Lonal Bureau of Standards

Library, I '^^^ MIH' O r.

^ccUnlccii *^^ote 92o. 3/3

ON THE EFFECT OF HEAVY IONS ON LF

PROPAGATION, WITH SPECIAL REFERENCE

TO A NUCLEAR ENVIRONMENT

J. RALPH JOHLER AND LESLIE A. BERRY

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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NATIONAL BUREAU OF STANDARDS

technical ^Ttcte 3/3

ISSUED June 7, 1965

ON THE EFFECT OF HEAVY IONS ON LF PROPAGATION,

WITH SPECIAL REFERENCE TO A NUCLEAR ENVIRONMENT

I

J. Ralph Johler and Leslie A. Berry

Central Radio Propagation Laboratory

National Bureau of Standards

Boulder, Colorado

k NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

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Contents

Page

Foreword iv

Abstract 1

1. Introduction to Ionosphere Models 1

1. 1. Ambient Model 1

1. 2. Ionization Introduced by Nuclear Detonations 7

2. Propagation Effects of Heavy Ions 9

3. Propagation in a Nuclear Environment 18

4. Conclusions 21

5. Acknowledgments 2 2

6. References 23

Figures 1 through 48 26

Glossary 74

111
Foreword

This paper is the annual comprehensive report on LF propagation

part of Advanced Research Projects Agency (ARPA) Order No. 183,

Amendment No. 13, Task IV, or NBS Project 51 013-12-51 0041 5. This

is a theoretical study of low frequency signals in the presence of ambient

and disturbed ionosphere models. In particular, this paper introduces

the effects of heavy ions into the theoretical analysis. These ions are

known to exist in the ambient atmosphere and ionosphere, but the effect

on propagation has not been studied in a systematic manner. Indeed

large quantities of ions, in addition to electrons, are produced by solar

disturbances, proton events, and high altitude nuclear detonations. This

paper introduces an equation of motion for a gas mixture of four constituents: positive ions, negative ions, electrons, and neutrals together with

the interaction of these constituents via collisions resulting from velocity

differentials and the superposed terrestrial magnetic field.

The resultant electrical properties of the magneto -plasma are

formulated in a format which can be readily introduced in the previously

published analytical methods of Johler and Harper [l962].

IV
On the Effects of Heavy Ions on LF Propagation,

with Special Reference to a Nuclear Environinent t

J. Ralph Johler and Leslie A. BerryNatural disturbances and high altitude nuclear

detonations produce large quantities of ions in the ionosphere

and in the atmosphere. The effect of such ionization on the

propagation of LF radio waves is not in general negligible.

In fact, physically realizable production rates can be postulated in which the ions rather than the electrons control the

propagation of radio waves around the terrestrial sphere.

Therefore, considering only an electron gas type plasma as an ionosphere model is subject to possible grave errors in

the theoretical prediction of LF propagation. The theoretical

solution of the heavy ion problem requires the introduction of

an equation of motion or hydrodynamic equation for each gas

constituent.

1. Introduction to Ionosphere Models

1.1. Ambient Model

The propagation of LF (low frequency) radio waves is, in large

measure, dependent upon the electrification in the upper atmosphere

and lower ionosphere. This electrification can be quantitatively

described as a microprocess in the plasma by a set of rate equations

[Chapman, 1 931 ; Nicolet and Aikin, I960; Ginzburg, I960; Grain, 1961;

Pierce and Arnold, 196Z; Arnold and Pierce, 1963; Pierce, 1963;

Arnold, 1 964; and Moler, I960];

^^ - Q - Ail^e - B^e^+ +(C + D) N_

dt

dJ,

dt

dt

= AN^ - (G + D) 7^_ - E#_7l^+

- Q - BN,N^ - EN.N^, (1.1)

where N+ = N^ + N_ and

^= -^ {N, + N.).

t This work was sponsored by ARPA under Order No. 183, Amendment

No. 13, Task IV or NBS Project 51013-12-5100415.
The number density, N^ is identified with three gas constituents by the

subscripts: e, elctrons; +, positive ions; -, negative ions. The quantities on the right side of the differential equations comprise ionelectron pair production rate, Q, causing dissociation into positive ions

and electrons, and the various rate coefficients, A, B, C, D, and E.

The electron attachment coefficient is designated by A, the electron-ion

recombination coefficient by B, the photo detachment coefficient by C,

The detachraent coefficient by D, and the ion-ion recombination coefficient by E. An extensive survey of the state of knowledge concerning

these rate coefficients has been given by Archer [1963].

The attachment coefficient, A, is calculated [Arnold and Pierce,

1963; Pierce, 1963; and Arnold, 1964] from atomic oxygen nunnber

density, cm~^, [O], molecular oxygen number density [Og] and nitrogen number density [Ng] temperature, T, °K (degrees Kelvin) obtained

from model atmospheres such a Minzner and Ripley [l956], Minzner,

Ripley, and Condron [1958], and Minzner, Champion, and Pond [1959]

by,

A~1.3[O](10-^^)+[O3](10-^^)+(;^^)[O3]{[O3] + i||J}3(10-^°), sec-^

(1.2)

This equation has recently been verified by Hirsch, Eisner, and Selvin

[1964]. Hirsch et al. , however, get 2. 1(1 0"^°) instead of 3(10"^° ) for

the numerical constant assuming T = 300°K. The electron-ion recombination coefficient, B, is [Arnold and Pierce, 1963]

B~2(10"'^), cm^ sec"\ (1.3)

This is valid for altitudes 40 to 100 km above the surface of the earth.

The photo detachment term C is [Arnold and Pierce, 1963; Pierce,

1963; and Arnold, 1964]

0. l[O3-]+1.4[O-]+5(10-^)[O.;]-H0-^[OH-]+10-"[NO3~] ^^_. ^^ -x [03]+[0-]+[03-] +[OH-] +[N03] cosx, sec

,

(1.4)

where X, the zenith angle of the sun, has been introduced. Several negative ions: ozone O3, OH", NOj, 0~, and O2, have also been included.

•2-
The detachment coefficient, D, comprises two parts, D = Dg + D^^ where Dg is the collisional detachraent and Da is the associative detachment. The collisional detachment, Dj, , is,

D, =^[03] P, 1.3(10-)(f^)exp(-f^)sec-. ,1.5)

Boltzmann' s constant, k(h ^ 1 . 38 ( 1 O"""" ^) ergs/deg Kelvin), and the

electron affinity, Eg^ , electron volts (1 electron volt ~ 1 . 602 (1 0""'"^) ergs),

together with the probability, Pj. , that detachment occurs for a particular ion, have been introduced. Here N_ is the sum of the concentrations

of all negative ions. The contribution to D^ from an ion except Og is

negligible. Hence, O3 is ordinarily the only negative ion used to calculate Dg . It has also been found that O2 is the only efficient molecule for

detaching the electron from Og. Pierce and Arnold [l962] pointed out

the wide variation in Ea estimates in the literature which strongly influences Dc . Indeed, published values of E* range from 0. 76 to 0. 15

electron volts. The value Ea = 0. 46 electron volts was recommended

by Pierce and Arnold [l962].

The associative detachment, Da, is,

sec""""

(1.6)

Atomic hydrogen concentration [H] has here been introduced. The detachment coefficient, D ~ Da has, in this paper, been increased by a factor of 50 in the daytime over the value given by Arnold and Pierce

[1963, 1964]. This was found to be necessary as a consequence of a study of the Loran-C ionospheric wave propagated between Cape Fear,

North Carolina, and Boulder, Colorado. Thus it was found necessary,

when calculating reflection coefficients and propagated fields at LF for

the Loran-C, to modify the model somewhat at this point in the procedure to obtain the correct values of attenuation, Doherty [1964],

Measurements of the ionic recombination coefficient, E, have

been given by Arnold and Pierce [ 1963 ] as ~ 2(1 0~^

) cm^ sec"""". More

recently, LeLevier [1964] has given estimates,

E ~ 3(10""^) to 7(10"^) cm^ sec"^. (1. 7)
The ionizing radiations during quiet conditions comprise cosmic

Lyman a and X-ray radiation. The cosmic radiation, q^ , for

qj, ~ 38 cos~^ 6, (1.8)

where q^ is the rate of ionization production in ion pairs per cm per

second per atmosphere pressure and 6 is the geomagnetic latitude, is

N N.

q,(h, 6) ~q„

^ -38 cos"* 6-^-38 co N

N N. 2. 55(10^^) —Ys\ , cm sec"-*-

(1.9)

where q^ is the rate of ionization production due to cosmic rays at a height, h; tV h is the total number density at height, h; iV^g is the number

density at height, h=:0. An annual variation for cosmic radiation exists

[Arnold and Pierce, 1963];

q, = 1. 5(10-^^) N^ cos"" e [1 - 22 (Y - 1964)]

(1964 ^ Y ^ 1967)

q„ = 1. 5(10-^^) N^ cos-* e [A_ + A. (Y - 1968)_

(1968 ^ Y < 1976),

where Y denotes the Gregorian calendar year,

a

(1.10)

(1.11)

The Lyman a radiation, qj^ , for

a

h = I exp sec X

:l. 2 J

(1.12)

where I is the incident flux of Lyman a equal to 3(10 ) photos cm

sec"''' and I^ is the flux at any height, h; and Pis the atmospheric

pressure at a height, h, in microbars, is

qS^ = Y^;n,{\), (1.13)

a . where q^^ is the production ionization at a height, h; Qj is the ionization

cross "section of the constituent, j; and -^^ is the number density of the

constituent, j. The dominant ionization from Lyman a in the ionosphere

is due primarily to Nitric Oxide, NO, according to Arnold and Pierce

[1963]. There is also an annual variation for Lyman a radiation given

by the factors:

-4-
qh = i [4 + (Y - 1964)] (1964 < Y < 1968)

qh = rt [14 - (Y - 1968)] (1968 ^ Y ^ 1975)

(1.14)

(1.15)

The ionization production due to X-rays is

qj; = 1. 8 (10^°) I^^ M, p, exp (- ^- ;"^^/P^

(1.16)

where q^ is the rate of ion production at height, h, [1^ is the mass

absorption coefficient; p^ is the mass density at a height, h; P^ is the

atraospheric pressure at a height, h; and I" is the incident flux. For,

0. 6 A < X < 20 A, \1^ = (3. 1) X

2 . 8 (1.17)

\ < 0. 25 A, \A^ = (0. 36) \

• 38

(1.18)

The rate of ion production represented by the incident flux is determined by a co'mplicated calculation involving a summation over all wavelengths. However, a reasonable approximation can be made by splitting

the flux into different "wavelength ranges. X-ray radiation also has an

annual variation given by:

l' (X) r 999 "1 lli^) = -^ [1 + -^ (Y - 1964) J (1964 ^ Y ^ 1968)

(X<8A),

f {X) = 7000 7000-999(Y-1968) (1968 ^ Y ^ 1975)

(1.19)

lU^)

l'oo(^) = lis [^ + 33 (Y - 1964)] (1964 ^ Y ^ 1968)

i^.(M=4^'^

{X> 8A),

315

315 - 4(Y - 1964) (1968 ^ Y ^ 1975),

(1.20)

where Ig3(X) is the intensity at solar maximui-n.

5-
Additional radiations exist which affect the ionosphere at greater

altitudes. Among these are meteoric ionizations, solar ultraviolet

radiation ionization, soft X-ray radiation ionization, and radiation ioniza^

tion resulting from chemical reactions which have been calculated by

Poppoff and Whitten [l963] and Arnold and Pierce [l963].

The equilibrium conditions for the ambient ionosphere permit

approximations to (1.1) using

dJe dN- dl\[+ ^ , . .

Q - ANe - BN^N^ + (C + D) il^_ ~ (1. 22)

AN - {C + D) N_ - BN_N^ ~ (1. 23)

Q - B^e^H- - BN_N^ ^ Q - B{N^f ^0. (1-24)

Since? B ~ E ~ 2(10""^) and N+ = N^ + N_, and introducing F = C + D,

4

(1.25)

(1.26) 1

(1.27)

•1'- - \bJ Va+ f +VQB J'

N - f^^f /" F + Vqb'

^'^ ~ VBy VA + F + yoB

Figure 1 illustrates theoretical estimates of the electron density

profile of the lower ionosphere during the day, J, and at night, A , according to the Arnold and Pierce [1963] method. The coUisional

detachment coefficient, Dg , has however been reduced by a factor of 20

over the value used by these authors, since higher values at the lower

altitudes do not give correct reflection coefficient for experimental

observations to be discussed below.

Grain [1964] uses B~2(10"^), E~(10"'').
Figure 2 illustrates the ambient daytime noon ionosphere model.

Positive ions, negative ions, and electrons are given. This profile

was deduced from Loran-C measurements of Doherty [1964] between

Cape Fear, North Carolina, and Boulder, Colorado. To produce the

observed attenuation of the first ionospheric wave hop relative to the

groundwave it was found necessary to increase D in (1. 6) by a factor of

approximately 200 and in addition increase the chemionization, q^ ^j

, by

a factor of 100 over those given by Popoff and Whitten [1963] and Arnold

and Pierce [1963]. Apparently, the best estimates of chemionization

production q^^^ and the detachment coefficient do not predict the correct

Loran-C pulse attenuation. It should be noted that the ionospheric wave

is variable with time and geographic location. This would indicate

temporal geographic variations in the profile. The effect of reflection

height in the above mentioned measurement was obtained from measurements of the first ionospheric wave delay and theoretically from a study

of the transmission coefficient Uj, [see (3. 2)] into the ionosphere. Thus,

the transmission coefficient, figure 20 for example, exhibits a sharp

break at approximately 23-24 km above the bottom of the ionosphere.

This resolves the effective reflection height within a very few kilometers

so that the remaining variable, the precise shape of the profile can be

resolved at this point. Figure 3 illustrates a profile predicted by the

theory at another geographic location. Figure 4 illustrates a possible

nighttime profile. Figure 5 illustrates a daytime profile similar to

figure 3 except the detachment coefficient has been increased by a factor

of 50, and the chemionization q^ jj is as given by Popoff and Whitten

[1963] and Arnold and Pierce [1963].

1. 2. Ionization Introduced by Nuclear Detonations

Abnormal ionization of the atmosphere follows nuclear detonations

as a consequence of beta and gamma radiation arising from the decay of

fission fragments in the atmosphere as a function of time after detonation.

A model for such an abnorraal ionosphere has been investigated by Crain

[1964] and Crain and Booker [l963, 1964], There are ionization peaks at

30 km as a result of gamma rays and at 65 km as a result of beta rays

if the debris from the detonation is above 80-90 km. Crain [l964]

estimates maximum production rates for fission debris Q^, of 10°, 10" , 10"^ depending upon fission yield, time, and distance from detonation.

Thus,

Q. = ^Hfl^.f' ^^^^^"/^^^' (1-28)

7-
where Fy is the fission yield in megatons, R^j^ is the distance from

detonation and t is the tinn^e elapsed. Production rates for the ambient

ionosphere can be estimates by an approximate formula, using cosmic

rays only:

Q = Qo f(z),

where f(z) is the ARDC norraalized model atmospheric nnass density,

[Minzner, Champion, and Pond, 1959], and Qq is 50 for a typical

Poambient low geomagnetic latitude. In the nuclear model ionosphere,

Qq ~ 10* to 1 . Figures 6 and 7 illustrate models developed by Grain

[1964]. Here, the conductivity parameter has been introduced

Vin

where v is the collision frequency. It should be noted that the conductivity, a, of an isotropic electron or ion plasma, using nunnber density,

N; mass, m; angular frequency, O), can be written

a = m(v+iUJ)

In the lower atmosphere, V > uu, at LF, or

Ne^ N

mv vm

In these models, the ions are assumed to be O2 . Based on these models.

Grain and Booker [1964] made estimates of the effect of the ions on

oblique ionospheric wave transmissions. It is of interest to note in

these models, figures 6 and 7, the conductivity, Q^ for the ions can be

greater than the conductivity for the electrons and in most cases of

interest certainly not completely negligible. Thus, for example, at

30 km, for a production rate per atmosphere of 10® —^ ~ 2. 6(10^°)

whereas for the electrons —|- ~ 10 ^ for the daytime model, figure 6. An extensive computer program has been developed by McKee and

Kostigen [1964] which can give electron, positive ion, and negative ion

profiles, provided the tinne after detonation, yield of weapon, height of

detonation, time of day, and distance from detonation are specified^

figures 8, 9, and 10 illustrate computations performed with the aid of

this computer program.

-8-
2. Propagation Effects of Heavy Ions

Ordinarily, a theory of propagation of radio waves involves electron plasmas and ion plasmas in the ionosphere in the form of profiles

N^(h.), iV^j(h), V(h) which exist as a consequence of natural phenomena.

Under natural conditions the effect of ions, N^ (h) is small and indeed is

usually neglected. In a previous paper [Johler, 1963] the effects of

heavy ions were not included. Johler and Berry [l962] have presented

an analytical procedure for taking these ions into account. Thus, the ion

gyro resonance is < 50 cycles per second, except for the hydrogen

nucleus which is ~ 800 cycles per second. In the case of a nuclear

environment in which fission and other radioactive debris is found in

large quantities in the upper atmosphere, the natural ionosphere model

is no longer appropriate for propagation of ionospheric waves. The effect

of heavy ions, in fact, is no longer a small effect. In fact, under certain

conditions these ions can exhibit a dominant role in the propagation.

The effect of the heavy ions, i. e. , the effect other than the collisions with electrons, cannot in general be neglected at extra low and

ultra low radiofrequencie s. The mathematical formulation of such a problem has been presented in a general manner by Ginzburg [I960],

for example, but considerable elaboration as to detail is required to

reduce the equations to practical computation. The mathematical

technique which has been employed on the IBM 7090 computer is therefore discussed here in some detail following Johler and Berry [1962].

The number of positive ions, il/+ , the number of negative ions, N_,

in addition to the number of electrons, N = N^ , are to be considered.

The convection current components are

Jx " - ^e V, = - e IN, VI - N^Vl + #_V1] = J^ + J^ + j;

Jy = - il^e Vy = - e [N^Vl - N^Vl + N_V^_^ = J^ + Jy + j; '

J, . - NeV, = - e [N,V\ - N^ VI +7l^_Vl] = J^ + J^ + J,". (2.1)

In the classical magneto -ionic theory collision frequency types, v can be described in connection with certain constant, C^ , Cg , C3, . . . , (see for example, Pfister [1955]),

Cr-= >'<•, "(II nic+mo

C,="e.-

ninie + "'-

Cz = 1", m+

•+ .., _L..., .

' ^^ =''^''' ;;^;+^o'

^'-''-•'' ;^^r+^o' ^"-''"•- mo + m-

" +• 7)i+ + m^ ^ + »i- + m+ "-^

?)7„ + m+

' ^»=''--

r7i7+7»;' ^'=''--' »r+^; ^^-''"' ^^^?^: (2. 2)

-9-
where Vg , q ^^ ^^^ electron -neutral molecule average collision frequency

Vg , _ is an electron-negative average collision frequency, etc. , where

the average differential velocity of like particles is assumed to be zero,

and mo , mg , m+ , and m_ are the masses of the neutral molecules,

electrons, positive and negative ions, respectively. The components of

the Langevin equation can then be written, [Johler and Berry, 1962] for

purposes of developing a practical computation form,

'""^^-+^^^+5^^" ^^ -"^e.^My ]+(c,+a+a)v,,,-c,Vo..-av_.,-av^,,^o

'"^^-+^^^+Sf^-^ ^x -Ve.K ]+(c,+a+a)v,,,-av,.„-av^,,-c,v+,,=o

'""^-^+i^^+^f^-^ ^V -Ve.y K ]+(c^+Cr^a)v,,,~c,Vo,.-av_,,-Qv^,,=o

'"^+-+^^^+^f^+- ^f^ -"^"+..H, ]+(c.+a-\-a)v^,,~c,Vo,.~av.,,-av„,=o

^'*'^+-+^'^^+^f^+- My -v+.v:^^ ]+{c,+c,+Ce)v^,,~c,Vo..-c,v_,,-av,,,=o

(ao+a.+a,)Fo.,-GoF_.,-aiF+.,-6'„F,,=o

(Cio+Cn +Cu)Vo.~C,oV_,~CuV+,~Q,V,,,=0,

where the components of E, and the velocity components of V are designated by the subscripts x, y, and z for plane local coordinate system at

the ionosphere boundary. "j^^ , M and U^ are the components of the

static magnetization.

-10
The simultaneous solution of these (2. 3) with Maxwell's equations

utilizing (2. 1) results in two coupled matrix equations:

an ^12 OlS ai4 an " pr

^21 ^22 ^23 O25 a28 Ey

«31 ^32 ^^33 036 aag J% E.

^41 044 045 046 O47 Jt E.

052 ^54 055 055 O58 Jt + Ey

«63 064 ^65 066 aeg Jt E,

an 074 O77 O78 O79 J-. E.

082 085 087 ^88 089 J-y Ey

.0 093 3 Oge O97 Ogg Ogg. JA [.E^_

and

6n 612 613 ~ -^x" ~C(Ji+j^+j:)-\

621 622 023 • ^. + C(Ji+j:+j-) ==0,

L^ai ^32 633 _ -eA .C{Jl+Jt +J;)_

where C = - l/i(Jueo» and

=

(2.4)

(2.5)

m,

a-i 1 - a2 2 - aga - ~^j" c---i.^^e")

3-1 2 - ~ a-

^la - a 31 -

_ Mo ^

z^-

^2 3-= - a32 = —if^ = 0, if Jt is in the yz -plane

'•14-3-2 5 = a -m

= " ^ ^^tG^^= + E

Ci Ci 1

10 )

ai7 = a23 = agg = ^

(^c^ + -^^^

^c

a.. =a32-a33=f^(Ce.%^)

11
3-44 = 3.55 = age - —^

^45 ~ "^5 4 ei7+

46 - - as 4 - _^J_^

^56 - ^6 5 _ l^o_^^ X - 0, if X is in the yz -plane

a^-? — acQ — 3-

eii/ +

58 - -59 - g2j_ ^-5 -r 47 ^^

10

^71 - 3-82 - a.93 - 2ji^

_ -m

an-74/I —- ao"^85= =~ a^^96 - T2

^0

i^.

_ _ _ m„ /* . y, C 7 Cio

'S, 3-7 7 - 3-8 8 - ^gg - 2^1^ ( - lUJ - 2.7 + )

Mo ^z a^s - a87 - _^^_

79 - - ag7 - ^^_

agg = - ag8 = —^ir*- = 0, if W is in the yz plane

where the Cj are defined in (2. 2) and 2j = C^ + Cj + i + Cj + g,

623=— az.f

12
b33=aT'^ +aTaL~l.

The two equations (2, 4) and (2. 5) are equivalent to the single equation,

Oil 012 ^13 an an 1

021 O22 ^23 025 028 1

Osi ^32 «33 ^36 039 1

041 an 045 «4o 047 1

«62 aoi 055 056 058 1

063 a^ 065 066 069 1

an au 077 078 079 1

082 085 Og? Ost Ogg 1

093 096 O97 Ogg O99 1

V c c 611 bi2 ^13 c c c ^21 &22 623 c c c 631 632 ^33

Jl

Jt

J\

Jy

J-y

Jl

Ey

E.A

(2.6)

The 12X12 matrix (2. 6), and the vector submatrices can be divided into

block matrices as indicated by the dashed line;

Then

and

"M9X9 jV9X3 "9X1

.^3X9 V3X3_ _-^3Xl_

M.J+N.K=0.

PJ+Q-K=(3.

=0. (2.7)

(2.8)

(2.9)

Then,

If M" exists, multiply (2. 8) by P- M~^ and subtract from (2. 9)

Q-K-P.M-'.N-K=(Q-P.M~^.N).K=0.

(2.10)

13
But,

Q-

'bn bi2 6i3

O21 O22 O23

.O31 O32 633-

,nndKE,

and P- M~ • N can be computed numerically [johler and Harper, 1962;

J ohler and Walters, I960], Thus (Q - P- M"^ • N) can be written as a matrix involving the complex number, C,. (Q - P- M"''^ • N)' K = has a nontrivial solution if, and only if, |Q - P* M""""- N | = 0. This yields a

polynominal in C which can be solved to find C [Johler and Walters,

i960]. These results depend on the existence of M"""" where M is the

original 9x9 matrix, (2. 4). If E exists, the nonexistence of M"""" would

imply that (2.4) has no unique solution.

Writing,

and letting

^n —«ii ^12 —«i2

O21 —a2i 622 —"22

^31 —«31 632 —Q;32

= —aLdr —Q!i2 d=—ai3

e = —arCiL —«2i

/ =(It — 1 —a22

^13 —«13

^23 —«23

^33 —«33

Q-PM-'N -0, (2.11)

then (2, 11) becomes

g=—aL

h = —a23

j = —a3i

k'=aifiT—0:32

I =aT^-\-aT(iL — 1 ~oizz, (2.12)

f'+o b c^+d

^ f+/ gnh

i^+j k I t{l-ic) + ^i-cj-id-kg) + ^\la+lf+bgi-fic-jd-kh) +nbhi

+bjg+ekc-fcj-idf-kag) + {ajl +bhj+ekd-jjd-kha-lbe)

,

f'+a b ct+d

^ f+J g^+h

ii+J k I

or.

-O4r'+a3r'+02f'+oir+«o

(2,13)

(2. 14)

where,

a3=aTa3i~aTai3-\~kaL

a2=la+lj'-\-baLaT~aT'^—a\3ai^^ka23 oJ = ba Ta.21 + baipi.^^ —eka r ~jaraa, —jatol^^ kaa^

(^O=ojl +ba23a3^—eka^3—j'a3^ai3 +kaa23—lbe. (2.15)

14-
The solution is now in the form presented previously by Johler and

Harper [l962], i, e, , the reflection and transraission coefficients, T and

U, at the lower ionosphere can now be calculated.

The index of refraction is found frora,

rf = Q^ + sin^ Cpi

where cp^ is the angle of incidence of the wave on the plasma, and

h=-^^

Also,

hL = - h sin I

hr = h cos I a = sin CPi

UO^ - N e^ I ZQTa, the plasma frequency squared

aL = sin cpj cos cp^

at = sin cpi sin cp^

(JUj^ = jige K/m, the gyro frequency

1 Sn = —5

and cpn is the magnetic azimuth reckoned clockwise from magnetic north,

I is the magnetic dip reckoned from the horizontal, |J,o a-nd Cq the

permeability and permittivity of space, \Xq = 4tt(10~ ), e is the electronic

charge, and me , m+ , m_, and mo are the electron, positive ion, negative

ion, and neutral mass, respectively.

The various collision frequencies V+ ^ , Vo+, "^-o' ^o -> • • • °^ ^^ general V^ j represent the average number of times an i-th type particle

collides with j type particles in one second. Assuming the positive ions

are NO"*" and the negative ions are O2 and the collision cross section for

collisions between i-th and j -th type particles is TTQ^ , where [McKee,

1964; see also Ginzburg, I960, p. 78 et seq. ]

a+p = a^+ =G_^ =Oo- = cro2N2 = 3. 45(10"^) cm,

-15-
then,

v+, = 3. 9(10^M P /t, (2.16)

VoH. = 1. 9(10-"M (1 + ^') ^e VtT (2. 17)

v_o = 3.7(10^M P ^/T, (2.18)

v,_ = 1. 86(10-^^) \V, VT (2.19)

V^._ . 2.16(10-^) \'il^e T-^Ln ^^-^^^-^^-^^ , (2.20)

[(l+2\)i^e] 3

V ^. = 2. 16(10"^) (l+\VeT"^Ln ^'^^^^

^ ^

^^ , (2.21)

[(l+2\Ve] 3

V,+ = 3. 62 (l+\) #„ T"^Ln ^-^ ^^^""^ J , (2.22)

N

V,- = (i;)-- = (-n-x')^-' '^•")

V,. .3.62 x'y,T"^ Ln

^•^('°°)T

_ (2.24)

^

v., =(y^)v,.=(i^)v.., (2.25)

v,„ = 1.6(10^M (I;). <2-26)

v„=1.6(10")(|^)(^) = (^)v.„. ,2.27)

where T is the temperature, °K, p is the mass density of neutral particles

(grams/cm^), \' - N_/N^, N.+ = N t, + N - = {I + A.') #o is the positive ion

concentration (cm~^), P is the pressure at the atmospheric height and

temperature concerned, and P^ is the pressure at ground level and

ambient temperature.

-16-
Equations (2. 1 6) to (2. 27) represent twelve possible collision

frequencies Vj ,

, i 7^ j. The following inequalities or approximations

can be noted:

Vo - « V+ - v„+ « v_+

for the height range 40 to 100 km, and assuming ambient conditions

illustrated in figures 1 and 2. Of course, these values change in the

case of disturbed or nuclear ionosphere, with the number densities such

that these approximations are no longer valid. In the ambient environment the neutral particle, Nq, are very much greater than any of the

other constituents near the surface of the earth to considerable height

(see Minzner, Champion, and Pond [1959]).

It is of interest to note that the velocities in the equations of motion

(2. 3) for each of the gas constituent are coupled by collisions. The ion

velocities in each equation of motion are also coupled by the charge, e, to Maxwell's equations. If the collision coupling is negligible, the

velocity equations of the ions are no longer coupled to the equations

representing neutral particles of the gas. Then, only neutral collisions

have an effect on the ion velocities. Thus, for example, only the 3x3

diagonal submatricies exist to the left and above dotted line in (2. 6).

This can be interpreted to mean that the velocity differentials between

gas constituents are negligible. Although this results in considerable

simplification of the analysis, the rigorous solution (2. 6) was retained

since the numerical significance for the collision coupling was indeed

established for this analysis. This was accomplished by comparing

numerical solutions of the reflection coefficient with and without collision coupling. Changes were noted in the first significant figure of the

LF-VLF reflection coefficient as a result of this comparison.

Some simplification can also be obtained by dropping the Lorentz

term j^Qe (V X M) in the case of the ions for f ^ fn where for the ions

fn < 100 c/s. To keep the analysis procedure general, however, the

Lorentz terms were retained. In fact, some interesting phenonnena

occur as the reflection process switches between the almost isotropic

ions and the anisotropic electrons during the progress of a wave in the

17-
gas mixture (figures 42, 43, and 44). Thus, the ions reflect at LF and

VLF as an isotropic plasma whereas the reflections from the electrons

produce an abnormal component resulting from anisotropy. Hence,

production rates, Qq = 10^, cause reflection from ions and zero

abnormal component T^^, T^^ ^ . On the other hand, reflections from

models with Qq =10^ cause reflections from anisotropic electrons with

absorption from the ions resulting frora attenuation of the waves in the

plasma,

3. Propagation in a Nuclear Environment

To illustrate the propagation of LF, VLF, ELF waves in a nuclear

environment, reflection coefficients were computed for the mixed ionelectron ionosphere models, shown in figure 6, as a function of frequency. These reflection coefficients were then used as input to the

wave hop (time mode) propagation program described in the previous

paper [Berry, 1964]. As a first approximation, the bottom of the ionosphere model was chosen as the reflection height. Figures 11, 12, and

13 show the propagation characteristics of the ground wave and various

hops as a function of frequency at a distance of 1609 km (1000 miles).

These curves can be compared directly with those for an ambient day

shown in figure 45 at 100 kc/s as a function of distance by Johler [1963].

The most significant differences are the decreased magnitude at all

frequencies, and the change in crest of the curves as a function of frequency.

The models shown in figure 6 and 7 start at much lower heights

than ambient day, and much of the effect mentioned above might be due

to this difference. It was also conjectured that the wave might travel a considerable distance into the model, losing energy by absorption,

before reflection. Such a change in reflection height would change the

characteristics of propagation versus distance, and would, probably be

frequency dependent. To clarify these points, propagation of waves into a stratified plasma was investigated.

The computer program used to calculate the reflection coefficient

for a wave incident on a stratified, anisotropic ionosphere [Johler and

Harper, 1962] can also provide information on the progress of the wave

into the ionosphere, in the form of a transmission coefficient. Let cp^ be the angle between the vertical plane containing the earth's magnetic

field vector and the direction of the incident ray and let cp^ be the angle

of incidence on the ionosphere. Let Ey , j be the normal component of

the incident electric field in the plane of incidence ("vertical polarization") and let E^^ , ^ be the component perpendicular to the plane of

-18-
incidence ("horizontal polarization"). Let Ey , ^ and E^ , ^ be the corresponding upgoing waves inside the ionosphere and Ey , ^ and E^ , ^ be the

,3 -^x ' u ^„ J Ey , downgoing waves. Then the ratios'^

^

and ^ ' " show the propagation of the waves into the ionosphere. In the Johler and Harper [1962]

formulation the quantity

Ue ~ f^^ COS cpi cos cp, (3. 1)

y ' u This is an equality for an isotropic plasma, in an anisotropic plasma

there are additional small terms caused by the anisotropy. Similarly,

U„ ~ |t^ sin cp, (3. 2)

Thus, the transraission of a vertically polarized wave into the

ionosphere can be conveniently studied when cpj^ = 0, while cpj^ = 270°,

90° is best for the horizontally polarized wave. Figures 14 through 20

show |Ue I and | Uj, | for both upgoing and downgoing waves as a function

of distance into the ionosphere. The J profile, figure 1, is the model,

cpj^ = 270° and cpj^ = 80°. Figure 14 is for a frequency of 1 kc/s, and the

succeeding figures for 2, 5, 10, 20, 50, and 100 kc/s. In figure 21

l^m' u I ~ -^ j^st inside the ionosphere (z ~ 0) shows that virtually no

energy has yet been reflected. The gradual decline of | U^ , „ | with

height shows that the wave is being partially reflected at each boundary,

so there does not seem to be a "reflection height". In the 10 kc/s case,

figure 17, \\J^ ,y | ~ 1 for 20 km into the ionosphere, then drops sharply

in the next few kilometers, defining a reasonably sharp reflection height.

The drop is even more pronounced at 100 kc/s, figure 20.

The same frequencies are shown for a more grazing angle of

incidence, cp^ ~ 83°, in figures 21 through 27. As expected, the wave

does not penetrate as far into the ionosphere, and at the lower frequencies,

the reflection height is not so well defined (see figures 16 and 23).

The penetration of the vertically polarized wave is illustrated in

figures 28 through 34 for cpj = 80". In these | Ug , ^ | ~ cos cp^ at the

bottom of the ionosphere. In figure 29, |Ug,y | grows slightly as the

wave progresses into the ionosphere due to addition of abnormal components coupled in by the magnetic field. There is a region of strong

coupling near z - 23 km, where |Ue , „ | peaks, and then drops rapidly.

St, Y . . . refer to transformed coordinate systems [Johler and Harper,

1962].

-19
The effect of the abnormal components decreases with increasing

frequency, and occurs at greater heights, figure 30 through 35. No

abnormal components are seen in | U^ , ^ | at 100 kc/s, figure 34, probably because the "wave is reflected before it reaches the region of strong

coupling. In figures 35 through 41 the angle of incidence is increased to

83°.

Grain and Booker [1964] employed an approximate formula to

determine the effective height of the ionosphere and the height at which

the principal contributions to reflection occur. This can be written,

= 2 cos cp^ e ^e(h) IV a \j.i. I ^ l^lh) J. >

.

eoUO L mg Vg nij Vj J

This formula in figure 27 gives a reflection height at 64. 5 km or 24. 5

kra within the ionosphere model (J -profile) 100 kc/s. This is just

beyond the point at which the attenuation of the upgoing wave Ug increases

rapidly. This subject, however, requires further study, since the

selection of the principal point of reflection does affect the propagation

in the guide below the ionosphere. Wait and Walters [l963] and Wait

[l965] have investigated this subject and conclude that the precise

principal point of reflection is not always clear. Indeed, it should be

noted that in general some reflection occrus all the way up the profile

until the field vanishes. Two regions of principal reflection can apparently occur as indicated in figures 42 and 43 in the case of a gas mixture.

In these examples, however, the effect of one such region cominates the

other.

For the J profile, then, frequencies rom 5 kc/s to 100 kc/s penetrate twenty or more kilometers into the ionosphere before being

reflected. In this range, the reflection height varies only a few kilometers with frequency. For field strength calculations, a reflection height

of about 65 km would be more realistic than 40 km, the height to the

bottom of the ionosphere model.

The conclusion above prompted investigation of the penetration of

waves into the mixed ion-electron plasmas shown in figure 6. The

Loran-C frequency, 100 kc/s, and an 82° angles of incidence were used.

The reflection height, h , was defined as the height at which the upgoing

wave was 10 db below the incident wave. For the normalized production

rate Qo =10* (figure 42). This occurred at z ~ 22 km, or a reflection

height of 58 km. For Q^ =10® (figure 43) the wave decreases gradually

with height so that no "natural" reflection height is apparent, but by the

definition above, h ' ~ 42 km. For Q^ =10^, h ' ~ 24 km (figure 44).

20-
Using these reflection heights, the propagation of a 100 kc/s wave

was computed as a function of distance. The propagation for an ainbient

day is shown first, in figure 45 [Berry, 1964], for comparison. The

reflection coefficients were modeled for a single plasma slab which

gives approximately the same attenuation at 100 kc/s as the exact

solution (multiple slabs) for the J -profile given in figure 1. The amplitude of the total field, the ground wave, and the first three hops are

shown. The vertical mark on each hop shows the location of its caustic,

or geometric -optic cut-off point. It is apparent that each hop diffracts

into its shadow zone, and remains dominant far beyond its geometric

optic cut-off point. The relative minimum in the second hop near 3200

km is caused by the pseudo -Brewster angle in the ground reflection

coefficient [Berry, 1964]. This does not occur in the first hop, since

it is not reflected from the ground; and the minimum is sharper in the

third hop, which is reflected twice. The pseudo -Brewster angle effect

is very small for propagation over sea water.

Figure 46 shows the propagation in a nuclear environment for

Qg = 10*, with effective reflection height, h =58 km. Comparison with

figure 11 shows the effect of the greater reflection height. Similarly,

figure 47, for Q^, =10®, and figure 48, for Q^, = 10^, can be compared

with figures 12 and 13, respectively.

The total field, for Q^ =10* and Q^ =-10®, is 15-20 db below that

calculated for ambient day (figure 45). This shows that the gas mixture

of ions and electrons is absorbing energy from the wave. Since the ion

conductivities are close to or greater than the electron conductivities,

figures 6 and 7, and since the effect of collision coupling discussed

above also has a nuraerical effect on the results it is clear that ions

play a significant role in the propagation of LF and VLF radio waves.

However-, for Qo= lO^, the propagation is almost as good as on an ambient

day. There are now enough ions for a fairly good reflector. In fact,

at 1000 km, the ambient day first hop is smaller than the first hop for

nuclear conditions. The explanation is that at this point, the angle of

incidence for the nuclear case is nearly five degrees greater because of

the much lower reflection height.

4. Conclusions

The ions produced by nuclear detonation debris will, in general,

produce increased attenuation of LF waves. The amount of this attenuation is dependent upon the ion production rate per atmosphere, Q^ , of

the debris. The detail, such as the shift in the peak of the amplitude

curve as a function of frequency is critically dependent on reflection

-21
height assumed for the model. From theoretical studies of the LF field,

as a function of reflection height and available experimental data, a model can be ascertained. However, the bottom of the model and the

point of almost total reflection of the wave are readily ascertained, and,

hence, the amplitude of the ambient and nuclear environment LF field

can be bracketed. It can be concluded that an increased attenuation of

LF wave can be anticipated when such a wave is propagated through the

nuclear environment. A comparison of the LF region (100 kc/s) with

the VLF region (10 kc/s) indicates better propagation at LF in a nuclear

environment. In fact, attenuations in excess of ground wave are possible

for the total field expressed as the sum of the wave hops.

5. Acknowledgments

The authors are indebted to Duane C. Hyovalti and Mary E.

Chrisman for their valuable contribution t® the numerical work reported.

Valuable conversations and discussions with other workers in the subject

area gave the authors considerable advantage in this study. In particular,

the following should be noted: E. T. Pierce, H. R. Arnold, C. M. Grain,

J. R. Wait, A. G. Jean, R. H. Doherty, J. McKee, T. Kostigen, and

G. R. Underhill. However, these individuals should in no way be held

responsible for any shortcomings in this technical note. Also, the work

performed in a companion project (NBS Project 5100441 initiated under

DASA RA-2 938/04, 067 dated February 27, 1964) supported by the

Defense Atomic Support Agency had a technical effect on the course of

this work.

This research was supported by the Advanced Research Projects

Agency, Nuclear Test Detection Office, and was monitored by

Major Hillman Dickinson, Contract No. 183, Amendment No. 13,

Task IV.

-22-
6. References

Archer, D. H. (1963), Reaction rate coefficients for ambient and heated

air, DASA 1437 RM 63 TEMP-45 (G. E. Tempo, Santa Barbara,

California).

Arnold, H. R. (1964), Comraents on a paper "Collisional detachment and

the formation of an ionosphere" by E. T. Pierce, Radio Sci,

J. Res, NBS/USNC-URSI 68D , No. 2, 215-217.

Arnold, H. R. , and E. T. Pierce (1963), The ionosphere below 100 km

(D-region), A simple model. Research Memorand\im 11 (Stanford

Research Institute, Menlo Park, California).

Berry, L. A. (Dec. 1964), Wave hop theory of long distance propagation of low frequency radio waves. Radio Sci. J. Res. NBS/USNCURSI 68p, No. 12.

Chapman, S. (1931), The absorbing and dissociative or ionizing effect

of monochromatic radiation in an atmosphere on a rotating earth,

Proc, Phys. Soc. 42, p. 26 (London).

Crain, C. M. (1961), Ionization loss rates below 90 km, J. Geophys,

Res. 66, No. 4, 117-1126.

Crain, C. M. (Nov. 1964), A note on persisting radio propagation effects

after high-altitude nuclear bursts, J. Geophys. Res. 66, No. 21,

4-117.

Crain, C. M. , and H. G. Booker (Apr. 1963), The effect of nuclear

bursts in space on the propagation of HF radio waves between

separated earth terminals, J. Geophys. Res.

Crain, C. M. , and H. G. Booker (Nov. 1964), The effect of ions on LF

and VLF propagation in an abnormally ionized atmosphere,

J. Geophys. Res. 69, No. 21, 4713-4716.

Doherty, R. H. (1964), Private communication on Loran-C measurements.

Ginzburg, V. L. (I960), Propagation of electromagnetic waves in

plasmas (Gordon and Breach, Inc. , New York, N. Y. ).

23
Hirsh, M. N. , P. N. Eisner, and J. A. Selvin (1 964), An experimental

investigation of the effects of radiation on the propagation of EM

signals, Annual Technical Report R-P73-4 (The G. C, Demg

Corp. , New York, N. Y. ).

Johler, J. R. (Sept. -Oct. 1963), Radio pulse propagation by a reflection

process at the lower ionosphere, J. Res. NBS 67D, No. 5, 481-499.

Johler, J. R. , and L. A. Berry (1962), Propagation of terrestrial radio

wave of long wavelength--theory of zonal harmonics, J. Res, NBS

66D , No. 6, 737-773.

Johler, J. R. , and J. D. Harper, Jr. (Jan. -Feb. 1962), Reflection and

transmission of radio waves at a continuously stratified plasma

with arbitrary magnetic induction, J. Res. NBS 66D (Radio Prop. ), No. 1, 81-99.

Johler, J. R. , and L. C. Walters (I960), On the theory of reflection of

low- and very low-radiofrequency waves from the ionosphere,

J. Res. NBS 64D (Radio Prop. ), No. 3, 269-285.

LeLevier, R. E. (Feb. 1964), Determination of the D-layer dissociative

recombination coefficient from a high -altitude nuclear explosion,

J. Geophys. Res. 69, No. 3, 481-485.

McKee, J. (1964), (G. E. Terapo), Private comrauniration.

McKee, J. , and T. Kostigen (1964), Computer program (G. E. Tenapo),

Private communication,

Minzner, R. A., K. A. W, Champion, and H. L. Pond (Aug, 1959), The

ARDC model atmosphere 1959, Air Force Surveys in Geophysics

No. 115, ARCRC, Bedford, Massachusetts,

Minzner, R, A. , and W. S. Ripley (1956), The ARDC model atmosphere

1956, ASTIA Document 110233,

Minzner, R. A. , W. S. Ripley, and T. P. Condron (1958), U. S. extension to the ICAO standard atmosphere tables and data to 300

standard geopotential kilometers (Geophys. Res. Directorate and

U. S. Weather Bureau, Washington, D. C. ).

Moler, W. F. (I960), VLF propagation effects of a D-region layer produced by cosraic rays, J. Geophys. Res. 65, No. 4, 1459-1468,

24-
Nicolet, M. , and A. C. Aikin (May I960), The formation of the D-region

of the ionosphere, J. Geophys. Res. 65, No. 5, 1469-1483,

Pfister, W. (1955), Conf. on Physics of the Ionosphere, Cambridge,

1954 (London, Physical Society) p. 394.

Pierce, E. T. (1963), Collisional detachment and the formation of an

ionospheric C-region, J. Res. NBS 67D (Radio Prop. ), No. 5,

525-532.

Pierce, E. T. , and H. R. Arnold (Oct. 1962), Sudden ionospheric

disturbances and the propagation of VLF radio waves, SRI Report

No. 3684.

Poppoff, B. , and R. C. Whitten (1963), Ionization and deionization in

the lower ionosphere, SRI Project 3624, Final Report.

Thrane, E. (1962), Private comraunication via R. H. Doherty.

Wait, J. R. , and L. C. Walters (1963), Reflection of VLF radio waves

from an inhomogeneous ionosphere, J. Res. NBS 67D (Radio

Prop.), Pt. I, No. 3, 261-367; Pt. II, No. 5, 519^^3; Pt. Ill,

No. 6, 747-752.

Wait, J. R. (1965), Concerning the mechanism of reflecti'^n of EM

waves from an inhomogeneous lossy plasma. To be published in

Radio Sci. J. Res.

• 25-
N(h) PROFILE

95

1 1 1 Mill 1 1 1 Mill 1 1 1 Mill 1 1 1 Mill 1 1 1 Mill

90

85 —

80

y h — ^^^'^^ THRAIME ll-l2/^/j -

75 y //

E 70 t

/ / "

X

liJ X 65

- Jj

^

^

60

55 —

( /\/ —

50 — /

—

45

~ 1 1 L

1 A' AND J /tHRANE 11-12

)^\\\ 1 1 1 Mini 1

E. T. PIERCE THEORETICAL "

EXPERIMENTAL HIGH LATITUDE

1 1 mill 1 1 1 Mill 1 1 1 iiiTT

10 10^ 10^ 10" 10=

N, e/cm^

Figure 1, Typical profiles. Thrane 11 -IZ and J are for daytime, A is a night profile.

-26-
ino

+o

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'®oo«

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-28-
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10 32

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10 20 30 40 50 60 70 80

HEIGHT, km

Figure 6. Daytime nuclear profiles (after Grain).

-31
30 40 50 60 70

HEIGHT, km

90

Figure 7. Nighttime nuclear profiles (after Grain).

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Figure 9. Daytime nuclear profiles of positive ion density for various

distances.

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10-K)0.

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50

LEGEND

ooo Ue UPGOING ooo Ug DOWNGOING

Dne Urn UPGOING ^^^ Uj^DOWNGOING

Figure 14. Penetration of horizontally polarized wave into model

ionosphere, 0^ = 270°, 0i = 80°, f = 1 kc/s, h = 40 km,

J profile.

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10+00,

A

10,-01..

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Figure 15, Penetration of horizontally polarized wave into model

ionosphere, 0» = 270", 0^ = 80°, i = 2 kc/s, h = 40 km,

J profile.

40-
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50

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Figure 16. Penetration of horizontally polarized wave into model

ionosphere, 0, = 270°, 0^ =80°, f = 5 kc/s, h = 40 km,

J profile.

41
0-K)0.

,0-01..

UJo

Q.<

10-02..

10-03,

niJ HHHHyHHmHB aannws^QQ,

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10 20 30

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o o

40 50

LEGEND

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Figure 17. Penetration of horizontally polarized wave into model

ionosphere, 0. = 270°, 0^ = 80°, f = 10 kc/s, h = 40 km,

J profile

-42
10,+00.

10-01..

Uio

Q.<

10^2..

10-03.

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§^

50

Figure 18.

LEGEND

^o Ue UPGOING ooo Ug DOWNGOING

Um UPGOING ^^^ U ^i DOWNGOING

Penetration of horizontally polarized wave into model

ionosphere, 0, = 270°, 0, = 80°, f = 20 kc/s. h = 40 km,

J profile.

-43
|Q-t-UU. ^K)0.J I

10^'-

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3

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10-03L

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40

I

4

50

LEGEND

Ue DOWNGOING

U m DOWNGO ING

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Figure 19. Penetration of horizontally polarized wave into model

ionosphere, 0^ = 270°, 0^ = 80°, f = 50 kc/s, h = 40 km,

J profile.

-44-
IO-K)0

UJo

3

I20 30

IN K I LOMETERS

50

LEGEND

o Ue UP GOING Q Um U PGO I N6oo o Ue DOWNGO I NG

^ ^ * Um DOWNGO I NG

Figure 20. Penetration of horizontally polarized wave into model

ionosphere, 0. = 270°, 0^ =80°, f = 100 kc/s, h = 40 km,

J profile.

45
10+00,

10-01..

UJo

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10-03.

10 20 30 40

Z IN KILOMETERS

LEGEND

o Ue UPGOING ooo

QB UmUPGOING ^^^

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m DOWN GOING

Figure 21 . Penetration of horizontally polarized wave into model

ionosphere, 0. = 270°, 0^ =83°, f = 1 kc/s, h = 40 km,

J profile.

46-
10+00^ TnA B

A ° Q

,0-01..

D

UJo

3

Q.<

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10-02..

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10-03j 1^

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10 30 To

K I LOMET ERS

40

o o o

D

LEGEND

Ue UPGOING

UmUPGOING

o o o AAA

U DOWNGOI NG

U m DOWNGOI NG

Figure 22. Penetration of horizontally polarized wave into model

ionosphere, 0^ = 270°, 0^ =83°, f = 2 kc/s , h = 40 , J profile.

47-
10"'^'-' 1+00

p

ay HnDBygJ

10,-OI..

UJo

3

Q.<

10-^2..

10-03.

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To

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O O Ue UPGOING o o o UmUPGOING aaa

U e DOWNGO ING

U m DOWNGO I NG

Figure 23 . Penetration of horizontally polarized wave into model

ionosphere, 0» = 270°, 0^ = 83°, f = 5 kc/s, h = 40 km,

J profile.

48-
10+00.

10-^'--

a

3

Q.s

<

10,-02..

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UPGOING ooo

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DOWNGO I NG

Figure 24. Penetration of horizontally polarized wave into model

ionosphere, 0, = 270^ 0^ = 83°, f = 10 kc/s, h = 40 km,

J profile.

-49-
I0-K50- i noaaciD HH il^ h u u H q ^ ,

^A-AAaaaaaaa^

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A A

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10-03j

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^

10 20 30 40

Z I N KI LOMETERS

50

O ^ D D

LEGEND

Ue UP GOING ooo

Um UPGOING ^^^

Ue

U

DOWNGO ING

m DOWNGO ING

Figure 25. Penetration of horizontally polarized wave into model

ionosphere, 0, = 270°, 0^ =83°, f = 20 kc/s, h = 40 km,

J profile.

50-
lo-wo.

10-01..

UJo

I0.<

10-02..

10-03.

20

I N

30

K

LOMETERS

50

LEGEND

ooo Ue UPGOING

no Um UPGOING

o o o AAA

U e DOWNGO ING

Um DOWNGO ING

Figure 26. Penetration of horizontally polarized wave into model

ionosphere, 0, = 270°, 0j =83°, f = 50 kc/s, h = 40 km,

J profile.

•51
1

,0+OOj

t^AAAAA^^*i^**"*^***iM^^^^

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a.<

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10-03.

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IN K ILOMETERS

40 5TD

LEGEND

o Ue UPGOING

DQ UmUPGOING

000

AAA

U e D0WN60ING

U rn DOWNGO ING

Figure 27. Penetration of horizontally polarized wave into model

ionosphere, 0. = 270\ 0^ =83°, f = 100 kc/s , h = 40 km,

J profile.

52-
lO+OOj.

o o o ^ ^ o

o o

o o

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10-03..

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50

LEGEND

oo Ue UPGOING

BOS UmUPGOING

©GO

AAA

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D W N G I N G

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Figure 28. Penetration of vertically polarized wave into model

ionosphere, 0^ = 0°, 0i = 80°, f = 1 kc/s, h = 40 km,

J profile.

53-
10">+00.

10-1-0 I..o o o o

o

3

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a.

10-02..

10-03.

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lb 20 30

Z IN KILOMETERS

40 50

LEGEND

o o o Ue UPGOING ©oo Ue DOWNGOING

Uj^UPGOlNG ^^^ U j^ DOWNGOI NG

Figure 29. Penetration of vertically polarized wave into model

ionosphere, 0. = ° , 0^ = 80° , f = 2 kc/s, h = 40 km,

J profile.

-54-
lo-wo

OOOOOOOOO^OOO 0000 000 0^

o

UJa

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10-03.

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°°'^'^/

AAAAAAAAAAAAAAAAAAaAAAAaJP

annD

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fo ZO 35 ?0

Z I N K I LOMETER S

50

LEGEND

o^o Ue UPGOING ©oo Ug D0WN60ING

BOB UmUPGOING ^aa \j^ DOWNGOING

Figure 30. Penetration of vertically polarized wave into model

ionosphere, 0^ = 0°, 0^ = 80°. f = 5 kc/s, h = 40 km,

J profile.

-55-
\0,400,

,Q-O1.OOOOGGGOOOGOOOGOG00OG

UJQ

13

Q.<

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LOMETERS

^

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LEGEND

<>O0 Ue UPGOING oog

Urn UPGOING ^^^

U e DOWNGO ING

Um DOWNGOING

Figure 31. Penetration of vertically polarized wave into model

ionosphere, 0^=0°, 0i = 80", f = 10 kc/s, h = 40 km,

J profile.

-56-
10,400.

10rOI..

UJo

r)

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10-^2..

101-03.

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50

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<> Ug UPGOING ooo Ue DOWNGOING QQ Um UPGOING ^^* Um DOWNGOING

Figure 32, Penetration of vertically polarized wave into model

ionosphere, 0. = ° , 0^ = 80^ f = 20 kc/s, h = 40 km,

J profile.

57-
10,+00,

10,-01..

UJo

ID

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10,-05.^

o

J^"^

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INK ILOMETERS

40 50

000

LEGEND

Ue UPGOING

Um UPGOING

GOO

AAA

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DOWNGO ING

DOWNGOING

Figure 33. Penetration of vertically polarized wave into model

ionosphere, 0^ = 0° , 0^ =80°, f = 50 kc/s, h = 40 km,

J profile.

-58-
10400,

10,-01..

UJo

3

a.<

1 0-02-

10-03.

20 30

Z I N KI LOMETERS

LEGEND

0OO Ue UPGOING

en UraUP GOING

o o o U e DOWNGO I NG

AAA u m DOWNGO ING

Figure 34. Penetration of vertically polarized wave into model

ionosphere, 0, = ° , 0^ = 80°, f = 100 kc/s, h ;: 40 km,

J profile.

-59-
^+00.

10-01..

Ijj o

Q.<

10,-02..

10-03.

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50

LEGEND

ooo Ue UPGOING ©o©

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Figure 35. Penetration of vertically polarized wave into model

ionosphere, 0. = 0\ 0^ = 83°, f = 1 kc/s, h = 40 km,

J profile.

.60-
10,+00,

10-OJ..

UJa

Z2

Q.<

10-0 2--

\01-03.

o o o o o o o

^o

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AAA AAA

A A

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50

LEGEND

o o o e a Ue UPGOING ooo

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Ue

U m

DOWNGO I NG

DOWNGO ING

Figure 36. Penetration of vertically polarized wave into model

ionosphere, 0^ = 0°, 0^ = 83°, f = 2 kc/s, h = 40 km,

J profile.

•61
lo-K^o

lo-oi..

UJa

3

Q.

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10,-02..

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LOMETERS

50

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LEGEND

Ue UPGOING

Um UPGOING

o o o AAA

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Figure 37, Penetration of vertically polarized wave into model

ionosphere, 0^=0", 0i = 83", f = 5 kc/s, h = 40 km,

J profile.

•62
10+00,

lO^I--

UJa

3

Q.<

10-02..

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10 20 30 40

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50

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/•^o Ue UP GOING ©oo

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Figure 38, Penetration of vertically polarized wave into model

ionosphere, 0» = 0°, 0^ = 83*, f = 10 kc/s, h = 40 km,

J profile.

•63-
10+00.

io-o«-

UJa

IQ.<

10,-02..

101-03.

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50

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Figure 39, Penetration of vertically polarized wave into model

ionosphere, 0^ = 0°, 0^ =83% f = 20 kc/s, h = 40 km,

J profile.

64-
,0-K)0,

10" 1..

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Figure 40. Penetration of vertically polarized wave into model

ionosphere, 0, = J profile.

01 =83°, f = 50 kc/s, h = 40 krn,

65-
10+00

10,-01..

IxJ o

10-^2..

10-03,

20

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30

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50

LEGEND

ooo Ue UPGOING ooo

Um UPGOING ^ ^ ^ Ue

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DOWNGO I NG

DOWNQO I NG

Figure 41. Penetration of vertically polarized wave into model

ionosphere, 0^ = \ 0^ = 83°, f = 100 kc/s, h = 40 km,

J profile.

• 66-
IQ+QO.U(-| BB nnBa Bn "^

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40 50

LEGEND

000 UE/COS PHI I INC ana UM INC

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Figure 42. Penetration into nuclear model ionosphere, Qo = 10 , gas mixture, daytime, h = 36 km, f = 100 kc/s, cp^ = 82°,

cpa = 270°.

-67.
10+00. |0«^^'n^

10-01..

Q

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10-02.. A* A

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LOMETERS

To

LEGEND

o o o o o o U E/COS

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PHI I INC UM INC

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Figure 43. Penetration into nuclear model ionosphere, Qo = 10 , gas mixture, daytinne, h = 26 km, f = 100 kc/s, cp^^ = 82°,

Cpa = 27 0°.

-68-
IO+004a

IO-OI--

UJQ

a.<

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20 30

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50

LEGEND

000 UE/COS PHI I INC

000 U E/COS PHI I RET

UM INC

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Figure 44. Penetration into nuclear model ionosphere, Qo - 1 , gas mixture, daytime, h = 12 km, f = 100 kc/s, cp^ =82°,

cp^ = 27 0°.

,69-
o

1

1 1 III 1 1 1 1

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10r7

UJ

IxJ

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3

Q.<

FREQUENCY = 100 kc/S

TYPICAL LAND H' = 58km

MIXED GAS, DAY 00=10^^

TOTAL

Figure 46

2000 2500 3000 3500

DISTANCE IN KILOMETERS

Propagation of 100 kc/s wave overland, Q^ = 10 .

4000 4500

71
10-

trLU

IUJ

en

I-

_J

o

>

UJQ

D

Q.

<

FREQUENCY = 100 kc/S

TYPICAL LAND H

' = 42 km

MIXED GAS, DAY Qq=IO'

TOTAL

1000 1500 2000 2500 3000 3500

DISTANCE IN KILOMETERS

4000 4500

Figure 47. Propagation of 100 kc/s wave overland, Qq = 10

-72-
10"

FREQUENCY = 100 kc/S

TYPICAL LAND H' = 24 km

MIXED GAS, DAY Qo=

10'

TOTAL

2000 2500 3000 3500

DISTANCE IN KILOMETERS

Figure 48, Propagation of 100 kc/s wave overland, Q,

4000 4500

= 10'

-73-
Glossary

A = electron attachraer^" coefficient (1. 1), (1. 2).

A Angstron (1. 18).

B electron-ion recombination coefficient (1. 1), (1. 3).

C photo detachment coefficient (1. 1), (1. 4).

C l/iuUSo

Cj i = 1, Z, 3 . . . collision process parameter (2. 2),

D detachment coefficient (1. 1).

Da associative detachment coefficient (1. 6).

Dc collisional detachment coefficient (1. 5).

E ion-ion recombination coefficient (1. 1), (1. 7).

E electric field in Maxwell's equations (2. 3).

Ea electron affinity, electron-volts (1. 5).

e electronic charge (2. 1 et seq. ).

So permittivity (2. 3).

Tj index of refraction (complex) (2. 14 et seq. ). Y Gregorian calendar year (1. 10).

H magnetic field is Maxwell's equations (2. 3).

H hydrogen (1. 2).

h height above surface or ground (1. 9).

34 fixed magnetic field (2. 3).

I Lyman a incident flux at great height (1. 12), 00

./ I^(x) -00* intensity of solar maximum (1. 19)

I^ x-ray flux at great height (1. 19)

Ijj Lyman a incident flux at any height (1. 12).

I magnetic dip (2. 14 et seq. ). J current in Maxwell's equations (2. 11)

74-
X' = N_/Ne (2. 16 to 2. 27).

X wavelength (1. 17).

m mass (2. 2).

|ijj mass absorption coefficient (1. 17).

|io permeability (2. 3).

N number density (1. 1).

N2 nitrogen (1. 2).

V collision frequency (2, I6 to 2. 27).

il^g number density at surface (1. 9).

71/^h n\imber density at height, h (1. 9).

il/" J number density of j constituent (1. 13).

O2, O oxygen (1. 2).

O3 ozone (1. 4).

(i) angular frequency (2. 3).

U^N angular plasma frequency squared (2. 14 et seq. ).

UUh gyro frequency (2. 14 et seq. ). Pj probability that detachment occurs for a particular ion (1. 5).

cPa magnetic azimuth reckoned clockwise.

cpi angle of incidence of EM wave on plasma (2. 14 et seq. ). Q production rate (1. 1).

Qo —^ production rate (1. 28).

qg production rate of cosmic rays at any height, h.

q^ cosmic radiation production rate per atmosphere pressure (1. 8),

q$ x-ray production rate at any height, h.

p density of atmosphere at any height, h (1. 28 et seq. ).

p atmospheric pressure,

a

Pq surface density of atmosphere (1. 28 et seq. ). S complex number root of a quartic equation (2. 14).

T temperature, degrees Kelvin (1. 2).

t time

-75-
= geomagnetic latitude (1. 8).

Ue transmission coefficient for transverse magnetic waves (3. 1),

U„ transmission coefficient for transverse electric waves (3. 2).

V velocity (2. 1).

[ ] indicates number density of a particular species (1. 2).

''-*" GPO 850-128