Antenna Design Consultant

Blog #3 describes how the atmospheric electric field was measured using two aircraft:  1. South Dakota School of Mines and Technology (SDSMT) armored T-28 aircraft, 2. New Mexico Institute of Mining and Technology (NMIMT) Special Purpose Test Vehicle for Airborne Research (SPTVAR).  The objective was to accurately measure the electric field produced by lightning storms. Five electric field mills which  were attached at specific locations on the fuselages of both aircraft.  [1]

The E – 100 electric field mill is shown in the following figure:

Its specification is given in the Appendix.

In a field mill, a conducting, grounded, rotating shutter alternately shields and exposes electrodes from the electric field to be measured. The charge induced on the electrodes, which is periodic, passes through an amplifier. After amplification, the signal is demodulated and filtered to produce a voltage that is proportional to the electric field.
Since the aircraft fuselage is also charged, it produces an electric field of its own that must be subtracted from the data through a calibration procedure. To calibrate the five field mills, self-test calibration flights was made which the roll, pitch and yaw of the aircraft were varied through most angles sensed by each electric field mill, and regression analysis was used to process the data. The placement of the mills is shown in the following figures:

In addition, for calibration purposes, intercomparison flights were made with both aircraft.

A typical result is shown in the next figure [1]
The top three plots are the heading, roll and pitch of the two aircraft, while the bottom three plots compare the electric field outputs of the two aircraft (kV/M) which are very close to one another.

References

1.    Rand E. Feind, Qixu Mo, and Andrew G. Detwiler, REPORT ON T-28 ELECTRIC FIELD MEASUREMENTS AND THEIR CALIBRATION, Division of Atmospheric Sciences, National Science Foundation, Institute of Atmospheric Sciences, South Dakota School of Mines and Technology, September 1998 http://www.eol.ucar.edu/projects/t28/publications/reports/R98-01.pdf

Appendix

MODEL E-100 DC ELECTRIC FIELD METER

SPECIFICATIONS

All you need to do is to place on a closed surface surrounding the object an electric surface current distribution Ke = nxH (Amp/Meter), and magnetic current distribution Km = -nxE (Volt/Meter) , where E and H are the time-varying electric and magnetic fields of the radar on the object surface, and n is the outward normal to the surface, x denotes vector cross product.  The resulting electromagnetic fields are the same as the original electromagnetic fields outside the object and E = 0, H = 0 inside the object. This is guaranteed by Love’s Equivalence Theorem. [1]. Therefore, the scattered fields have been eliminated!

The difficult problem remains: to generate the required electric and magnetic current distributions on the closed surface. The electric current sheet can be achieved by curved conducting wires driven by a current source. The magnetic current sheets are much more difficult to realize but can be approximated as a doublet of two electric surface currents fed by oppositely directed current sources. [2], [3], [4].  (Patent pending, 6/17/2010)

Example of a metal sphere of radius R illuminated by a plane wave
E = e^-jωz/c (0, 1, 0), H = -(1/Zo) e-^jωz/c (1,0,0), Zo=377 ohms,  ω = angular frequency, c = speed of light

This can be converted into spherical coordinates
Ke on the sphere = n x H = e^-jωz/c ((z/R), 0, (x/R)}
Km on the sphere = -n x E = e^-jωz/c ((0, (-z/R)), (y/R))

Where x = Rsin(θ)sin(φ), y = Rsin(θ)cos(φ), z = Rcos(θ)
.
These equations simplify for the magnitude of the currents.  Οn the sphere, in the x-z plane, |Ke| are circles, ((1 – (y/R)2)0.5 and in the y-z plane,  |Km| are also circles ((1 – (x/R)2)0.5.
The phase factors are given by  e^-jωz/c

More ideas on how to realize these currents will be given in the next blog.
1.    A. E. H. Love, “The Integration of Equations of Propagation of Electric Waves,” Phil. Trans. Roy. Soc. London, Ser A, 197, 1901, pp. 1 – 45.
2.    S. A. Schelkunoff, “Some Equivalence Theorems of Electromagnetics and Their Application to Radiation Problems,” Bell System Technical Journal, Vol. 15, 1936, pp. 92 – 112
3.    S. Rengarajan, Y. Rahmat-Samii, “The Field Equivalence of the Non-Intuitive Null Fields, “ IEEE Trans. on Antennas and Propagation Magazine, Vol. 42, No. 4, August 2000
4.    S. A. Schelkunoff, “Antennas Theory and Practice,” John Wiley & Sons, NY, 1952,  pp. 44 -45.