obtained explicitly as simple convolution integrals where a temporal signal function is present at the integrands.