Magnetospheric MHD Resonances and ULF Pulsations - Ultra and Extremely Low Frequency Electromagnetic Fields - page 254

Fig. 6.15 A schematic drawing of current fluctuations in the vicinity of large-scale atmospheric
inhomogeneities
200 km and the total vertical current in this region was 25 A, which is much
greater than the contribution of an isolated thunderstorm ( 0:4 A). In the region
surrounding the thunderstorm, the atmospheric current density reached a peak value
of about .3:5-1:2/ 10 9 A=m 2 . Interestingly, both the atmospheric current in the
MCS-trailing stratiform region and the mean current due to lightnings discharges
were upward-directed. Considering the important role played by the atmospheric
background current in formation of the global electric circuit, it is expected that the
random current fluctuations may attribute to the electromagnetic noise.
In this notation the atmospheric current flowing in the vicinity of large-scale
atmospheric inhomogeneities such as thunderstorms or hurricanes is treated as a
stochastic process. We estimate the spectrum and amplitude of correlation function
of the electromagnetic noise caused by the random current and conductivity
fluctuations and discuss whether such a noise contributes to natural electromagnetic
background in the range of 10 4 -10 2 Hz.
Following Surkov and Hayakawa ( 2007 ) we assume that the current variations
are upward or downward inside the perturbed region and are zero outside, as shown
in Fig. 6.15 . To simplify the problem the actual inhomogeneous region labeled 1 is
replaced by a cylindrical region with the radius a and the height h labeled 2. As
before the random current fields are assumed to be steady, uniform, and isotropic
inside the inhomogeneity, which, in turn, implies that the spectral density of the
process is delta-correlated. To relate the electromagnetic spectra with current fields,
a transfer matrix should be found, and then we can calculate the correlation matrix
and power spectra of the random electromagnetic field.
In order to derive the main results we consider a simple way using the following
line of reasoning. First, we note that the fluctuations of the atmospheric current