“Chapman behaviour” in the lower ionosphere

“Chapman BehaviouP

in the lower ionosphere

Abstract-It is shown that CEAPNIAN’S reMions for the variation of critical layer with soles zenith angle can be applied to any point on that layer and assume monochromatic radiation. These results szuuthen applied to electron and it. is shown that “Chapman behaviour” can be detected to a height of 160 scale height of 10 OP 15 km.

CONSIDER

a

f’requen.cy and height of a that it IS not necessary to density vs. height profiles km being consistent with a

eont,inuum of solar radiation acting on an isothermal atmosphere. electron production rate can be written down immediately using ( 193 1) well-known equations for monochromat~ic radiation:

The resulting CHAPMAK’B

4(2,) = JP(z) exp [L -

(zO -

z) -

Ch ly exp ----(zO -

.z)>. dz

(1)

where zOis the height, (measured in units of scale-height) above some fixed datum level q(z,) electron production rate at z,, P(z) an unknown weighting factor depending on the frequency distribution of the incident radiat$ion and t,he radiation absorption coefEcient Ch y is Chapman’s function of solar zenith angle In equation (1) each elementary layer, due to a single band of radiation, is referred to conditions at the sub-solar point, and, by displacing the origin by log Ch y, may be referred to t,he maximum at the zenith angle under consideration. ~q~~ation (1) then becomes: q(zo j-

log 6% y) = pTij /P(z) / s ,$j

P&J

exp {l -

definition

(zO -- z) -

of

qo(zo)

exp (zO -

z)> . dz

(2)

(3)

It will be noticed that the integral in equation (2) is now independent of Ch y and is constant provided P(z) does not vary. If we introduce the equation of cont’inuity:

where N is ekctron density M recombination coefficient 229

then under quasi-equilibrium

and introducing

conditions:

equation (5) in equation

(3) we get:

N(z, + log Ch y) = Ch-” y X&)

(6)

provided cc is approximately constant with height. We see then that a layer due to non-monochromatic radiation formed in an isothermal atmosphere with large but uniform recombination coefficient preserves its shape and identity after being scaled by Ch-” y and lowered by log Ch y, and also the well-known Chapman relations s=N,Ch-“y and

(7)

h = h, + NlogChly

(8)

radiation or refer only to the are not necessarily consequences of monochromatic maximum of ionization. As the experimental data is in the form of h’(f) curves and Narf2 equation (6) may be rewritten: f(h,, + W log Ch ?/~u> = Ch-& yap 19) where H is the scale height of the atmosphere

and h, is the height in kilometres.

2. “CHAPMAN” BEHAVIWR IN TKE LOWER IONOSPHERE FOR QUASI-EQUII,IBRTUMCONDITIoxS It is We now have a method for testing Chapman behaviour in the ionosphere. first necessary to know the scale height. Various workers (MITR~, 1952) have estimated a height of t,he order of 10 km for the E-Inyer. Here separate va’fues of 5, 10, 15 and 20 km have been used. Curves of electron density vs. height at Christchurch, New Zealand were reduced to true height curves by KIXG’S met,hod (1954, 1956) for midday on one calm day each month of 1954; together with midday curves for each day of June 1954. Values of I* for different heights and different scale heights were calculated using equation (9). The mean and variance for each group was computed and Chapman behaviour judged by the fit of the two curves. These results are shown in Fig. 1. The curves show that the valnes isT = 10 km and f_t = 15 km give the best fit while Chapman behaviour has fallen off above h, = 160 km. 3. IIAIbv

VARIATIONS

Previous workers (MITRA, 1952, p, 295) hate found a good fit of E- and F&layer critical frequency to the lawf = j’a Ch-* 7) extending over large ranges of y). Hence it was decided to test the daily variations of the lower ionosphere by using equation

230

“Chapman Behaviour”

in the lower ionosphere

(9). June 1954records were again chosen. All suitable records at 0800, 1000, 1200, 1400 and 1600 hours i%WtT were reduced and values off for various heights computed. A scale height of 10 km was used. These results are plotted in Fig. 2.

O-2

0.4 0.6 ‘9 fo

Fig. 1. Values oft”

08

Fig. 2. Values

I.0

0.2

0.8

0.4 ‘9

0.6

0.8

fo

for two scleeted groups of data during 1954.

I.2

1.4

1.6 0.8 M.M.T., hr

I.0

l-2

of log f at a height of h, + H log Ch y for June 1954 showing daily variation. The dotted line give the expected form of the variation.

Here the fit is not so good and reasonable agreement is found only below 150 km. The poor agreement and large spread at 110 km may be attributed to the large gradient of electron density with height existing at the bottom of the E-layer. Any small error in height or slight perturbation will then make a la.rge error in logf. The 231

km

150

...j_2.

_.._J.-L_ ._i._.. j_-_

140 130 12Q

]

110

;?OOkm

0.9

0.9

07 %_ 8‘ O-E

35

04

effecting their critical frequencies, or due to the inherent di~~ulties itr ~o~~~~uti~g true heights. Let us try and eliminate the second possible cause. A record suitable for reduct.iou to a true height curw should be free from sporadic-24 aad have good clean unambiguous traces free from oblique ccboes. The ionograms of June 1954 were not entirely suitable for redu&ion but were as good as could ‘be expected from a long series of records. The most likely ~a3w3 of error in a reduction is an error in t
As a check of t’he results given in Fig. 2 the records for the 1 May 1956 were examined. These were a particularly good set and had t’he following characteristics: (a) they were free of sporadic-E: (b) good clean unambiguous traces free from oblique echoes. (c) non-infinite El crit’ical frequencies thus eliminating any possible effects due to valleys between layers. In Fig. 3(a) values of log j at a height determined by equat’ion (9) are plotted. Also plotted are values of log foEl and log f. Ch-’ yf for an arbitrary value off, h’li:l and /ho + log Ch y for an while plotted in t’he upper curve are IL,~,, El; arbitrary value of h,. The same dat’a are again plotted in Fig. 3(b) but this time each record is referred to lb,,, El as the basic height, measure thus eliminating their reliance on h’E1. Fig. 3(a) shows considerable variation from that expected and it is impossible to give a range of height or y where Chapman behariour is present. Furthermore as shown in Fig. 3(b) the differences are not explainable in t,erms of the most likely source of error (viz. h/El). It then appears t’hat differences are most likely explainable in terms of a perturbation of a Chapman layer. 4. APPLICATIOK TO EARLY S~XRISE-RECORDS At Christchurch before ground sunrise the E-layer appears first as a ledge on the bottom of the F-layer which gradually descends and forms a separate layer, this one we will call the E2-layer. Close to ground sunrise the layer stratifies and the lower critical frequency increases until it usually blankets the EB-layer. This layer preserves its identity during the rest of the day as the El layer. Initially it was hoped to use this early morning E2-layer as a clue to the process of electron removal above 160 km but the results were paradoxical and seem worthwhile reporting. Using equation (5) and previous estimates of CI,then q as a function of height can be computed. Midday curves and R’YDBECK’S (1946) values were used. By inserting these in equation (3) and using a scale height of 10 km the electron production rate at given heights near sunrise were found. The total number of electrons produced at a given height over a period was then compared with t,he number observed at the end of that period. In Fig. 4 pq(y, h) dt integrated numerically for va,rious values of h are compared with the N,h curves for y = yO. Values of q&z,,) were computed from the nearest suitable noon h’f curves in order to minimize possible variations of P(Z). The observed values of N are about an order of magnitude higher than that expected by extrapolation from the midday curves and show considerable variation between different mornings. A different value of scale height would not improve matters and it does not seem likely that the accepted value of recombination coefficient is out by a factor of ten. As the regular El-layer forms as a stratification below this E2-region it seems unlikely that the extra ionization is produced by radiation normally absorbed in the D-layer at small values of y. A layer with a critical frequency smaller than 1 MC (i.e. lower than the limit of the recorder) could affect the N,h curves but could not materially affect the general conclusions that the electron production rates are too high. It is possible that such a lower layer is present in t’he ,TV,h curve for 2 September 1955. 4

233

5. TOTBL SOL&a FLUX As was shown in the preceding section the electron production rate for conditions of overhead sun can be oomput’ed‘ We may use values of ~~(~~)below I60 km with some reliance and find the total electron production rate below this level. On the assumption that no appreciable number of seeondary electrons are formed in the ionizat&m process we may equate this to the number nf solar photons absorbed in this region. Using midday June 1954 curves for H = X0 km jq&h,,) * dh, is equal to l-3 >: IO9 photons.

Fig. 4. Comparison of total number of skctrons produced aver 8 given sunrise period (as extrapolated from t,he noon curves) to the number actually observed nt the end of that. period.

By extrapolating the ~*(~~)curve to 180 km (this should ncrtbe seriously in error) and by using a mean scale height of 45 km above 180 km together with Bradbury’s hypothesis as demonstrated by RATCLIFFE(1956) we may estimate the total ionizing photon flux for the ionosphere as 5.7 x 10s photons. On assuming a 6000°K black-body sun the photon flux is 1-O x 1Of0photons/cm” per see for energies above the first ionization potential of molecular oxygen and 9.3 x 10s ~llotons~enl~per see for energies above the first ionization pot.ential of atomic oxygen.

It has been found that it is possible to detect Chapman behaviour in the Iower ~ollosphere from curves below 160 km being consistent with a scale height of 10 or 15 km, The agreement was not as close as that found with the E-layer critical frequency. The aceuraoy of the method however does not preclude Chapman behaviour of the Fl-region which has its maximum above 160 km. It was found that departures from Chapman behaviour did exist which were more likely to be real pert~~rbat~ions than due to the inadequney of height resolution of the equipmer& It has also been found that the pre-sunrise E-layer could not be explaiued in terms of Chapman behaviour in an isothermal atmosphere with constant recombination coefficient. No explanation is oRered for this phenomenon. From the derived Nth curves the total solar flux absorbed in the ionosphere 234

“ChapmanBehaviour” in

the

lower ionosphere

has been estimated. This indicates that the flux is not seriously different from that expected from a black-body at 6000°K. Acknowledgements-This work is Observatory of the New Zealand The iV,h curves were computed BRAND and myself. This paper intendent, Mr. J. W. BEAGLEY.

part of the research programme of the Geophysical Department of Scientific and Industrial Research. by Mr. G. 8. M. KIITG. Mrs. R. Mason, Miss J. was published by kind permission of the Super-

REFERENCES CHAPMAN S. KING G. A. M. KING G. A. M. MITRA S. K.

Proc. Phys. Sot. Lond. 43, 26.

1931 1954 1956 1952

J. Atmosph. Terr. Phys. 5, 245. J. Atmosph. Terr. Phys. 8, 184. The Upper Atmosphere. The Asiatic Society Monograph

1956 1946

Phil. Trans. 248, 621. Chalmers Tek. HGgsk. Handl.

Series, Vol. V. RATCLIFFE RYDBECK

J. A. 0.

235

h-o. 53.