Poynting flux

The above reasoning has led to the fireball internal-external shocks model. This model is rather independent of the nature of the central engine. The latter one is just required to produce highly relativistic outflow, either in the form of kinetic energy or as Poynting flux. The radiation is produced in (collisionless) shocks. These can either occur due to interaction of the outflow with the cir-cumstellar material ( external shocks ) or due to interactions of different portions of the outflow with different Lorentz-factors, so-called internal shocks . 

The average energy flux in the evanescent wave is given by the real part of the Poynting vector S = (c/47t)ExH. However, the probability of absorption of energy per unit time from the evanescent wave by an electric dipole-allowed transition of moment pa in a fluorophore is proportional to lnfl - El2. Note that Re S and pa E 2 are not proportional to each other they have a different dependence on 0. 

To see this, let us introduce some definitions first. The Poynting vector G represents energy flux density (units esu2cm-3 s-1 = ergcm2s 1). It is a capability of the electromagnetic field to perform work defined as... 

The energy flux or intensity (energy transported across unit area per unit time across unit area) is given by the Poynting vector... 

In turn, the flux of energy is given by the real part of the complex Poynting vector... 

Flux of the Poynting Vector Through a Sphere of Large Radius... 

Let us consider the flux F, per unit of time, through a sphere S of large radius, of the Poynting vector of the field, created by the transition current between two states, of an electron bound in an atom. If we consider the energy E released at each transition, the ratio F/E gives the number of transitions per... 

The radiant raiCTgy flux is given by Poynting vector ... 

The constant A can be expressed in terms of the power flux density namely the z component of the Poynting vector is... 

A piezoelectric Poynting energy flux akin to those defined for nonpiezoelectric acoustic waves and electromagnetic waves is given by — (TyUj — (pDj). 

The expressions for the radiative rates, Eqs. (1.371,1.373) have been obtained considering the flux of the Poynting vector of the total field (the dipolar source plus the field scattered from the sphere) over a spherical surface with radius r oo. The expressions for the total decay rates have been obtained from Eq. (1.345). 

Not only but also y " can be obtained by skipping the calculation of the Poynting vector flux. To this aim it is central the standard electrodynamics equation ... 

The flux of the Poynting vector will thus be continuous when the discontinuity is collinear to the tangential field E . 

The flux density of an electromagnetic wave is described by the Poynting vector. For the case of the plane wave field one obtains for the time average in the direction of propagation... 

The energy flux propagated by the electromagnetic wave is give by P, the Poynting vector defined as P = E x H, or... 

The time-varying Poynting vector, which represents the directional energy flux density of the electromagnetic field, is thus given by... 

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