RADIO SCIENCE Journal of Research NBS jUSNC- URSI Vol. 69D, No. 3, March 1965 Study of the Phenomenon of Whistler Echoes T. Laaspere, W. C. Johnson, and J. F. Walkup Contribution From the Radiophysics Laboratory, Thayer School of Engineering, Dartmouth College, Hanover, N.H. (Received July 6, 1964; revi sed Nove mbe r 5, 1964) In considering the propagation of long whistle rs and whistle r echo trains, the question arises about where the downcoming whistlers are refle cted. The several s uggestions that have been made include ground reflection and refl ection at the lowe r boundary of the ionosphere. In either case, the echo of a daytime whistler would make several more passes through the absorbing V region than the whistler itself, a nd we should expect whistl ers occurring a round noon to have a much smaller probabil­ ity of havin g echoes than whistlers occurring at ni ght. An analysis of several years of data obt ained a t the Da rtmouth Co ll ege whistl e r stati on yield s the result, however, that although the ave rage whi stl er rate is muc h hi ghe r at ni ght than during the day, the probability of a whi stl er having a n echo shows little cha nge from midnight to midday. Consistent with this observati on are the results of anoth er study showing that the diffe rence in the intensity of a noo ntime whis tle r and its echo may be onl y a few decibels. If th e th eoreti cal predicti ons about absorption of whi s tle r-mode waves a re even nearly correct, our results on whi stl e r echoes a re in compatible with the lowe r-boundary or ground·re fl ecti on model. In no cases studied by us has the whis tler echo been more inte nse th a n the whi s tl e r itself, a nd we do not at present favor th e id ea that whistle r echoes are a mplifi ed in the magne tosphere. A model consistent with our results is one in whi ch a la rge fraction of the e ne rgy of a down coming whi stl e r is refl ected above V·region heights. In this model a whistl er may be pictured as bounc in g bac k a nd forth between th e ionospheres of the two opposite he mispheres, with some of the e nergy " leaking through" to the ground at one or both ends of the path . Whistle r observations could also be explain ed by a model in whi c h the daytime transmission loss fo r VLF e ne rgy is hi gh onl y for the first upwa rd pene tra­ ti on of the ionosphere, bu t small once the e nergy is propagating in the " whi stler mode." Eckersley [1928] appears to have been the first 1. Introduction to give a description of whistler echo trains. They Whistlers are a type of audio·frequency electro­ were described in more detail in Storey's [1953] magnetic waves of natural origin. Most whistlers are classic paper in the context of the theory that whistlers undoubtedly initiated by lightning fl ashes, but they are travel from hemisphere to hemisphere along mag­ also known to be generated in other impulsive events, netic lines of force. The height of refl ecti on of whist­ such as nuclear explosions. The frequency versus lers at the e nd of the path received little scrutiny by time be havior of whistlers is determined by the di s­ Storey, who spoke simply of reRection " from the persive propagation of the initiating impulse along a earth's surface." A paper by Smith [1961] , however, propagation path following, more or less, lines of force speaks explicitly of reRection " from the lower layers" of the e arth's magneti c fi eld. A "short whistler" is (of the ionosphere), and Helliwell [1963] discusses in initiated by an impulse in the hemi sphere opposite to some detail the conditions which would lead to reflec­ that of the receiver and undergoes a one·way trip tion of a downcoming whistler at the lower boundary through the magnetosphere; a " long whistler" is initi­ of a model ionosphere. A nighttime rocket flight has ated in the hemisphere of the receiver, where it is recently shown that whistlers may indeed be present observed after it has been returned from the other in the ionosphere, but not at the ground below [Cart­ hemi sphere. The " echo" of a short whistler will wright, 1964]. thus have traveled through the magnetosphere three The height of reflection of whistler-mode waves has times, the echo of a long whistler four times. Often also been considered by Helliwell, Katsufrakis, and an echo has echoes of its own, resulting in a string of Carpenter [1962] in their study of propagation of echoes of increasing dispersion - a whistler echo "whistler-mode" waves from Navy VLF stations. train. F or observational results concerning the They suggested that rapid changes in the index of whistler phenomenon the reader is referred to the refraction, such as may be caused by a valley of ioni­ papers of Helliwell and Morgan [1959] ; Helliwell and zation between the E and the F regions, could protect a Carpenter [1961] ; and Laaspere, Morgan, and Johnson round-trip signal from absorption in the D regi on of the [1963] . Whis tler propagation theory has recently hemisphere opposite to the receiver. From the diur­ been summarized by Gallet [1963] . nal variation of the whistler-mode waves in both hemi- 407 spheres they concluded, however, that at the frequen­ GROUND TRAPPING cies involved the reflection probably takes place at the REFLECTION lower boundary of the ionosphere or from the ground. MODEL MODEL SHORT FIRST 5 FIRST Altman and Cory [1962] have recently predicted WHISTLER ECHO that even in the frequency range 3-5 kc/s, where they find the minimum transmission loss for whistler-mode waves, absorption introduces a loss of about 15 dB in 4 a one-way passage through the ionosphere during the day and about 2 dB at night. Altman and Cory's calculations are in general agreement with those of Leiphart, Zeek, Bearce, and Toth [1962], who arrived at an absorption loss of 27 dB for the day and 2 dB for the night for a wave of 18 kc/s. (To the 18 kc/s figures 3 just quoted, Hodara [1962] adds a reflection loss of 12 dB during the day and 10.5 dB at night.) Similar theoretical results on the transmission loss have been obtained by Swift [1962] and by Jesperson and Pitte­ way [1963] by a full-wave solution. Field intensity measurements in the ionosphere at 18 kc/s appear to 2 support the high theoretical values of the transmission loss [Leiphart, Zeek, Bearce, and Toth, 1962; Lomax, SOURCE LONG FIRST SOURCE LONG FI RST 1961] . WHISTLER ECHO WHISTLER ECHO In the presence of the high transmission loss pre­ dicted by Altman and Cory and others, a daytime FIGURE 1. Two models of whistler propagation. whistler echo would be an extremely unlikely event if reflection were at the ground or at the lower boundary of the D region, since in both of these models the echo sphere. In figure 1 the space between the two ground makes four more transits of the absorbing region than surfaces is divided only into three regions by two par­ the whistler itself. From observations such as those tially reflecting layers, interfaces, or other gradients to be discussed in sections 3 and 4 we know, however, existing in the ionosphere: regions 2 and 4 should be that it is not particularly uncommon for a daytime considered to represent the lower ionospheres of the whistler to have one or even several echoes. We will two hemispheres, region 3 the upper ionosphere and also show that the intensity decrement between a the magnetosphere. It is probable that the actual daytime whistler and its echo is sometimes only a situation is best represented by a trapping model few decibels. We conclude that either the daytime involving more than two reflecting regions. Our ionospheric transmission loss of whistlers is much considerations could easily be extended to the more lower than the theories predict, or the models involv­ general case, but this has not been done in this paper ing whistler reflection at the ground or at the lower to keep the arguments as simple as possible. boundary of the ionosphere are inapplicable at least The intensity decrements between component waves during the observing periods around noon when the in a whistler echo train are derived in the appendix D-region absorption reaches its maximum value. for several different propagation models. As shown by (1), in the ground reflection model the intensity 2. Models of Whistler Propagation decrements are determined by reflection losses suf­ fered by a component wave at all of the interfaces of We suggest that the low values of intensity decre­ figure 1 and by absorption losses in passing twice ments in a daytime whistler echo train can be ex­ through each of the regions 2, 3, and 4. If the whis­ plained by "ionospheric trapping", which is based on tler echo train is trapped in region 3, however, then, the idea of reflection of the downcoming wave in the as is shown by (5), the intensity decrements are in­ ionosphere. In this model a whistler may be pic­ dependent of absorption in regions 2 and 4, being tured bouncing back and forth between the iono­ determined only by absorption in region 3 and by the spheres of the two hemispheres, with reflections oc­ reflection coefficients of the interfaces 3-2 and 3-4.