SELF

14

S.B. Karavashkin and O.N. Karavashkina

2. Comparison of experimental results

For this aim, we have used the well-analysed experimental results on the investigation of the near EM field at a long-wave band, as described in the survey monograph by the team of authors led by Ya.L. Alpert [18, p. 836- 845]. In the Chapter VI, "The radio waves velocity", they study the regularity of variation of the additional phase  ficut.gif (844 bytes)*  in the near field of the source of transverse EM waves. As the authors conclude, "… the formula of vertical component of the electric field of dipole … , noting the phase of wave, has the following form:

(19)

where  E z is the vertical component of the electric field of dipole;

WSigmabottom.gif (824 bytes)  is the source power in kilowatts;

 slash.gif (845 bytes)f(rocut.gif (841 bytes))slash.gif (845 bytes) is the module and  ficut.gif (844 bytes)  is the phase of the attenuation function   f(rocut.gif (841 bytes)) ;

  is the so-called num distance,erical ;
is the wave number for air (here we take for air n0 = 1 );

lumbdacut.gif (841 bytes) is the wavelength;

epsiloncut.gif (833 bytes) is the dielectric constant of the Earth surface. However, (19) is true only at the distances  r equmore.gif (841 bytes)(4 from_to.gif (828 bytes) 5)lumbdacut.gif (841 bytes)  from the radiator" [18, p. 837]. In other words, only in the region exceeding five lengths from the radiator we can think true the assumption that the long waves propagate in the wave guide layer between the Earth surface and ionosphere, on whose basis (19) has been obtained.

"But the phase structure of electromagnetic field and the velocity of radio waves have … some features just at nearer distances immediately bordering on the antenna. In this region we have to use for calculations more complex formula having the following form [19]:

(20)

where k2k1(epsiloncut.gif (833 bytes)')1/2k1[epsiloncut.gif (833 bytes) - i(4picut.gif (836 bytes)sigmacut.gif (843 bytes)/omegacut.gif (838 bytes))]1/2 and sigmacut.gif (843 bytes) is the electric conductance of the Earth. The values slash.gif (845 bytes)f(rocut.gif (841 bytes))slash.gif (845 bytes) and  ficut.gif (844 bytes)  are calculated in a complex way with the help of series" [18, p. 837]. "The above formulas relate to the case of vertical dipole placed on the Earth surface. In approach to the radiation point, at distances  r equless.gif (841 bytes)lumbdacut.gif (841 bytes)  the finite size of the antenna begins to have an effect. So (20) becomes invalid for exact calculations of the field structure. There are no rigorous formulas of electromagnetic field that take into account both the finite size of antenna and finite conductance of the Earth. However the field structure analysis showed that at these distances the formulas derived for the case when the conductance of the Earth is taken infinite are quite valid. In this case the phase fibigcut.gif (846 bytes)z  of vertical component E   is determined as

(21)

[18, p. 838- 839], where R1R2 , R0 is the distance to the top, bottom and mirror ends of antenna correspondingly, and taucut.gif (827 bytes)0  is so-called shortening of antenna meaning the section adding the length of antenna to  lumbdacut.gif (841 bytes)/4 .

fig3.gif (6011 bytes)

Fig. 3.  Theoretical dependence of phase fibigcut.gif (846 bytes)z wish respect r/lumbdacut.gif (841 bytes) to in the near of antenna: 1 is the antenna with the lebhthing at   sigmacut.gif (843 bytes) = infinity.gif (850 bytes), 2 is antenna with the shortening at sigmacut.gif (843 bytes) = infinity.gif (850 bytes), a is vertical dipole at sigmacut.gif (843 bytes) = 1,7*106 CGSE , epsiloncut.gif (833 bytes) = 4. [17, p. 840, Fig. 122.4]

 

"The curves of regularity fibigcut.gif (846 bytes)z with respect to r/lumbdacut.gif (841 bytes) constructed on the basis of (21) for different values taucut.gif (827 bytes)0 (see Fig. 3) illustrate the details of variation of the wave phase near the antenna; for comparison, in the same figure we show the curve fibigcut.gif (846 bytes)z  calculated by (20) for sigmacut.gif (843 bytes) = 1,7*106 CGSE and  epsiloncut.gif (833 bytes) = 4 " [18, p. 839].

We see from this plot that the curves calculated by both above formulas predict the end of near field in limits  r = lumbdacut.gif (841 bytes) , though, as the authors said, the region of near field is much larger. Another drawback of these curves is the bad correlation between the curves a and 2, while a well correlates with 1 immediately near the radiator. None the less, the data of plot show that in the near field of EM radiator the phase is not constant, as implied in the absence of travelling wave in this region. This additionally evidences that it would be incorrect to neglect the delay phase in the near field, as we indicated it in [11].

Contents: / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17 /

Hosted by uCoz