Electromagnetic field longitudinal

Metal contained in the channel is subjected to forces that result from the interaction between the electromagnetic field and the electric current in the channel. These inward forces produce a circulation that is generally perpendicular to the length of the channel. It has been found that shaping the channels of a twin coil inductor shown in Figure 10 produces a longitudinal flow within the channel and significantly reduces the temperature difference between the channel and the hearth (12). 

The approach by Chubykalo and Smirnov-Rueda further includes longitudinal modes and Coulomb long-range electromagnetic fields that cannot be described by the Lienard-Wiechert potentials [2,57]. 

The process of total reflection of an incident wave in an optically dense medium against the interface of an optically less dense medium turns out to be of particular and renewed interest with respect to the concepts of nontransverse and longitudinal waves. In certain cases this leads to questions not being fully understood in terms of classical electromagnetic field theory [26]. Two crucial problems that arise at a vacuum interface can be specified as follows ... 

Whittaker [27,28] derived equations defining the electromagnetic field in the vacuum in terms of functions / and g with the units of magnetic flux directed longitudinally in the axis of propagation (Z)... 

M. W. Evans, P. K. Anastasovski, T. E. Bearden et al., Longitudinal Modes in Vacuo of the Electromagnetic Field in Riemannian Spacetime, submitted to Optik, 2000 (in press). 

The electromagnetic field of the composite photon contains advanced and retarded components, without any causality breach. The forcefield of doublet is described by the symmetric Maxwell s equations [87b]. Three different regions appear in the forcefield inner, near-field, and far-field. Longitudinal components of force are always present. However, in the far field, they dissapear for practical purposes. In this sense, the equations developed contain the standard set as a limiting case. 

M. W. Evans et al., AIAS group paper, longitudinal modes in vacuo of the electromagnetic field in riemannian space-time, Optik (in press), acknowledgement of receipt (2000). 

It is essential that plasmons are longitudinal electric waves, that is, that the electric field strength vector is parallel to the wave vector q. For a plane wave, the vector potential of electromagnetic field is... 

The Einstein coefficient of absorption of radiation for the longitudinal (along the z axis) and the transverse (perpendicular to the z axis) electromagnetic fields can be obtained from these matrix elements and are given by... 

Figure 2. Qualitative behavior of the field strength of the evanescent wave as a function of the angle of incidence (nt — 1,51 n -= 1.0). Contrary to the behavior of the electromagnetic field of normal" light the evanescent field comprises a longitudinal component, too. E and E respectively indicate the direction of polarization of the incident light.

We have used scalar diffraction theory in this calculation, which is an approximation in two parts. The first part consists of approximating the electromagnetic field as a transverse field. We have derived the conditions under which it is permissible to do so. In the Appendix, we discuss the conditions under which it is possible to replace the vector Helmholtz equation by the scalar Helmholtz equation for transverse fields. In a sense, we have reduced the problem to a solution of the scalar Helmholtz equation. The second part of the approximation consists of exploiting the reduction of the vector Helmholtz equation to a scalar Helmholtz equation. Scalar diffraction theory is based on the scalar Helmholtz equation. Hence, when it is permissible to neglect the longitudinal and cross-polarized components of the Gaussian beam, we may use solutions of the scalar Helmholtz equation for transverse fields and may take over the results of scalar diffraction theory with confidence for this special case. 

The linear polarization of longitudinal component of electromagnetic field caused by a characteristic geometry of the system (cylindrical geometry in an optical fiber or spherical in the case of field generated by a local source) can be measured in a nondemolition way with the aid of the Aharonov-Bohm effect. 

The free electromagnetic waves have the transverse polarization. The longitudinal and scalar polarization are introduced in Eq(54) artificially and should vanish in the expression for any observable. This can be achieved by imposing the Lorentz condition (40). Then the contributions of the longitudinal and scalar polarizations cancel in the expressions (42), (43) for the field strength and for the energy of electromagnetic field ... 

Another method for pulse length determination uses the electromagnetic fields produced by the electron bunch itself to measure the longitudinal length of the bunch, and therefore derive the pulse width. A pulse of a given width has a characteristic microwave power spectrum as shown in Figure 5. 

Radiation from a plasma consists mainly of Bremsstrahlung, emitted as a continuum by deceleration of electrons in collision, synchrotron radiation caused by rotation in a magnetic field and atomic emission radiation, better known as line spectra associated with transition between electronic energy levels. The equilibrium between all modes of radiation in a large plasma causes the emission of black-body radiation. The interaction between plasma particles and electromagnetic fields causes internal wave motion of both longitudinal and transverse types. 

Comparing Eq. (1.43b) with Eq. (1.42), we see that oop = ft)Lo- This means that plasma oscillations take place along the direction the electric field and therefore manifest themselves as longitudinal waves. Consequently, they do not interact with the transverse electromagnetic field (1.3.7°). In quantum mechanics, the particle with the energy cjOpfi is called the volume plasmon. 

By design, in a traveling wave tube, the speed of electrons in the electron bean u (m/s) and the longitudinal phase velocity of microwave electromagnetic field in the slow-wave structure transmission line v (m/s) are made approximately equal. When an electron comes out of the electron gun, the speed of an electron is... 

Nuclear relaxation is the return to thermodynamic equilibrium of a spin system excited by an appropriate ft equency of an electromagnetic field. The interaction of magnetic moments of excited spins with the environment creates microscopic local magnetic fields that fluctuate. These magnetic fluctuations are related to molecular motions. The longitudinal R and transverse Ri relaxation rates are modulated by the phenomenon of molecular distribution and... 

Electromagnetic interaction due to the transverse degrees of freedom of the electromagnetic field (as opposed to the Coulomb interaction, which is due to the longitudinal degrees of freedom, when Coulomb gauge is employed). Two-component spinor... 

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