Wave hop theory of long distance propagation of low-frequency radio waves

Abstract

The idea that long radio waves propagating between th e earth and ionosphere via di screte hops ean be extended far into the shadow region by evalu ating a series of complex in tegrals is exploit ed in t hi s paper. I llustrative calcu lations of LF and VLF hops and total fields are shown as a function of distance. The second and higher hops show a p seudoBrewst er angle just before the caust ic and attenuate like ground waves in the shadow region.The form of the series of in tegrals for an an isotropic ionos phere is given , and a model anisotropic ionosph ere varyin g with height is used in a sample calcu lation .On ly a s rnaJl error is caused by writing eac h hop as the product of an e ffective ionos ph"rie r eflection coefficient and an integral which is a function only of the other characteris ties of the path .

Wave-hop method of calculating propagation at LF and VLF, and stationary phase

“…It is calculated as follows from the relation between the phases of ,,R,, at two different heights. If the phase at zero height is 9 0 and at height h r it is 9 r , then this relation is [5] 9 r = 9 0 + 2kh r cos (1) It is known that the phase of ,,/?,, is nearly constant and equal to n over a range of angles of incidence near grazing if h r is given an appropriate value. To find this value put 9 r = n in eqn.…”

“…The wave-hop technique of calculating propagation at LF and VLF has been employed with success for many years following its introduction by Berry and others [1,2] in 1964. A computer program by Berry and Herman [3] has been in widespread use for this purpose.…”

On the effect of heavy ions on LF propagation, with special reference to a nuclear environment

“…The reflection height, h , was defined as the height at which the upgoing wave was 10 db below the incident wave. For the normalized production rate Qo =10* (figure 42 [Berry, 1964] [Berry, 1964]. This does not occur in the first hop, since it is not reflected from the ground; and the minimum is sharper in the third hop, which is reflected twice.…”

“…figure 6, as a function of frequency. These reflection coefficients were then used as input to the wave hop (time mode) propagation program described in the previous paper [Berry, 1964]. As a first approximation, the bottom of the ionosphere model was chosen as the reflection height.…”

Zonal harmonics in low frequency terrestrial radio wave propagation.

“…Equation The solution for the vertical electric field, E r , can be written, [Berry, 1964b] figure 1. Thus, the first ionosphere wave, j = 1, has a reflection point [l, 1 ], located in the middle of the propagation path.…”