A Maximum of Temperature in the Middle Ionosphere
J. FUCHS1 has already pointed out the fact that from the change of electron-density (N) with height (h) conclusions as to the temperature in the ionosphere can be drawn. It was, however, not possible then to carry out exact calculations for two reasons: first, the electron-density was only known to be dependent on the apparent height (h′), and secondly, the process of electron loss was not known in more detail, so that Fuchs had to calculate with a recombination-coefficient constant as to space and time.
Studies of the new ionospheric model: II
ZusammenfassungDie vom Central Radio Propagation Laboratorium (National Bureau of Standards, Boulder) seit einiger Zeit veröffentlichtenN (h)-Profile für die Station Puerto Rico wurden dazu benutzt, die seinerzeitigen Modellvorstellungen weiter auszubauen. Als eine wertvolle Ergänzung hierzu wird die Variation der Elektronenkonzentration mit der Höhe herangezogen, wie sie mit Hilfe von Mondreflexionen oder mittels der Radar-Streuecho-Methode beobachtet wurde. Die wichtigsten, so gewonnenen Erkenntnisse sind:a)Der Vorgang der Elektronenvernichtung kann rein formal dargestellt werden durch den Ansatz
$$\begin{gathered} L = \alpha _0 \cdot \sqrt p \cdot N\,bei\,Quasi - Anlagerung, \hfill \\ L = \alpha _0 \cdot T \cdot N^2 \,bei\,Quasi - Wiedervereinigung, \hfill \\ \end{gathered} $$
 worinL die pro Zeit- und Raumeinheit verschwindende Anzahl von Elektronen,p den Druck,T die absolute Temperatur undN die Elektronenkonzentration bedeuten.Beide Ansätze ergeben jedoch in ihrer Ausdeutung, daß die Zahl der verschwindende Elektronen direkt proportional der TemperaturT gesetzt werden muß.b)Die SkalenhöheH weist im Bereich von rund 200 km Höhe tagsüber ein markantes Maximum auf. Oberhalb dieses Bereiches findet man daher einen negativen GradientendH/dh. Erst im Bereich desF2-Maximums geht der Betrag dieses Gradienten auf sehr kleine Werte zurück; man wird dort praktisch mit einer von der Höhe unabhängigen Skalenhöhe rechnen können.c)Die Skalenhöhe für diese räumlich annähernd isotherme Region variiert mit der Jahres- und Tageszeit. (Höchste Werte etwa Sommer-Mittag).d)Das Maximum der Skalenhöhe wächst bis etwa Mittag ungefähr proportional
$$\sqrt {\cos \chi } $$
 (χ=Zenithwinkel der einfallenden Strahlung) an, nimmt hingegen am Nachmittag nur langsam ab. Gleichzeitig ändert sich auch die Höhenlage, in der dieses Maximum auftritt: Am Vormittag findet man eine rasche Verlagerung in größere Höhen, am Nachmittag ein nur langsames Absinken.e)Dichte-Profile zeigen diesem Skalenhöhe-Maximum entsprechend in rund 200 km Höhe einen Wendepunkt-ähnlichen Verlauf, wie er auch aus Satellitenbahnen errechnet wurde.f)Die Vorgänge bei Ionosphärenstürmen können derzeit noch nicht mit voller Sicherheit erfaßt werden. Es wären hierfür laufende Mondecho-Beobachtungen (mit der Zweifrequenzen-Methode) dringend erforderlich.SummaryStarting-point for our study was the static balance equation where the electron production is equated to the effective recombination. For the latter process we use the generally valid formula
$$L = \alpha _0 \cdot p^k \cdot T^n \cdot N^{m + 2} $$
 as introduced byBurkard. It was one of our first tasks to find appropriate numerical values for the constantsk, m, n. Thereby the following possibility presented itself: TheN(h) profiles derived from observations are represented in power series, that is in powers of «x», wherex designates the height from the layer peak upwards. Similarly, we can also set up such power series for the scale heightH, the pressurep and the density ρ. A comparison of coefficients thus should enable us to computeH (h) profiles.It turned out, however, in the course of this study that the accuracy of the observational material [e.g. theN (h) profiles at hand] is not sufficient for such a comparison of coefficients, so that we had to look for other ways.We were finally successful in determining from the observational material the numerical values for the hitherto undefined constantsk, m, n. Here two different possibilities result, according as we assume quasi-recombination or quasi-attachment. In many cases, so for instance in the derivation ofH (h) profiles, it did not prove necessary to decide upon one of these two possibilities, so that the computed values are valid for both models.One fact is probably of special importance, namely that the process of electron loss is found as a linear function of the temperature of the neutral gas (or the electron gas). Here further studies will be necessary, in order to interpret this result on the basis of molecular or atomic theory.The model presented in this study is mainly based onN (h) profiles, but agreement is also excellent with observations obtained by the moon-echo method, moreover, with determinations of density derived from satellite orbits. In this connection valuable information is obtained fromH (h) profiles which were computed for many cases and which show the diurnal variation of the scale height. Additional calculations were performed in order to determine the seasonal variation of the scale height at least basically.TheH (h) profiles show that at a height of about 200 km a considerable increase in temperature can be observed in the daytime. There the scale height varies between about 80 km and 170 km (Station Puerto Rico, July). At higher altitudes, however, those variations are considerably smaller, amounting to only about 30 km. In these altitudes we also find gradients of the scale height whose derivation from zero is very slight. Calculation of anN (h) profile obtained by the Scatter-Radar-Method (Bowles) yielded an almost constant scale height from a height of about 340 km upwards to altitudes of 700 km. Seasonal variations, however, proved to be much higher. For the layer maximum under consideration relatively small values for the scale height were found for winter-time and values 1.4 times larger for summer-time. Also the diurnal variation at a height of about 200 km is much less noticeable in the winter-time. The maximum of the scale height changes its height also with the time of the day and the year reaching its maximum at summer noons.Since the present study deals with models only, some of the expressions used for calculation had to suffer a few neglects in order to avoid unnecessary complications. Thus the variation of gravity with height was neglected. Also the diffusion of electrons was not taken into account and present results indicate that those processes of diffusion do not prove as important as is generally assumed.In conclusion we make a few suggestions as to an effective continuation of the investigations reported here.
The formation of the ionospheric layers F-1 and F-2
Abstract Detailed investigations of the electron distribution in the F-2 region have recently shown ( Ratcliffe et al., 1956) that the F-2 layer could be formed by the ionizing agency which has its peak of electron production in the F-1 layer, if the loss-coefficient varies with height in a certain way, explained in the paper referred to. The implications of a loss-coefficient varying in this way are examined in detail in the present paper, and it is shown that it would explain the known facts about the splitting of the F layer into separate F-1 and F-2 layers. The question of what determines the height of the F-2 electron peak is also discussed.