On the Spectrum of Ultralow-Frequency Oscillations of the Ionosphere in the Pc1 Range

Abstract—The concept of Alfvén waves plays a key role in the theory of ultralow-frequency (ULF) electromagnetic oscillations of extraterrestrial origin. This article is dedicated to the 80th anniversary of the discovery of Alfvén waves. It focuses on the ionospheric Alfvén resonator (IAR). IAR excites ultralow-frequency oscillations in the Pc1 range (0.2–5 Hz). When computing the oscillation spectrum within the standard model, it is assumed that the IAR is an autonomous dynamical system. In contrast, in this paper, IAR is treated as a specific subsystem of the general system of Alfvén oscillations of geomagnetic field lines. In other words, we proceed from the idea that IAR, in general, is not an autonomous oscillatory system. The problem about IAR spectrum is discussed in the context of the general problem on the spectrum of magnetohydrodynamic oscillations of the Earth’s magnetosphere. The corresponding Sturm–Liouville problem is formulated. Analytical solutions of the problem are considered in the Wentzel–Kramers–Brillouin approximation. It is pointed out that the problem of IAR spectrum has to be solved by numerical methods due to the rather complicated distribution of the Alfvén velocity along the geomagnetic field lines.