Dynamics of Alfvén waves in the night-side ionospheric Alfvén resonator at mid-latitudes

Abstract

Abstract.A numerical solution of the problem on dynamics of shear-mode Alfvén waves in the ionospheric Alfvén resonator (IAR) region at middle latitudes at nighttime is presented for a case when a source emits a single pulse of duration τ into the resonator region. It is obtained that a part of the pulse energy is trapped by the IAR. As a result, there occur Alfvén waves trapped by the resonator which are being damped. It is established that the amplitude of the trapped waves depends essentially on the emitted pulse duration τ and it is maximum at τ =(3/4)T , where T is the IAR fundamental period. The maximum amplitude of these waves does not exceed 30% of the initial pulse even under optimum conditions. Relatively low efficiency of trapping the shear-mode Alfvén waves is caused by a difference between the optimum duration of the pulse and the fundamental period of the resonator. The period of oscillations of the trapped waves is approximately equal to T , irrespective of the pulse duration τ . The characteristic time of damping of the trapped waves τ dec is proportional to T , therefore the resonator Q-factor for such waves is independent of T . For a periodic source the amplitude-frequency characteristic of the IAR has a local minimum at the frequency π/ω=(3/4)T , and the waves of such frequency do not accumulate energy in the resonator region. At the fundamental frequency ω=2π /T the amplitude of the waves coming from the periodic source can be amplified in the resonator region by more than 50%. This alone is a basic difference between efficiencies of pulse and periodic sources of Alfvén waves. Explicit dependences of the IAR characteristics (T , τ dec , Q-factor and eigenfrequencies) on the altitudinal distribution of Alfvén velocity are presented which are analytical approximations of numerical results.

Modeling diurnal variations of the IAR parameters

“…According to these calculations, dependence of resonant frequencies on harmonic number n was approximated as x n =X A ' ð2n þ 1Þ=3, whereas the interval between eigenfrequencies was Dx=X A ' 2=3, where X A is the resonator fundamental frequency. In our model the ratio Dx=X A ¼ 1:18 for UT = 4, and 0.86 for UT = 16, which is different from 0.66 in (Alpatov et al 2005).…”

“…The factor in the linear regression a ¼ À0:95 is also very close to 1. Therefore, the dependence of TEC (measured in TECU = 10 16 m À2 ) on Df is well approximated by formula We compare our modeling results with the spectral relationships from Alpatov et al (2005) numerical model based on approximation of n A ðzÞ and a perfectly reflecting E-layer. According to these calculations, dependence of resonant frequencies on harmonic number n was approximated as x n =X A ' ð2n þ 1Þ=3, whereas the interval between eigenfrequencies was Dx=X A ' 2=3, where X A is the resonator fundamental frequency.…”

Use of the International Reference Ionosphere 2012 model to calculate emission frequency scale of the ionospheric Alfvén resonator

“…here T 0 is the Alfvén travel time between the resonator walls, or the bounce period in terms of Alpatov et al (2005); l bottom and l top are the positions of the resonator lower and upper walls, respectively; A(l) is the Alfvén speed…”

“…Pokhotelov et al (2000) found frequency dispersion of the IAR eigenmode due to the Hall conductivity. Alpatov et al (2005) calculated the characteristics of the Alfvén waves propagating between the Earth's surface and the upper ionosphere using a numerical model. They analyzed two types of external wave sources: pulse and monochromatic oscillations.…”