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The conductivity of lower ionosphere deduced from sudden enhancements of strength (SES) of v.l.f. transmissions
Journal ofAtmospheric andTerrestrial Physics, lfl39, Vol.31,pp.1049-1057. Pergamon Press.Printed inNorthern Ireland
The conductivity of lower ionosphere deducedfrom sudden enhancements of strength @ES) of v.1.f. transmissions NICHIKO YAMASHITA The Research Institute of Atmospherics, Nagoya University, Toyokawa, Aichi, Japan (Received 24 December 1968) Ab&&--The modal equation is solved with use of the sharply-bounded and homogeneous ionospheric model. The oonductivity parameter of the lower ionosphere is discussed comparing the theoretical results with experimental data of SES phenomena on the v.1.f. transmissions reported by KAUFBMNN. As the result, it is seen that, under the undisturbed ionosphere, the reflection height of v.1.f. is about 70 km and its ionospheric conductivity parameter UJ,is about 2-5 x 104/set. 1. INTRODUCTION THE SIG~NAL,strength and the phase of v.1.f. trans~ssions have been observed for a long time. Especially, the effects of sunset and sunrise and the directional dependence of the propagation characteristics of v.1.f. waves have been investigated both empirically and theoretically. As is well known, an S.I.D. (sudden ionospheric disturbance) is produced by an abrupt increase of the X-rays emitted from the sun during a solar flare, and normally the signal stren~h and the phase of v.1.f. waves change during the S.I.D. because the wave-guide formed by the earth and the ionosphere changes in height and effective conductivity. As a result, the sudden enhancement of signal strength and the sudden phase anomaly are produced. Among many works, CROMBIE and KAUFMANN attempted to explain the reflecting height of v.1.f. and its conductivity under the undisturbed ionosphere by the use of the SES phenomena. In the present paper, we assume a sharply-bounded and homogeneous ionospheric model to solve the modal equation, and then by this solution and KAUFMANN’S (1967, 1968) SES data, the conductivity parameter in the lower ionosphere is discussed with regard to the SES phenomena.
2. CAL~U~TIONS
OF THE NODAL EQUATION OP THE SPHERICAL EARTE
IN THE CASE
Only the first order mode is considered for a long path propagation because all other modes are highly attenuated. The solution of the spherical earth modal equation is shown in detail by WAIT (1962):
where t = -
lea w3
() T
c2,
t _ y. =
-
% (
2!3(cf)2, 1
C’ =
(c2 + y)l’2,
(2)
1050
MICHIKO
YAMASHITA
a is the radius of the earth, H the height of the ionsphere and C is a root of the modal equation (P = 1 - S2)
Ai = [n? - (S’)2]1’2/ni2
Ai,
(4)
where o0 and E, are the conductivity and the dielectric constant, respectively, of the ground, and np is the refractive index of the ionosphere. In equation (l), N denotes the mode number, and V,(t) and W2(t) (or Wi(t - y,,) and W2(t - yJ) are the Airy functions, and the prime indicates the derivative with respect to t (or t - y,). They are expressed in terms of Hankel functions of order one third, ~)1’2H$$j(
W,(t) = exp (--iGj?~) (W2(t) = exp (ign) ( -
“‘H$@
:)
-t)3/2]
,
( -Q312].
(5)
Since y,, - t is large compared with unity, equation (1) can be obtained use of the asymptotic expansion of equation (5) as follows: w,‘(t)
-
!LW2(Q
w,‘(t)
-
a,~dt)
Ri exp [ -ijka(C’)3]
= exp (-42&V)
with the
(6)
where R,
Ri is the ionospheric as
t
=C’-At c-q&
reflection coefficient.
R,R,
exp { --i$ka[(C’)3
(7)
’
If (4)
> 1, equation (6) can be rewritten
- C3]} = exp (42747
(8)
where
R, is the reflection coefficient at the ground equation (8) can be represented as R,R,
exp (42kHC)
surface.
Furthermore,
if C2 > H/a,
= exp (-4277N).
Equation (10) is the well known modal equation for the flat-earth case. simplify the numerical calculation, the following assumptions are made: (i) The earth is a (ii) The effect of sharply-bounded and gation characteristics
(10) Here, to
perfect conductor (q, = 0). the earth’s magnetic field is neglected and the ionosphere is Thus, the directional dependency of the propahomogeneous. The refractive index of the ionosphere for is not considered.
Deductions from sudden enhancements of strength of v.1.f. transmissions
1051
v.1.f. is represented as niz
=
. q2 (-Gl-_iZ!? WV
1 -
(11)
0
where o, = oo2/v, o0 and v are the plasma frequency and the collisional frequency is the conductivity of the ionosphere, in which o, is called respectively. ui = QCC), the conductivity parameter. By considering the grazing incidence of v.1.f. waves, the ionospheric reflection coefficient _?$becomes R,r
-exp
(aICY’)= -exp
[al(C2
+
:)““I.
(12)
For Ai > C and with assumption (ii),
2(1-i?)
2 al
s
--N-
(13)
Ai -
From equations (12) and (13) and assumption (i), it can be shown that
The complex values of C2 in equations (14) can be obtained making use of Newton’s
iteration method. The field intensity is given by
where P is the radiation power, 3,the wavelength and d the path length. The attenuation coefficient in decibels per 1000 km along the propagation path is given by a =
-I,(#)
x
F
x
8.68 X lo3
(dB/lOOOkm).
(16)
Some samples of the calculation of attentuation coefficients vs. CD,are shown in Fig. 1. 3. EXPLANATION OF THE SES PHENOMENA
The experimental data on the SES and SPA phenomena under the disturbed ionosphere have been reported by KAUFMANNet al. (1967). Simultaneous observations of the signal strength and the phase are now being carried out at SBo Paula, Brazil. Forty events in 1966 (KAUFMANN et al., 1967) and 122 events from January to May, 1967 (KAUFMANN and MENDES,1968) are reported. Table 1 shows the v.1.f. stations, frequency used and propagation distance. From this data, the following observations can be made.
(a) At frequencies above 15 kHz, the ratio of the signal strength E,/E, is unity or
1052
MICHIPO
1
104
YAMASHITA
105
1
106
F=25 kHr
4
i
104 r 4
F=20 kHz
F=l5 ktir
105 WI, see-1
Fig. 1. The calculation of attenuation coefficientsvs. w, when H = 70 km.
Table 1. v.1.f. stations, frequency and propagation distance Call letters
Frequency (kHz)
Omega GBR NPG GBZ WWVL NSS NBA NPM
13.6 16-O 18.6 19.6 20.0 21.4 24.0 26.1
Path length (km) 4100
9500 10900 9500 9300 7600 5100 12900
Deductions from sudden enhancements
of strength of v.1.f. transmissions
1053
larger. Suffixes s and N stand for the S.I.D. and the normal condition of the ionosphere, respectively. (b) At 13.6 kHz, the ratio varies from less than unityto greater than unity. Hence, the turnover frequency seems to come below 15 kHz, and it is likely that the turnover frequency depends upon the solar flare type, zenith angle of the sum and so on. (c) As is seen from Fig. 2, the lowering height AH comes dominantly lower than 3 km. Making use of the field strength ratio Es/EN and the height variation LW derived from the observed phase advance, the change in attenuation Aa = aN - a, can be easily estimated from equation (15). The relation Aa vs. frequency is shown in
JO-
O-l
l-2
2-3
3-4
4-5
5-6
6-7
7-6
B-99-
AH, km Fig. 2. The lowering height AH and its ooourrence frequency.
Fig. 3 with the assumption of HN = 70 km. Figure 4 shows the relation between the conductivity parameter cc), and the height of the ionosphere. This was derived from the height distribution of electron concentration and the collisional frequency obtained by DEEKS(1966). Also, from investigations of SEA (sudden enhancement of atmospherics) phenomena some workers found that the electron density during an S.I.D. increases to about 7 to 35 times the normal value. From Figs. 1 and 4, taking the above fact into consideration, the relation Aa vs. frequency is obtained theoretically in Fig. 5. For the ionospheric parameters of the normal condition, (w,), = 2 x 104, 3 x 104, 4 x 104,5 x 104/sec, HN = 70 km and for the disturbed ionosphere, (w~)~= 1 x 105, 2 x 105, 3 x 105, 4 x 10”/sec, H, = 68 km are assumed. For all frequencies, Aa decreases as (o,), increases. For
. . l
8
1
. : :
.
: :
l
.
l .
+”
.
.
.
:
I
.
~
l
Frequency,
kkit
Fig. 3. Making us0 of KA‘a SES data, the change in at~nuati~~ W - cc,estimates with the assumption of Eix = 70 km,
w,,
Fig.
4.
&a -
set-’
The relation between the conduotivity parameter o, and the height of the ionosphere derived from DBEKS’ (1966) experimental data.
Deductions from sudden enhancements of strength of v.1.f. transmissions
1055
Fig. 5(a). Aa vs. frequency obtained theoretically when (a,)~ = 2 x lO*/sec and HN =‘7Okm. = 1 x 105/sec,H, (w,), = 2 x 105/sec,H, (c+)~ = 3 x 105/sec,H, (w,), = 4 x 105/sec,H,
(w,),
- - - -o--x-
= = = =
68 km. 68 km. 68 km. 68 km.
13.6I5
r 25
20 Frequency,
30
kHz
Fig. 6(b). Aa vs. frequency obtained theoretically when (a,.)~ = 3 x 104/sec and HN = 70km. (w,), = 2 x lOb/sec,H, = 68 km. - - (or& = 3 x lOb/sec,H, = 68 km. -o(o,& = 4 x 105/sec,H, = 68 km. -x(w,), = 5 x 105/seo,H, = 68 km.
Ii-6I;
1 20 Frequency,
1 25 kHz
30
MICHIKO YAMASHITA
1056
I.O-
II ”
I
I
I
13.6IS
0
20 Frequency,
25
30
kHz
Fig. 5(c). Aa vs. frequency obtained theoreticelly when (0,)~ - - --
= 4 x 104/seo and
RN =7Okm. (o,.)~ = 3 x 106/sec, H, = 68 km. (CD,), = 4 x 105/sec, H, = 68 km.
1.0,
”
,,i
115
I 20
Frequency,
/ 25
kHz
Fig. 5(d). Aa vs. frequency obtained theoretically when (o,.)~v = 5 x 104/sec and HN = 70 km. (u+)~ = 4 x 105/sec, H, = 68 km. - - - - (o,.)~ = 5 x 105/sec, H, = 68 km.
Deductions
from sudden enhancements of strength of v.1.f. transmissions
1057
frequencies greater than 15 kHz, it is seen that the negative value of Au, which corresponds to the case EJE, = 1, may occur when (1) ( o,)~ is small and (o,), becomes relatively large. (2) (cu,)~,, is
large and (w,)/~ becomes relatively small. 4.
CONCLUSION
Consideration was not given here to solar flare types, the dependence on the sun’s zenith angle and so on. The reflection height of v.1.f. waves and the conductivity parameter are, from the viewpoint of SES phenomena, 70 km and 2-5 x 104/sec, respectively. These values are very close to those in BUDDEN’S(1953) results, in which H = 69 km and o, = 4.5 x 104/sec. However, the above conductivity parameter is very small compared with WAIT’S (1957) result, i.e., o, = 2 x 105/sec. If the conductivity parameter of the undisturbed ionosphere is assumed to be 2 x 105/sec, it is impossible to interpret SES phenomena as shown in Fig. 1. Since the attenuation coefficients increase at frequencies above 15 kHz as w, increases during S.I.D., the sign of Aa is always negative for frequencies greater than 15 kHz. Acknowledgement-The author wishes to express her thanks to Professor K. Sao of the Research Institute of Atmospherics, Nagoya University for his helpful discussions and continuous en-
couragement .
K.G. CROMBIE D.D. DEEKS D.G. KAUFMANN P.,SCHAAL R.E.,LOPES and ARAKAKIL. KAUFMANNP.~~~MENDESA.M. K&IVSK~ L. WAIT J. R. WAIT J. R.
REFERENCES
BUDDEN
W.
1953 1965 1966 1967
Phil. Mug. 44, 504. Proc. I.E.E.E. 53,2027. Proc. R. SOL, Ser. A. 291, 413. J. Atmosph. Terr. Phys. 29, 1443.
1968 1965 1957 1962
J. geophy. Res. 73, 2487, 6404. BAC, 16, 126. Proc. I.R.E. 45, 760. Eleotromugnetic Wavee isStrati&dMedia, Chapter VII, p. 196. Pergamon Press, Oxford.
The conductivity of lower ionosphere deducedfrom sudden enhancements of strength @ES) of v.1.f. transmissions NICHIKO YAMASHITA The Research Institute of Atmospherics, Nagoya University, Toyokawa, Aichi, Japan (Received 24 December 1968) Ab&&--The modal equation is solved with use of the sharply-bounded and homogeneous ionospheric model. The oonductivity parameter of the lower ionosphere is discussed comparing the theoretical results with experimental data of SES phenomena on the v.1.f. transmissions reported by KAUFBMNN. As the result, it is seen that, under the undisturbed ionosphere, the reflection height of v.1.f. is about 70 km and its ionospheric conductivity parameter UJ,is about 2-5 x 104/set. 1. INTRODUCTION THE SIG~NAL,strength and the phase of v.1.f. trans~ssions have been observed for a long time. Especially, the effects of sunset and sunrise and the directional dependence of the propagation characteristics of v.1.f. waves have been investigated both empirically and theoretically. As is well known, an S.I.D. (sudden ionospheric disturbance) is produced by an abrupt increase of the X-rays emitted from the sun during a solar flare, and normally the signal stren~h and the phase of v.1.f. waves change during the S.I.D. because the wave-guide formed by the earth and the ionosphere changes in height and effective conductivity. As a result, the sudden enhancement of signal strength and the sudden phase anomaly are produced. Among many works, CROMBIE and KAUFMANN attempted to explain the reflecting height of v.1.f. and its conductivity under the undisturbed ionosphere by the use of the SES phenomena. In the present paper, we assume a sharply-bounded and homogeneous ionospheric model to solve the modal equation, and then by this solution and KAUFMANN’S (1967, 1968) SES data, the conductivity parameter in the lower ionosphere is discussed with regard to the SES phenomena.
2. CAL~U~TIONS
OF THE NODAL EQUATION OP THE SPHERICAL EARTE
IN THE CASE
Only the first order mode is considered for a long path propagation because all other modes are highly attenuated. The solution of the spherical earth modal equation is shown in detail by WAIT (1962):
where t = -
lea w3
() T
c2,
t _ y. =
-
% (
2!3(cf)2, 1
C’ =
(c2 + y)l’2,
(2)
1050
MICHIKO
YAMASHITA
a is the radius of the earth, H the height of the ionsphere and C is a root of the modal equation (P = 1 - S2)
Ai = [n? - (S’)2]1’2/ni2
Ai,
(4)
where o0 and E, are the conductivity and the dielectric constant, respectively, of the ground, and np is the refractive index of the ionosphere. In equation (l), N denotes the mode number, and V,(t) and W2(t) (or Wi(t - y,,) and W2(t - yJ) are the Airy functions, and the prime indicates the derivative with respect to t (or t - y,). They are expressed in terms of Hankel functions of order one third, ~)1’2H$$j(
W,(t) = exp (--iGj?~) (W2(t) = exp (ign) ( -
“‘H$@
:)
-t)3/2]
,
( -Q312].
(5)
Since y,, - t is large compared with unity, equation (1) can be obtained use of the asymptotic expansion of equation (5) as follows: w,‘(t)
-
!LW2(Q
w,‘(t)
-
a,~dt)
Ri exp [ -ijka(C’)3]
= exp (-42&V)
with the
(6)
where R,
Ri is the ionospheric as
t
=C’-At c-q&
reflection coefficient.
R,R,
exp { --i$ka[(C’)3
(7)
’
If (4)
> 1, equation (6) can be rewritten
- C3]} = exp (42747
(8)
where
R, is the reflection coefficient at the ground equation (8) can be represented as R,R,
exp (42kHC)
surface.
Furthermore,
if C2 > H/a,
= exp (-4277N).
Equation (10) is the well known modal equation for the flat-earth case. simplify the numerical calculation, the following assumptions are made: (i) The earth is a (ii) The effect of sharply-bounded and gation characteristics
(10) Here, to
perfect conductor (q, = 0). the earth’s magnetic field is neglected and the ionosphere is Thus, the directional dependency of the propahomogeneous. The refractive index of the ionosphere for is not considered.
Deductions from sudden enhancements of strength of v.1.f. transmissions
1051
v.1.f. is represented as niz
=
. q2 (-Gl-_iZ!? WV
1 -
(11)
0
where o, = oo2/v, o0 and v are the plasma frequency and the collisional frequency is the conductivity of the ionosphere, in which o, is called respectively. ui = QCC), the conductivity parameter. By considering the grazing incidence of v.1.f. waves, the ionospheric reflection coefficient _?$becomes R,r
-exp
(aICY’)= -exp
[al(C2
+
:)““I.
(12)
For Ai > C and with assumption (ii),
2(1-i?)
2 al
s
--N-
(13)
Ai -
From equations (12) and (13) and assumption (i), it can be shown that
The complex values of C2 in equations (14) can be obtained making use of Newton’s
iteration method. The field intensity is given by
where P is the radiation power, 3,the wavelength and d the path length. The attenuation coefficient in decibels per 1000 km along the propagation path is given by a =
-I,(#)
x
F
x
8.68 X lo3
(dB/lOOOkm).
(16)
Some samples of the calculation of attentuation coefficients vs. CD,are shown in Fig. 1. 3. EXPLANATION OF THE SES PHENOMENA
The experimental data on the SES and SPA phenomena under the disturbed ionosphere have been reported by KAUFMANNet al. (1967). Simultaneous observations of the signal strength and the phase are now being carried out at SBo Paula, Brazil. Forty events in 1966 (KAUFMANN et al., 1967) and 122 events from January to May, 1967 (KAUFMANN and MENDES,1968) are reported. Table 1 shows the v.1.f. stations, frequency used and propagation distance. From this data, the following observations can be made.
(a) At frequencies above 15 kHz, the ratio of the signal strength E,/E, is unity or
1052
MICHIPO
1
104
YAMASHITA
105
1
106
F=25 kHr
4
i
104 r 4
F=20 kHz
F=l5 ktir
105 WI, see-1
Fig. 1. The calculation of attenuation coefficientsvs. w, when H = 70 km.
Table 1. v.1.f. stations, frequency and propagation distance Call letters
Frequency (kHz)
Omega GBR NPG GBZ WWVL NSS NBA NPM
13.6 16-O 18.6 19.6 20.0 21.4 24.0 26.1
Path length (km) 4100
9500 10900 9500 9300 7600 5100 12900
Deductions from sudden enhancements
of strength of v.1.f. transmissions
1053
larger. Suffixes s and N stand for the S.I.D. and the normal condition of the ionosphere, respectively. (b) At 13.6 kHz, the ratio varies from less than unityto greater than unity. Hence, the turnover frequency seems to come below 15 kHz, and it is likely that the turnover frequency depends upon the solar flare type, zenith angle of the sum and so on. (c) As is seen from Fig. 2, the lowering height AH comes dominantly lower than 3 km. Making use of the field strength ratio Es/EN and the height variation LW derived from the observed phase advance, the change in attenuation Aa = aN - a, can be easily estimated from equation (15). The relation Aa vs. frequency is shown in
JO-
O-l
l-2
2-3
3-4
4-5
5-6
6-7
7-6
B-99-
AH, km Fig. 2. The lowering height AH and its ooourrence frequency.
Fig. 3 with the assumption of HN = 70 km. Figure 4 shows the relation between the conductivity parameter cc), and the height of the ionosphere. This was derived from the height distribution of electron concentration and the collisional frequency obtained by DEEKS(1966). Also, from investigations of SEA (sudden enhancement of atmospherics) phenomena some workers found that the electron density during an S.I.D. increases to about 7 to 35 times the normal value. From Figs. 1 and 4, taking the above fact into consideration, the relation Aa vs. frequency is obtained theoretically in Fig. 5. For the ionospheric parameters of the normal condition, (w,), = 2 x 104, 3 x 104, 4 x 104,5 x 104/sec, HN = 70 km and for the disturbed ionosphere, (w~)~= 1 x 105, 2 x 105, 3 x 105, 4 x 10”/sec, H, = 68 km are assumed. For all frequencies, Aa decreases as (o,), increases. For
. . l
8
1
. : :
.
: :
l
.
l .
+”
.
.
.
:
I
.
~
l
Frequency,
kkit
Fig. 3. Making us0 of KA‘a SES data, the change in at~nuati~~ W - cc,estimates with the assumption of Eix = 70 km,
w,,
Fig.
4.
&a -
set-’
The relation between the conduotivity parameter o, and the height of the ionosphere derived from DBEKS’ (1966) experimental data.
Deductions from sudden enhancements of strength of v.1.f. transmissions
1055
Fig. 5(a). Aa vs. frequency obtained theoretically when (a,)~ = 2 x lO*/sec and HN =‘7Okm. = 1 x 105/sec,H, (w,), = 2 x 105/sec,H, (c+)~ = 3 x 105/sec,H, (w,), = 4 x 105/sec,H,
(w,),
- - - -o--x-
= = = =
68 km. 68 km. 68 km. 68 km.
13.6I5
r 25
20 Frequency,
30
kHz
Fig. 6(b). Aa vs. frequency obtained theoretically when (a,.)~ = 3 x 104/sec and HN = 70km. (w,), = 2 x lOb/sec,H, = 68 km. - - (or& = 3 x lOb/sec,H, = 68 km. -o(o,& = 4 x 105/sec,H, = 68 km. -x(w,), = 5 x 105/seo,H, = 68 km.
Ii-6I;
1 20 Frequency,
1 25 kHz
30
MICHIKO YAMASHITA
1056
I.O-
II ”
I
I
I
13.6IS
0
20 Frequency,
25
30
kHz
Fig. 5(c). Aa vs. frequency obtained theoreticelly when (0,)~ - - --
= 4 x 104/seo and
RN =7Okm. (o,.)~ = 3 x 106/sec, H, = 68 km. (CD,), = 4 x 105/sec, H, = 68 km.
1.0,
”
,,i
115
I 20
Frequency,
/ 25
kHz
Fig. 5(d). Aa vs. frequency obtained theoretically when (o,.)~v = 5 x 104/sec and HN = 70 km. (u+)~ = 4 x 105/sec, H, = 68 km. - - - - (o,.)~ = 5 x 105/sec, H, = 68 km.
Deductions
from sudden enhancements of strength of v.1.f. transmissions
1057
frequencies greater than 15 kHz, it is seen that the negative value of Au, which corresponds to the case EJE, = 1, may occur when (1) ( o,)~ is small and (o,), becomes relatively large. (2) (cu,)~,, is
large and (w,)/~ becomes relatively small. 4.
CONCLUSION
Consideration was not given here to solar flare types, the dependence on the sun’s zenith angle and so on. The reflection height of v.1.f. waves and the conductivity parameter are, from the viewpoint of SES phenomena, 70 km and 2-5 x 104/sec, respectively. These values are very close to those in BUDDEN’S(1953) results, in which H = 69 km and o, = 4.5 x 104/sec. However, the above conductivity parameter is very small compared with WAIT’S (1957) result, i.e., o, = 2 x 105/sec. If the conductivity parameter of the undisturbed ionosphere is assumed to be 2 x 105/sec, it is impossible to interpret SES phenomena as shown in Fig. 1. Since the attenuation coefficients increase at frequencies above 15 kHz as w, increases during S.I.D., the sign of Aa is always negative for frequencies greater than 15 kHz. Acknowledgement-The author wishes to express her thanks to Professor K. Sao of the Research Institute of Atmospherics, Nagoya University for his helpful discussions and continuous en-
couragement .
K.G. CROMBIE D.D. DEEKS D.G. KAUFMANN P.,SCHAAL R.E.,LOPES and ARAKAKIL. KAUFMANNP.~~~MENDESA.M. K&IVSK~ L. WAIT J. R. WAIT J. R.
REFERENCES
BUDDEN
W.
1953 1965 1966 1967
Phil. Mug. 44, 504. Proc. I.E.E.E. 53,2027. Proc. R. SOL, Ser. A. 291, 413. J. Atmosph. Terr. Phys. 29, 1443.
1968 1965 1957 1962
J. geophy. Res. 73, 2487, 6404. BAC, 16, 126. Proc. I.R.E. 45, 760. Eleotromugnetic Wavee isStrati&dMedia, Chapter VII, p. 196. Pergamon Press, Oxford.