Table Of ContentThe Pennsylvania State College
The Graduate School
Department of Physics
Vertical Incidence Ionospheric Propagation at Low Frequencies
A Dissertation
by
Robert James Nertney
Submitted in partial fulfillment
of the requirements
for the degree of
Doctor of Philosophy
August 1951
Approved:
Department of Physics
o ( M
The Engineering Experiment Station
ABSTRACT
The problem of the propagation of long electromagnetic waves in the
ionosphere at vertical incidence is studied theoretically.
It is shown that it is necessary to solve a pair of coupled wave
equations in order to obtain the wave solutions. In the homogeneous
medium these equations become independent and define two characteristic
modes of propagation.
A method is first developed for obtaining solutions to the two in
dependent wave equations which are obtained if one neglects the coupling
between the two characteristic modes mentioned above.
It is next shown that the method of nvariation of parameters" may
be used to obtain approximate solutions to the coupled equations from
our solutions to the uncoupled equations if the coupling is not too great.
A diurnal and seasonal model representing the S and D regions of
the ionosphere above State College, Pennsylvania is presented. This
model consists of a Chapman-like-E region and an electron D-region.
Approximate 150 Kc/sec wave solutions including coupling are obtained
for this model. These wave solutions, of course, exhibit the well known
reflection condition corresponding to an electron density of around 3000
electrons/cm^. It is shown that the effect of the coupling is to cause a
wave traversing a coupling region to excite a new wave propagated in the
direction of propagation of the incident wave and also a back scattered
wave propagated in the reverse direction. The back scattered wave will
appear as a reflected wave originating in the coupling region. This
forward scattered wave due to the downgoing wave from the upper "reflec
tion” level also must be considered in calculating the polarization of
ionospherically reflected waves.
It is shown that, in the case of 150 Kc/sec waves, the coupling
effects occur in the neighborhood of N = 300 electrons / cm^ which
corresponds to the "classical reflection" level for the "ordinary" wave.
The coupling effects become greater as the V associated with the coupling
N value decreases toward Vc f°r the night-time models. This results in
stronger split echoes and greater departure from circularity in the
polarization ellipses.
The effect of the D-region is to introduce adsorption and phase
delay on the "ordinary" and "extra-ordinary" waves traversing it.
It is shown that the differences in phase path and absorption
experienced by the ordinary and extraordinary waves give us two addi
tional parameters with which to deduce the properties of the D-region
since it is these differences which help to determine the polarization
of the down coming wave. The experimental results to be expected from
this model are compared in detail with our 150 Kc/sec. polarization,
absorption and height results. The predicted experimental results are
compared qualitatively with the actual experimental results at several
other frequencies.
This work has been supported in part by Contract No. AF19(22)-44
with the U. S. Air Force, through sponsorship of the Geophysical
Research Directorate, Air Material Command.
TABLE OF CONTENTS
ABSTRACT
TABLE OF CONTENTS
LIST OF ILLUSTRATIONS
INTRODUCTION
A. The Ionosphere
B. The General problem
C. The Specific Problem
D. The Method of Attack
II. THE MAGNETO-IONIC THEORY
A. The Appleton-Hartree Equation
B. The Wave Theory
C. The Uncoupled Equations
D. General Considerations
III. THE SOLUTION OF THE UNCOUPLED EQUATIONS
A. The Method
B. The Ionospheric Problem
C. The Extraordinary Wave
D. The Ordinary Wave
E. Application of the Method
F. An Example
G. The Reflection Coefficient
H. Physical Interpretation and Remarks
I. Numerical Results
J. Comparison with Experiment
K. The Height of Reflection
L. The Absorption
M. The Polarization
IV. THE COUPLED EQUATIONS
A. General Considerations
B. Variation of Parameters
C. The Application of Variation of Parameters to the
Ionospheric Problem
D. Numerical Results
E. The Height of Reflection
F. The Absorption
G. The Polarization
V. THE D-REGION
A. General Considerations
B. A D-layer Model
C. Results
VI. THE COMPLETE E-LAYER - D-REGION MODEL
A. General Considerations
B. The Height of Reflection
C. The Absorption
D. The Polarization
E. Resume
F. Plans for Future Study
VII. ACKNOWLEDGEMENTS
VIII. BIBLIOGRAPHY
APPENDIX A.
A. The A-H. Dispersion Equation
APPENDIX B.
A. Approximate Solutions to the Uncoupled Equation
B. Ray Optics
C. The W.K.B. Method
D. The Mptt Solutions
E. A Simple Example
APPENDIX C.
A. The Chapman Ionization Theory
B. Deviations from the Monochromatic Chapman
Distribution
C. The Collisional Frequency
APPENDIX D.
A. An Outline of the Method
LIST OF ILLUSTRATIONS
1. The E—layer N— V vs. height curves in linear coordinates.
2. The E-layer N- V vs. height curves in logarithmic coordinates
(N = 10^ to lO^ electrons/cm^).
3. The E-layer II- TS vs. height curves in logarithmic coordinates
(N - 1 to 10^ electrons/cm^).
A. A typical yuv. vs. height curve (f*c = 2.2 mc/sec).
5. A typical y-i. vs. height curve (fc =2.2 mc/sec).
6. R, f, G (f) vs. height (fc = 3.0 mc/sec).
7. I, v, H (f, v) vs. height (fc = 3.0 mc/sec).
8. R, f, G (f) vs. height (fc = 0.55 mc/sec).
9. I, v, H (f, v) vs. height (fc = 0.55 mc/sec).
10. R, f, G (f) vs. height (fc = 1.1 mc/sec).
11. I, v, H (f, v) vs. height (fc = 1.1 mc/sec).
12. R, f, G (f) vs. height (f*c = 2.2 mc/sec).
13. I, v, H (f, v) vs. height (fc = 2.2 mc/sec).
1A. R, f, G (f) vs. height (fc = l±. 4 mc/sec).
15. I, v, H (f, v) vs. height (fc = U.4 mc/sec).
16. The boundary value problem.
17. The filter analog.
18. The phase integrands for the ordinary wave.
19. The absorption integrands for the ordinary wave.
20. The absorption integrands for the extra-ordinary wave.
21. Comparison of the np” phase integrand with the ray optics.
22. Comparison of the "p" absorption integrand with the ray optics.
23. A typical diurnal absorption curve.
24. The subscript system for the unperturbed waves.
25. The chart relating N and -y to the complex wave polarization.
26. The complex polarization (-^ ) , vs. height (fc = 0.55 mc/sec).
27. The complex polarization (^-)# ^ vs.h eight( fc = 1.1 mc/sec).
23. The complex polarization vs. height (fc = 2.2 mc/sec).
29. The complex nolarization vs» height (fc = 3.0 mc/sec).
30. The complex polarization vs. height (fc = 4.4 mc/sec).
31. The quantity GM, related to the u.g.b.s. wave, vs. height
(fc = 0.55 mc/sec).
32. The quantity GM, related to the u.g.b.s. wave, vs. height
(f*c = 1.1 mc/sec).
33. The quantity GM, related to the u.g.b.s. wave, vs. height
(fc = 2.2 mc/sec).
34-. The quantity GM, related to the u.g.b.s. wave, vs. height
(fc = 3.0 mc/sec).
35. The quantity GM, related to the u.g.b.s. wave, vs. height
(fc = 4..4 mc/sec).
36. The quantity FM, related to the d.g.f.s. wave, vs. height
(fc = 0.55 mc/sec).
37. The quantity FM, related to the d.g.f.s. wave, vs. height
(fc = 1.1 mc/sec).
38. The quantity FM, related to the d.g.f.s. wave, vs. height
(fc = 2.2 mc/sec).
39. The quantity FM, related to the d.g.f.s. wave, vs. height
(fc = 3.0 mc/sec).
40. The quantity, FM, related to the d.g.f.s. wave, vs. height
(fc = 4.4 mc/sec).
4.1. The addition of two circularly polarized waves.
4.2. Theoretical diurnal variation of 0 and Kf/ for the E-layer alone.
4-3. Diagram showing mechanics of propagation in the E— layer, D-layer
model.
4.4.. The N distribution for the D-layer vs. height.
4.5. The quantities KQX x, K0"X 0, and K0 x -J^D) for a typical
D-layer model.
4-6. The quantities Y anc^ I log p) vs» D-layer ionization.
4.7. The seasonal variation of the D-layer ionization.
4-3. Seasonal variation of E-layer critical frequency.
4.9. Theoretical diurnal variation of jlog p|.
50. Theoretical diurnal variation of .
51. Theoretical diurnal variation of © .
52. Height of the E-layer critical points vs. operating frequency
(fc = 0.55 mc/sec).
53. Height of the E-layer critical points vs. operating frequency
(fc = 1.1 mc/sec).
54.. Height of the E-layer critical points vs. operating frequency
(fc = 2.2 me/sec).
55. Height of the E-layer critical points vs. operating frequency
(fc = 3.0 mc/sec).
56. Height of the E-layer critical points vs. operating frequency
(fc = 4-.4- mc/sec).
57. Height of the D-layer critical points for 16 Kc/sec and 150 Kc/sec
vs. D-layer ionization.
58. E-layer h'-t and h-t vs. diurnal time (summer).
59. E-layer h’-t and h-t vs. diurnal time (winter).
60. Temperature vs. height from rocket flight.
61. Height and virtual height vs. diurnal time for an operating
frequency of 100 Kc/s.
62. Height and virtual height vs. diurnal time for an operating fre
quency of 325 Kc/s.
63. Height and virtual height vs. diurnal time for an operating
frequency of 565 Kc/s.
64* Height and virtual height vs. diurnal time for an operating
frequency of 850 Kc/s.
65. Height and virtual height vs. diurnal time for an operating
frequency of 100 Kc/s and 300 Kc/s.
66. Height and virtual height vs. operating frequency (1.0 mc/sec
to 3.2 mc/sec).
67. Virtual height vs. seasonal time (16 Kc/sec).
63. Monthly average absorption vs. diurnal time.
69. Absorption vs. seasonal time (16 Kc/sec and 70 Kc/sec).
70. Monthly average values of the angle O vs. diivrnal time.
71. Monthly average values of the angle vy vs. diurnal time.
IA. The coordinate system.
IB. The boundary value problem showing that the W.K.B. solutions are
reflectionless.
2B. The np" solution example.
