Related papers: RF Basics I and II
This lecture starts with a brief historical introduction and an explanation how to get from Maxwell's Equations to a simple cavity. After simplifying and adapting the equations for their application to Radio Frequency problems, the most…
The fields in rectangular and circular waveguides are derived from Maxwell's equations by superposition of plane waves. Subsequently the results are applied to explain cavity modes. Interaction of the cavity modes with a charged particle…
Maxwell equations (Faraday and Ampere-Maxwell laws) can be presented as a three component equation in a way similar to the two component neutrino equation. However, in this case, the electric and magnetic Gauss's laws can not be derived…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
Two questions connected to the macroscopic Maxwell equations are addressed: First, which form do they assume in the hydrodynamic regime, for low frequencies, strong dissipation and arbitrary field strengths. Second, what does this tell us…
The generalized Maxwell equations are considered which include an additional gradient term. Such equations describe massless particles possessing spins one and zero. We find and investigate the matrix formulation of the first order of…
We discuss the construction of Maxwellian electrodynamics in 2+1 dimensions and some of its applications. Special emphasis is given to the problem of the retarded potentials and radiation, where substantial differences with respect to the…
We shall give conditions on the illuminations $\varphi_{i}$ such that the solutions to Maxwell's equations \[ \left\{ \begin{array}{l} {\rm curl} E^{i}=i\omega\mu H^{i}\qquad\text{in }\Omega,\\ {\rm curl}…
The lecture notes document the mathematical theory of microwave and optical waveguides. We start with reviewing preliminary background from Maxwell's equations. Then we discuss hollow waveguides, and inhomogeneously-filled waveguides,…
The covariant formulation of Maxwell's equations can be expressed in a form independent of the usual systems of units by introducing the constants alpha, beta and gamma into these equations. Maxwell's equations involving these constants are…
The robustness of XRD methods for the determination of the lattice parameters of crystals is well established. These methods have been extended to helical atomic structures using twisted x-rays \cite{friesecke_twisted_2016}. Building on an…
The main purpose of this article is to disseminate among a wide audience of physicists a known result, which is available since a couple of years to the \emph{cognoscenti} of differential forms on manifolds; namely, that charge conservation…
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
This note offers a conceptually straightforward and efficient way to formulate and solve problems in the electromagnetics of moving media based on a representation of Maxwell's equations in terms of differential forms on spacetime together…
The integral formulation of Maxwell's equations expressed in terms of an arbitrary observer family in a curved spacetime is developed and used to clarify the meaning of the lines of force associated with observer-dependent electric and…
Novel analytic solutions are derived for integrals that involve the generalized Marcum Q-function, exponential functions and arbitrary powers. Simple closed-form expressions are also derived for the specific cases of the generic integrals.…
In classical treatment of Maxwell equations, the initial and boundary conditions are introduced by mathematical consideration rather than strictly using the Maxwell equations. As a result, the initial and boundary conditions are not logic…
This paper deals with the techniques of transport of high-power radiofrequency (RF) power from a RF power source to the cavities of an accelerator. Since the theory of electromagnetic waves in waveguides and of waveguide components is very…
Using the Einstein gravitation theory we show how to obtain the basic equations which predict the gravitational waves. This paper was written to graduate and post-graduate students of Physics. We deduce the equations didactically following…
The complex form of Maxwell equations has been constructed as one equation for 3-dimensional complex A-vector. The real and imaginary parts of this vector are described with use of electric and magnetic tensions accordingly. With using a…