Preface to the lecture, 1

80

 

physical interpretation!

 

field vector:  = E, H, j, B or D

 

1. Borderline case: no conductivity (vacuum) 

 

 

(5.12)

 

(damping by potential vortices) 

2. Borderline case: ideal conductivity (superconductor) 

 

(5.12*)

 

(damping by eddy currents) 

3. Diffusion equation 

(5.12**)

 

(vortex) 

Fig. 5.3:       Two borderline cases of the damping of waves 

and 

the diffusion equation for the decay of vortices 

---

Derivation and interpretation

 

81

 

5.3 Physical interpretation of the fundamental field equation

 

In nature the different types of equations always occur in a combined manner.

 

1. Let's take the concrete case of the particle-free vacuum. Here the specific conductivity 

is zero. The relaxation time constant 

 responsible for the decay of vortices tends

 

towards infinity according to equation 5.3 and the terms (c) and (e) are cancelled from the 

field equation 5.7. What remains is the by potential vortices (d) damped wave equation (b) 

(equation 5.12).

 

2. The reversed case (with 

) will consequently occur in materials without

 

resistance, super conducting materials. We now are dealing with the well-known case of 

the wave damped by eddy currents (equation 5.12*).

 

V i r t u a l l y  all in nature existing materials however don't fulfil these boundary conditions, 

from which it follows that both damping terms always occur together and in addition the

 

stationary term (e) becomes active.

 

It is true that every antenna demonstrates that the electromagnetic wave is convertible in 

high-frequency alternating currents and voltages, which then are amplified in the receiver. 

But until this fundamental equation was written down it however was not understood that 

this transition takes place by means of a vortex. Used are either antennas from well con- 

ducting material, or wave guides and horn radiators, which only have a minimal conduc- 

tivity, because they are filled with air. Actually the wave can be converted in two dual

 

ways; by means of the rolling up to current eddies or to potential vortices (fig. 1.4). 

Now we finally are capable to explain, why wave guides make possible a better degree of 

effectiveness: Owing to the concentration effect of the potential vortex the HF-power is 

bound in the inside and not emitted until the antenna is reached as happens for a wire for

 

reason of the skin effect.

 

Therefore, physically, one has to imagine this relation, which describes the transition of an 

electromagnetic wave into a vortex, in the way that the wave spontaneously can roll up to

 

a vortex in case it is disturbed from the outside. The more vortices are generated, the

 

larger consequently is the damping of the wave (equations 5.12 and 5.12*).

 

3. The life span of the vortices is limited and is determined by the electric conductivity. 

The at first stored vortices decay with their respective time constant   This process is 

described by the diffusion equation 5.12**. The final stage of the decaying vortices 

finally is described by the Poisson equation (a, e: equation 5.8).

 

If the vortex falls apart, it converts the in the vortex stored energy in heat. These processes 

are known from the eddy current. We speak of heating losses, that the stationary currents 

cause in the conductor material.

 

But new is the concept that such vortex phenomena can occur as dielectric losses in 

capacitors or in the air. The microwave oven or induction welding are good examples of

 

this.

 

---

82

 

phenomenological interpretation

 

 

Fig. 5.4:        The dependency on height of the ionisation 

in the 

ionosphere for medium latitudes .

 

left curve:     for a minimum of sun spots 

right curve: for a maximum of sun spots

 

:     H.L. Konig: Unsichtbare Umwelt (Wetterfuhligkeit), 5. Aufl., Bild 6, 

Seite 11, Verlag Moos & Partner Milnchen, ISBN 3-89164-058-7

 

---

Derivation and interpretation

 

83

 

5.4 Phenomenological interpretation of the fundamental field equation

 

How does a damping by vortices take effect in practice? First of all we notice that the 

reception of broadcastings gets worse. "The information signal is neglectable regarding 

the noise" explains the radio engineer and means, the number of vortices increases at the 

expense of the wave intensity.

 

Why, does the pupil ask, is it so cold in space? There the sun shines day and night and in

 

addition much more intensely than on earth! The correct answer would have to read that

 

because of the extremely small conductivity no diffusion process can take place. We owe

 

the warmth on our earth solely the here taking place decay of vortices. Responsible is the

 

conductivity of the atmosphere.

 

In 60 km to 500 km height over the earth's surface, the region which is called the

 

ionosphere, the gases predominantly exist in ionized form. There a very good conductivity

 

prevails and eddy current losses are the result. Correspondingly high are the measurable

 

temperatures. Besides the diffusion process the eddy currents carry out a damping of the

 

cosmic radiation. We say the sunlight is filtered and reduced to a for nature bearable

 

intensity.

 

But not all frequencies are damped in the same way (fig. 2.8). We observe a blue shift, if

 

we look into the actually black sky. The blue sky doesn't show any spots or clouds. The

 

reason is to be sought in the skin effect of the eddy currents, which strive outwards. Since

 

no edge of a conductor is present here, no skin can form. The vortices spread evenly over

 

the ionosphere.

 

The potential vortex however is able to structure. It merely needs a bad conductivity and 

this it finds in lower heights between 1 km and 10 km. It damps the wave and with that

 

also the light, for which reason we say it becomes darker, the sun disappears behind

 

clouds.

 

The clouds well visibly form the discussed vortex balls and vortex strings. Clouds can

 

form virtually from the nowhere during intense solar irradiation, i.e. the waves can roll up

 

to vortices. But as a rule this takes place above the oceans. Here also the phenomenon of

 

transport has an effect. Because of the high dielectricity the water surface favours the

 

formation of potential vortices. So the vortices bind individual water molecules and carry

 

them away. If a diffusion process takes place, in which the vortex decays, then it rains.

 

This can happen in two different ways:

 

1. Either the conductivity increases. If for instance during intense solar irradiation air ions 

form, the sun is able to break up clouds and fog. Or when the air is raised in higher 

layers with better conductivity, because a mountain forces this, then it rains at the 

mountain edge.

 

2. For potcntial vortices the electric field is standing perpendicular to them. If at one point

 

an exceptionally lot of vortices join together, which let the cloud appear particularly

 

dark to black, then the danger exists that the ionization field strength for air is reached,

 

in which case a conductive air channel forms along which the stored up charges

 

discharge. Also lightning is a diffusion process, in which potential vortices decay and

 

rain can form.

 

In connection with the electromagnetic environmental compatibility great importance is

 

attributed in particular to the storage and the decay of electric vortices. There not only is

 

an academic-scientific interest in the question, how many potential vortices are generated,

 

how many are stored and how many decay, if we make a telephone call with a handy, if

 

we are staying under a high-tension line or if we are eating food, which has been heated

 

up in a microwave oven. The necessary mathematical description is provided by the

 

fundamental field equation 5.7.

 

---