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Some general theory of electron density irregularities in the ionospheric E-region
SOME GENERAL IRREGULARITIES
THEORY OF ELECTRON DENSITY IN THE IONOSPHERIC E-REGION B. D. COLE*
Antarctic Division, Department
of External Affairs, Melbourne
AbstrH--The effect of electromagnetic forces on Eregion ionization is discussed from a geae& standpoint. Amoqst other things it is found: (a) Of strong fargsscale ~~~tr~~ons of Gregion ionization (i) they are stron@y correlated with the horizontaf component (IS) of the geomagnetic field. (ii) they are correlated with negative deviations of Ii. (b) Of weak small-scale irregulanties: They can be formed by small-scale perturbations in (i) neutral particle density (ii) ionospheric current density. (c) That E-region ionization may be maintained at night by compression of ionization downwards from higher levels. (d) The strongest auroral electrojets may manifest the pinch effect.
Irregularities in the ionosphere observed by radio means are i~eg~l~ities in the electron density. The initial cause of ionization is sofar radiation or corpuscular bombardment= The former is the principal cause in low and temperate latitudes but the latter may be dominant at times in aurora1 regions. Unless especially mentioned it will be taken for granted in this paper that low and temperate latitude phenomena are being discussed.
It is assumed in the following that there is only one kind of positive ion in the ionosphere and no negative ions but electrons. The rate of change of electron density at a point in the ionosphere is given by
an
-zzz
at
q-L-V.(nv),
where n = electron density q = r&e of production of electrons L = rate of r~~ombinatioR v = drift velocity of ionization. Considering only the action of electromagnetic forces(fl, nv = qSjx B
(2)
where 4 = (m,~$ + me~J-l, a scalar function of the neutral particle density in the E-region m,*, = mass of ions, electrons VS.8= collision frequencies of ions, electrons B = total geomagnetic field. V.(nv)=jxB.V$ftfB.Vxj-#j.VxB.
Now *Present address: aviation,
Upper Atmosphere N.S.W., Australia.
Section, ~rnmo~w~th 7.59
(3 Scientific and Industrial
Research
760
K. D. COLE
Assuming L = an2, an
(4) It will be seen later that, except in the strongest aurora1 electrojets, the term 4j2 in (4) is negligible. It is therefore immediately obvious from (4) that to produce an accumulation of ionization by electromagnetic forces there is required (i) a gradient of I$ (i.e. a gradient of neutral particle density) in the opposite direction to j x B or (ii) a component of V x j in the opposite direction to B.
3. STRONG LARGESCAZE IRREGULARITIES (&Iw n) In this case each of the electromagnetic (a) The term j x B . V#
terms in (4) must be comparable with an2.
lj x B . V$l > un2 requires I+j x B/an21 > INV4l.
(5)
Assuming there are no irregularities in neutral particle density except the natural height variation, then V+ is vertically upwards and we can write
-j x B . V# = H(V+)j,,
(6)
where j, = westward component of j. H = horizontal component
Thus concentration
of the geomagnetic field (B).
of ionization into a layer occurs when
Since + 523(mpJ_l, and vi is proportional to neutral particle density, then the scale height of 4 (= 4/V+) is the same as the scale height of neutral particle number density. The latter is given in Table 1 for the model atmosphere chosen (ARDC 1959,t2)). In the height range of interest assume a = lo-s, n = 10s, H = O-3 gauss, and, in the absence of a model for the current assume j = 7 x lo-l2 e.m.u. (a value appropriate to quiet variations in the geomagnetic field). The table shows values of $jH/cw2 calculated from equation (7). It is seen that with the model atmosphere chosen the natural scale height of 4 (i.e. of neutral particle density) is less than this value in the height range in which sporadic E is observed@). It is therefore suggested that, in the real atmosphere, westwards ionospheric current can cause concentration of ionization in the E-region into a thin layer. At greater heights the value of j falls off (4) so that the value of I#jH/an21 b ecomes less than the scale height and the term j x B . 04 becomes ineffective. The action represented by the term j x B in the present context can be understood as follows: ionization is depressed by westward current into the atmosphere but its mobility becomes progressively less with depth in the atmosphere so that it piles up at some level. (b) The term +B . V x j Assuming that ionospheric current is everywhere horizontal and that horizontal gradients of it are negligible compared to vertical (z) gradients, then, -+B
. V x j = +Haj,Jaz.
(8)
SOME
GENERAL
THEORY
OF
ELECTRON
DENSITY
IRREGULARITIES
761
Thus +B.Vxj>ans requires
The scale height of j, (i.e. j,/(aj&z)) may commonly be less than 10 km.t4) From Table 1 it is then clear that condition (9) may exist at times in the E-region. Equation (8) shows that there is a tendency for strong sporadic E to form on the under side of a westward current and on the top side of an eastward current. TABLE 1 (A
number a x 10b is written a”.)
Height (km)
nn
mi
+
80 90 100 110 120 130 140 150
4.414 5.91” 7*818 1*21* 3.1” 1.311 6~4~” 3.81°
29 29 28.8 28.7 28.6 28.5 28.4 28.3
9.81a 71’ 5.318 3.519 1.340 3.2”’ 6P 1.1”
* N.B.
Scale height (km)
: 6 8.6 14 20 25.5 31
QjH/an’ (km) 2-a 1.5-l ::: 21 69 140 220*
cd/H V + (e.m.u.) 15-o 2-10 3-l’ 8-U 3-u 2-m 1.2-l’ g-n
At greater heights 4 jH/an’ decreases because of the decrease of j.
Thus one would expect the height of E, to be lower during the night than during the day at a place of the latitude of Maui, for the S, current is eastwards in daytime and westwards at night at this latitude. This effect is observed at Maui@). One would expect the opposite trend at White Sands. However this trend is not obvious in the data from White Sands exhibited by Smith @). One would expect similarly the sporadic E-layer during the day to be higher at Maui than Washington.- This is observed@) . In the case of strong large irregularities equation (4) may then be written
an -=
at
q-
ana + j,HV#
+ H@j,Jaz.
It is clear from this equation that the formation of strong large scale sporadic E should be highly correlated with the horizontal component (H) of the geomagnetic field. This has been observed by Heisler and Whiteheadfs). Whitehead@) invoked vertical shears in horizontal winds to explain this kind of sporadic E. Such shears may create significant aj,/az. It is seen from the above theory that though sufficient, such shears are not necessary to explain the effect of accumulation of ionization in a thin layer. Westwards currents become effective in causing such accumulation whenever jco>
Im21HD41.
Assuming a = lo-*, n = 106, H = O-3, ma/H V C$is shown in Table 1. It is seen from this table that the larger j, the lower in the E-region it is able to create accumulation of ionization. The last two columns of Table 1 must be regarded as very rough indicators only, since they depend on a, n, j all of which have to be estimated roughly. However these parameters are sufhciently well known to illustrate the operation of terms of equation (10).
762
K. D. COLE
A westward current would produce a decrease in the horizontal component of the geomagnetic field, Wilkes and McNicol f7)have observed a correlation of a decrease of I$ with the presence of sporadic E at Brisbane. Once the formation of large scale sporadic E commenced through the action of the term j x B . Vd;, the term $B .V x j would increase in importance due to the formation of significant aj,/az. (c) The term #j2 Current in the E-region may be due chiefly to Hall drift v, of electrons@). Thus the term $j2 will be greater than an2 when (puttingj = nev,) 1 a u, > e J 5’ Of course the value of u, calculated from this formuia is sensitive to a and 4. However, adopting the values above for illustration, equation (11) yields v, % 5105 cm set-l. Such electron speeds may be acquired only in the strongest of aurora1 electrojets(g). This justifies the neglect of this term for general discussion of strong large-scale sporadic E. (d) Steady-state v&es of n In general, in the quasi-steady state @n/i% w 0) equation (10) yields
This equation demonstrates simply how racan be augmented or diminished by the action of westward current. It is expected that E,, greater than a given frequency (say 5 MC/S), should be of more frequent occurrence during the day (q # 0) than during the night (q = 0), except of course in aurora1 regions. 4. WEAK SMALL-SCALE
IRREGULARITIES (&I < n)
Returning to equation (4) it is seen that during the day q maintains a density n, = (q/a)*. To explain weak irregularities the electromagnetic terms have only to exceed a term 2cm,&. Some observers have suggested &z/no M lOA in a large cIass of weak irregularities. It is clear from equation (4) that there are two classes of causes which can be called upon to explain weak irregularities, (i) ~regula~ties in #, i.e. in neutral particle density, (ii) irregularities in the current density j(V x j term). The movement of the latter irregularities has been discussed by a number of people(10-12). (a) Let us discuss the first type of cause, viz. irregularities in 4. In order that &fat be positive it is required that j x B Now, to a good approximation,
.
V+ > 2ano6n.
+ = l/m,v,. Taking O,+ as ion as an example,
% + M 4.2 x lO-1* p1II see-l t where FZ~= neutral particle number density. Whence V$ % -Vn,J4*2 x 10-l* m,n,“.
(13)
SOME
GENERAL
THEORY
OF ELECTRON
DENSITY
IRREGULARITIES
763
Thus (13) requires Vn > 8.4 n
x
lo-lo uno6nm,n,e
.
(14)
jB
Putting j = 7 x IO-l2 e.m.u., B = O-4gauss, no = lo6 cm3, n, = 1012cm-3 at 110 km, (14) becomes Vn, > l-6
x
104
6n = 10s cmA, cc = 10d,
cm-l FW
(15)
6 x 10-s n, cm-l (at 110 km). This is an extremely small gradient. Suppose Vn, exists as a sound wave of wavelength 1 = GnJVn, = Vg
(16)
where V, = speed of sound T = period of wave. During the period of a wave the irregularity in n established is (given that (13) is true) (17) Aj x BVn,/4-2 Thus where
x
(+I(?), Kl+
lo-lo m,n,2v,.
(18)
(19)
. 8
Assuming V, = 3 x IO4cm see-l and the values of the other parameters following equation (14), Kl M 0.05 at 110 km. At 130 km (n, = 1011cm-a), Kl w O-5. During magnetic disturbance or at the aurora1 zones, when and where j is substantially increased, Kl is correspondingly increased. It is clear that weak irregularities in n can be generated by spatial variations in mobility of ionization caused by fluctuations (either moving or static) in n, within ionospheric currents responsible for magnetic variations. Irregularities in n so generated would tend to drift with their own characteristic speed(12p13). Let the current associated with these irregularities be Sj, then the electromagnetic term 13 may be written (jo+~j)xB.V~=joxB.V~+6j~B.V+
(20)
where j, is the background current in the absence of irregularities of any kind. Whilst the irregularities remain weak, the term Sj x B . 04 will in general be negligible compared to j. x B . V$. It follows that the morphology of the irregularities in n will be determined by the action of j. x B on the irregularities in 4 (i.e. in n,). The action of Sj x B . V+ will be a superimposed second order effect. However if there were phase identity of a wave in Sj and a wave in 04, then dj x B . V+ may be constant over long periods of time, allowing build up of ionization thereby. The conditions for this build up would be sporadic and very critical.
764
K. D. COLE
It is to be expected that an object passing through the E-region would create perturbations in neutral particle density in its wake and so give rise to perturbations in ionization density in the wake. This would give such an object a radar cross section greater than its own dimensions. (b) The second type of cause of weak irregularities, viz. the term $B . V x j in (4), requires $B . V x j > 2c&jn. (21) In this case, it is required that ] V X jl > 2~~~~~~~B. (22) Using the same values as used after equation (14), equation (21) becomes (at 110 km), IV X j[ > 5 X 10w20e.m.u. cm-l.
(23)
Irregularities in current would propagate through the ionosphere with a certain phase speed V, of order lo4 cm set-l. Suppose the irregularities in current exist in the form of a wave of-wavelength A. Then during the period ofa wave the irregularity in n established is (provided (21) is true) 6n R+$B , (V x j) . 2/V, (24) % $Bdj/V, where Sj is the amplitude of the wave, Thus
(25)
where Ka has values similar to Kr discussed above. Thus it is clear that irregularities in current (e.g. hydromagnetic waves) propagating into the ionosphere produce irregularities in the electron density. Whitehead(14) has just proposed a theory of formation of equatorial sporadic E ionization on the basis of the phase coupling of a sound wave and an irregularity of ionization density. His m~ha~srn employs the term $B . V x j, su~esting that it remains of the same sign for long times in a frame of reference moving with the sound wave (and the irregularity). The compressions and rarefactions of the sound wave are supposed to generate a component of V x j in phase with that of the moving irregularity causing the Iatter to become stronger with the passage of time. The conditions for the functioning of this mechanism appear to be critical. (iii) If #jz > 2an&, it is required that
where f = &z/n. With $ = 10” condition (26) could be fulfilled in moderately strong aurora1 electrojets. It is clear that small scale irregularities can be generated by small-scale pe~urbations in neutral particle density and in current density.
SOME GENERAL THEORY OF ELE@TRoN DENSTI-Y IRREGULARITIES
It is usu;tl to suppose q = 0 at night. Equation (4) becomes, negkzting and also assuming only large-scale processes are operative (see Section 3)
765
the last term,
This suggests that although it may be normally expected that E-region ionization vanish at night because af the high recombination rate, electromotive forces driving current may force ionization down to the lower E-region and so maintain detectable ionization there, What is required is that jWV$ f ~~j~~~z > 0. (WI Since it is to be expected that ~j~~~~be negative (28) requires that the scale height for current be less than the scale height of # (i.e. of air density). 6. DISCUSSJXIN of concentrations of ionizations in the E-region has been discussed in simple general terms and some features of strong large-scale sporadic E have been explained thereby. It has been shown how small scale irregularities can be formed. Further work is desirable to apply this general theory to specific detailed ionospheric models. The formation
writer thanks Dr. D. F. Martyn, Officxv-in-Charge,Upper Atmosphere Section, C.S.I.R.O., Camden, for the: invitation to join his group’s discussions of upper atmosphere probleMs. For Acknowh&enzen&--The
stimuiating discussians he thanks tie foltowiq members of the group, Dr. E. B. Armstrong, Mr. R. A. Duncan, Dr. S. KatG, Dr. D. F. Matip,
Dr. J. H. Piddiigtcx~and Dr. 3. D. Whitehead.
1, D. F. MANYN, Prac. Roy. SOG.A246,306 (1953). 2. P. J. NAWRCKXI and R. PAPA,Atmospheric Processes. Geophysics Corp. of America, Bedford, Mass,
(1961). 3. E. K. SMIIX,JR., World-wide Occurrence of Sporadic E, NJ3.S. Circular 582 (1957). 4. W. G. BAKERand D. F. MARTYN,Proc. Roy. SOC. A246,281 (1953). 5. L. H. HEJSLER and J. D. WHITEHEAD, Nature 187,676 (1960). 6. J. D. WHITEMUQJ. Afmos. Terr. Phys. 20,49 (1961). 7. J. R. WILKES and R. W. E. MCNICOL,Aust. J. PIIYS.15, 236 (1962). 8. K. WEEKES, J. Atmos. Terr. Phys. Special supplement,p. 12 (1957). 9. K. D. C'o~~,Plonet, Space Sci, 10, 129 (1963). 10. J. W. DUNG=, Co&& ~~ecir~y~~~ics. Cambridge University Press (1958). 11. S. UT~, Rep. kvwy&. Z$kw Res. Japmz 13, 62 (1959). 12‘ K. D. COLE,Atrsr, J. I%hys.13,484 (2960). 13. C. F. CUMMOWand M. A. JORNSON, R, A&m. fem. Phys Z&21 (f959). 14. 3. D. wI.nTEHE AD,J. Atmog. Terr. P&,w.f1953j.
Pesrwae-C%cy%~aeTc~ c o6qet TOVXIItrpe~-~wrunx~we af~ewrp~raar~~~~hl~ c~jf ~a aommaqmo .&oPiJraCTH. Memgynpowna HBxOT[WT,YTO-(a)
(6)
@f 0-f 3
THEORY OF ELECTRON DENSITY IN THE IONOSPHERIC E-REGION B. D. COLE*
Antarctic Division, Department
of External Affairs, Melbourne
AbstrH--The effect of electromagnetic forces on Eregion ionization is discussed from a geae& standpoint. Amoqst other things it is found: (a) Of strong fargsscale ~~~tr~~ons of Gregion ionization (i) they are stron@y correlated with the horizontaf component (IS) of the geomagnetic field. (ii) they are correlated with negative deviations of Ii. (b) Of weak small-scale irregulanties: They can be formed by small-scale perturbations in (i) neutral particle density (ii) ionospheric current density. (c) That E-region ionization may be maintained at night by compression of ionization downwards from higher levels. (d) The strongest auroral electrojets may manifest the pinch effect.
Irregularities in the ionosphere observed by radio means are i~eg~l~ities in the electron density. The initial cause of ionization is sofar radiation or corpuscular bombardment= The former is the principal cause in low and temperate latitudes but the latter may be dominant at times in aurora1 regions. Unless especially mentioned it will be taken for granted in this paper that low and temperate latitude phenomena are being discussed.
It is assumed in the following that there is only one kind of positive ion in the ionosphere and no negative ions but electrons. The rate of change of electron density at a point in the ionosphere is given by
an
-zzz
at
q-L-V.(nv),
where n = electron density q = r&e of production of electrons L = rate of r~~ombinatioR v = drift velocity of ionization. Considering only the action of electromagnetic forces(fl, nv = qSjx B
(2)
where 4 = (m,~$ + me~J-l, a scalar function of the neutral particle density in the E-region m,*, = mass of ions, electrons VS.8= collision frequencies of ions, electrons B = total geomagnetic field. V.(nv)=jxB.V$ftfB.Vxj-#j.VxB.
Now *Present address: aviation,
Upper Atmosphere N.S.W., Australia.
Section, ~rnmo~w~th 7.59
(3 Scientific and Industrial
Research
760
K. D. COLE
Assuming L = an2, an
(4) It will be seen later that, except in the strongest aurora1 electrojets, the term 4j2 in (4) is negligible. It is therefore immediately obvious from (4) that to produce an accumulation of ionization by electromagnetic forces there is required (i) a gradient of I$ (i.e. a gradient of neutral particle density) in the opposite direction to j x B or (ii) a component of V x j in the opposite direction to B.
3. STRONG LARGESCAZE IRREGULARITIES (&Iw n) In this case each of the electromagnetic (a) The term j x B . V#
terms in (4) must be comparable with an2.
lj x B . V$l > un2 requires I+j x B/an21 > INV4l.
(5)
Assuming there are no irregularities in neutral particle density except the natural height variation, then V+ is vertically upwards and we can write
-j x B . V# = H(V+)j,,
(6)
where j, = westward component of j. H = horizontal component
Thus concentration
of the geomagnetic field (B).
of ionization into a layer occurs when
Since + 523(mpJ_l, and vi is proportional to neutral particle density, then the scale height of 4 (= 4/V+) is the same as the scale height of neutral particle number density. The latter is given in Table 1 for the model atmosphere chosen (ARDC 1959,t2)). In the height range of interest assume a = lo-s, n = 10s, H = O-3 gauss, and, in the absence of a model for the current assume j = 7 x lo-l2 e.m.u. (a value appropriate to quiet variations in the geomagnetic field). The table shows values of $jH/cw2 calculated from equation (7). It is seen that with the model atmosphere chosen the natural scale height of 4 (i.e. of neutral particle density) is less than this value in the height range in which sporadic E is observed@). It is therefore suggested that, in the real atmosphere, westwards ionospheric current can cause concentration of ionization in the E-region into a thin layer. At greater heights the value of j falls off (4) so that the value of I#jH/an21 b ecomes less than the scale height and the term j x B . 04 becomes ineffective. The action represented by the term j x B in the present context can be understood as follows: ionization is depressed by westward current into the atmosphere but its mobility becomes progressively less with depth in the atmosphere so that it piles up at some level. (b) The term +B . V x j Assuming that ionospheric current is everywhere horizontal and that horizontal gradients of it are negligible compared to vertical (z) gradients, then, -+B
. V x j = +Haj,Jaz.
(8)
SOME
GENERAL
THEORY
OF
ELECTRON
DENSITY
IRREGULARITIES
761
Thus +B.Vxj>ans requires
The scale height of j, (i.e. j,/(aj&z)) may commonly be less than 10 km.t4) From Table 1 it is then clear that condition (9) may exist at times in the E-region. Equation (8) shows that there is a tendency for strong sporadic E to form on the under side of a westward current and on the top side of an eastward current. TABLE 1 (A
number a x 10b is written a”.)
Height (km)
nn
mi
+
80 90 100 110 120 130 140 150
4.414 5.91” 7*818 1*21* 3.1” 1.311 6~4~” 3.81°
29 29 28.8 28.7 28.6 28.5 28.4 28.3
9.81a 71’ 5.318 3.519 1.340 3.2”’ 6P 1.1”
* N.B.
Scale height (km)
: 6 8.6 14 20 25.5 31
QjH/an’ (km) 2-a 1.5-l ::: 21 69 140 220*
cd/H V + (e.m.u.) 15-o 2-10 3-l’ 8-U 3-u 2-m 1.2-l’ g-n
At greater heights 4 jH/an’ decreases because of the decrease of j.
Thus one would expect the height of E, to be lower during the night than during the day at a place of the latitude of Maui, for the S, current is eastwards in daytime and westwards at night at this latitude. This effect is observed at Maui@). One would expect the opposite trend at White Sands. However this trend is not obvious in the data from White Sands exhibited by Smith @). One would expect similarly the sporadic E-layer during the day to be higher at Maui than Washington.- This is observed@) . In the case of strong large irregularities equation (4) may then be written
an -=
at
q-
ana + j,HV#
+ H@j,Jaz.
It is clear from this equation that the formation of strong large scale sporadic E should be highly correlated with the horizontal component (H) of the geomagnetic field. This has been observed by Heisler and Whiteheadfs). Whitehead@) invoked vertical shears in horizontal winds to explain this kind of sporadic E. Such shears may create significant aj,/az. It is seen from the above theory that though sufficient, such shears are not necessary to explain the effect of accumulation of ionization in a thin layer. Westwards currents become effective in causing such accumulation whenever jco>
Im21HD41.
Assuming a = lo-*, n = 106, H = O-3, ma/H V C$is shown in Table 1. It is seen from this table that the larger j, the lower in the E-region it is able to create accumulation of ionization. The last two columns of Table 1 must be regarded as very rough indicators only, since they depend on a, n, j all of which have to be estimated roughly. However these parameters are sufhciently well known to illustrate the operation of terms of equation (10).
762
K. D. COLE
A westward current would produce a decrease in the horizontal component of the geomagnetic field, Wilkes and McNicol f7)have observed a correlation of a decrease of I$ with the presence of sporadic E at Brisbane. Once the formation of large scale sporadic E commenced through the action of the term j x B . Vd;, the term $B .V x j would increase in importance due to the formation of significant aj,/az. (c) The term #j2 Current in the E-region may be due chiefly to Hall drift v, of electrons@). Thus the term $j2 will be greater than an2 when (puttingj = nev,) 1 a u, > e J 5’ Of course the value of u, calculated from this formuia is sensitive to a and 4. However, adopting the values above for illustration, equation (11) yields v, % 5105 cm set-l. Such electron speeds may be acquired only in the strongest of aurora1 electrojets(g). This justifies the neglect of this term for general discussion of strong large-scale sporadic E. (d) Steady-state v&es of n In general, in the quasi-steady state @n/i% w 0) equation (10) yields
This equation demonstrates simply how racan be augmented or diminished by the action of westward current. It is expected that E,, greater than a given frequency (say 5 MC/S), should be of more frequent occurrence during the day (q # 0) than during the night (q = 0), except of course in aurora1 regions. 4. WEAK SMALL-SCALE
IRREGULARITIES (&I < n)
Returning to equation (4) it is seen that during the day q maintains a density n, = (q/a)*. To explain weak irregularities the electromagnetic terms have only to exceed a term 2cm,&. Some observers have suggested &z/no M lOA in a large cIass of weak irregularities. It is clear from equation (4) that there are two classes of causes which can be called upon to explain weak irregularities, (i) ~regula~ties in #, i.e. in neutral particle density, (ii) irregularities in the current density j(V x j term). The movement of the latter irregularities has been discussed by a number of people(10-12). (a) Let us discuss the first type of cause, viz. irregularities in 4. In order that &fat be positive it is required that j x B Now, to a good approximation,
.
V+ > 2ano6n.
+ = l/m,v,. Taking O,+ as ion as an example,
% + M 4.2 x lO-1* p1II see-l t where FZ~= neutral particle number density. Whence V$ % -Vn,J4*2 x 10-l* m,n,“.
(13)
SOME
GENERAL
THEORY
OF ELECTRON
DENSITY
IRREGULARITIES
763
Thus (13) requires Vn > 8.4 n
x
lo-lo uno6nm,n,e
.
(14)
jB
Putting j = 7 x IO-l2 e.m.u., B = O-4gauss, no = lo6 cm3, n, = 1012cm-3 at 110 km, (14) becomes Vn, > l-6
x
104
6n = 10s cmA, cc = 10d,
cm-l FW
(15)
6 x 10-s n, cm-l (at 110 km). This is an extremely small gradient. Suppose Vn, exists as a sound wave of wavelength 1 = GnJVn, = Vg
(16)
where V, = speed of sound T = period of wave. During the period of a wave the irregularity in n established is (given that (13) is true) (17) Aj x BVn,/4-2 Thus where
x
(+I(?), Kl+
lo-lo m,n,2v,.
(18)
(19)
. 8
Assuming V, = 3 x IO4cm see-l and the values of the other parameters following equation (14), Kl M 0.05 at 110 km. At 130 km (n, = 1011cm-a), Kl w O-5. During magnetic disturbance or at the aurora1 zones, when and where j is substantially increased, Kl is correspondingly increased. It is clear that weak irregularities in n can be generated by spatial variations in mobility of ionization caused by fluctuations (either moving or static) in n, within ionospheric currents responsible for magnetic variations. Irregularities in n so generated would tend to drift with their own characteristic speed(12p13). Let the current associated with these irregularities be Sj, then the electromagnetic term 13 may be written (jo+~j)xB.V~=joxB.V~+6j~B.V+
(20)
where j, is the background current in the absence of irregularities of any kind. Whilst the irregularities remain weak, the term Sj x B . 04 will in general be negligible compared to j. x B . V$. It follows that the morphology of the irregularities in n will be determined by the action of j. x B on the irregularities in 4 (i.e. in n,). The action of Sj x B . V+ will be a superimposed second order effect. However if there were phase identity of a wave in Sj and a wave in 04, then dj x B . V+ may be constant over long periods of time, allowing build up of ionization thereby. The conditions for this build up would be sporadic and very critical.
764
K. D. COLE
It is to be expected that an object passing through the E-region would create perturbations in neutral particle density in its wake and so give rise to perturbations in ionization density in the wake. This would give such an object a radar cross section greater than its own dimensions. (b) The second type of cause of weak irregularities, viz. the term $B . V x j in (4), requires $B . V x j > 2c&jn. (21) In this case, it is required that ] V X jl > 2~~~~~~~B. (22) Using the same values as used after equation (14), equation (21) becomes (at 110 km), IV X j[ > 5 X 10w20e.m.u. cm-l.
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Irregularities in current would propagate through the ionosphere with a certain phase speed V, of order lo4 cm set-l. Suppose the irregularities in current exist in the form of a wave of-wavelength A. Then during the period ofa wave the irregularity in n established is (provided (21) is true) 6n R+$B , (V x j) . 2/V, (24) % $Bdj/V, where Sj is the amplitude of the wave, Thus
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where Ka has values similar to Kr discussed above. Thus it is clear that irregularities in current (e.g. hydromagnetic waves) propagating into the ionosphere produce irregularities in the electron density. Whitehead(14) has just proposed a theory of formation of equatorial sporadic E ionization on the basis of the phase coupling of a sound wave and an irregularity of ionization density. His m~ha~srn employs the term $B . V x j, su~esting that it remains of the same sign for long times in a frame of reference moving with the sound wave (and the irregularity). The compressions and rarefactions of the sound wave are supposed to generate a component of V x j in phase with that of the moving irregularity causing the Iatter to become stronger with the passage of time. The conditions for the functioning of this mechanism appear to be critical. (iii) If #jz > 2an&, it is required that
where f = &z/n. With $ = 10” condition (26) could be fulfilled in moderately strong aurora1 electrojets. It is clear that small scale irregularities can be generated by small-scale pe~urbations in neutral particle density and in current density.
SOME GENERAL THEORY OF ELE@TRoN DENSTI-Y IRREGULARITIES
It is usu;tl to suppose q = 0 at night. Equation (4) becomes, negkzting and also assuming only large-scale processes are operative (see Section 3)
765
the last term,
This suggests that although it may be normally expected that E-region ionization vanish at night because af the high recombination rate, electromotive forces driving current may force ionization down to the lower E-region and so maintain detectable ionization there, What is required is that jWV$ f ~~j~~~z > 0. (WI Since it is to be expected that ~j~~~~be negative (28) requires that the scale height for current be less than the scale height of # (i.e. of air density). 6. DISCUSSJXIN of concentrations of ionizations in the E-region has been discussed in simple general terms and some features of strong large-scale sporadic E have been explained thereby. It has been shown how small scale irregularities can be formed. Further work is desirable to apply this general theory to specific detailed ionospheric models. The formation
writer thanks Dr. D. F. Martyn, Officxv-in-Charge,Upper Atmosphere Section, C.S.I.R.O., Camden, for the: invitation to join his group’s discussions of upper atmosphere probleMs. For Acknowh&enzen&--The
stimuiating discussians he thanks tie foltowiq members of the group, Dr. E. B. Armstrong, Mr. R. A. Duncan, Dr. S. KatG, Dr. D. F. Matip,
Dr. J. H. Piddiigtcx~and Dr. 3. D. Whitehead.
1, D. F. MANYN, Prac. Roy. SOG.A246,306 (1953). 2. P. J. NAWRCKXI and R. PAPA,Atmospheric Processes. Geophysics Corp. of America, Bedford, Mass,
(1961). 3. E. K. SMIIX,JR., World-wide Occurrence of Sporadic E, NJ3.S. Circular 582 (1957). 4. W. G. BAKERand D. F. MARTYN,Proc. Roy. SOC. A246,281 (1953). 5. L. H. HEJSLER and J. D. WHITEHEAD, Nature 187,676 (1960). 6. J. D. WHITEMUQJ. Afmos. Terr. Phys. 20,49 (1961). 7. J. R. WILKES and R. W. E. MCNICOL,Aust. J. PIIYS.15, 236 (1962). 8. K. WEEKES, J. Atmos. Terr. Phys. Special supplement,p. 12 (1957). 9. K. D. C'o~~,Plonet, Space Sci, 10, 129 (1963). 10. J. W. DUNG=, Co&& ~~ecir~y~~~ics. Cambridge University Press (1958). 11. S. UT~, Rep. kvwy&. Z$kw Res. Japmz 13, 62 (1959). 12‘ K. D. COLE,Atrsr, J. I%hys.13,484 (2960). 13. C. F. CUMMOWand M. A. JORNSON, R, A&m. fem. Phys Z&21 (f959). 14. 3. D. wI.nTEHE AD,J. Atmog. Terr. P&,w.f1953j.
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