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## Reflection from the ionosphere and exit to the ground of whistler wave packets: A dynamical model

In the theory of wave propagation in near-Earth space, there is a long-standing but still unsolved problem —

this is the problem of whistler exit to the ground after passing through the magnetospheric trajectory. Snell’s

law forbids exit of a wave to the ground if the angle between the wave normal and the vertical is outside the

penetration cone, which is almost always true, at least for middle and low latitudes. However, whistlers are

often recorded at ground stations, where they were first discovered. Most of the previous theoretical works

considered the exit of whistlers to the ground as a stationary problem, taking the wave field in the form

**E **= Re[𝐄_0(ℎ) exp(𝑖𝜅𝜉 − 𝑖𝜔𝑡)] with a constant frequency 𝜔 and a constant wave number 𝜅, where ℎ and 𝜉 are

the vertical and horizontal coordinates, respectively. Taking the field in this form assumes that the parameters

of the medium are time independent and change only in the vertical direction. However, those are necessary,

but not sufficient conditions for using the above given form of the wave field. It is clear that the real problem

is not stationary, and the wave packet incident on the ionosphere from above is limited both in vertical and

horizontal directions. Investigation of the whistler wave packet reflection from the ionosphere and exit to the

ground as a non-stationary two-dimensional problem is the subject of this work.