Source of seed fluctuations for electromagnetic ion cyclotron waves in Earth’s magnetosphere

• EMIC wave development is closely related to and depends on wave activity in the Pc 4–5 ULF range.
• A nonlinear energy cascade from the Pc 4–5 range into the frequency range of Pc 1–2 pulsations is able to supply a level of seed fluctuations that guarantees growth of EMIC waves up to an observable level during one pass through the near equatorial region where the ion cyclotron instability takes place.
• A suggested generalization of the diffusion approximation is a valid phenomenological approach for studying the turbulence energy cascade under different physical conditions.

We consider a nonlinear wave energy cascade from the low frequency range into the higher frequency domain of electromagnetic ion cyclotron (EMIC) wave generation as a possible source of seed fluctuations for EMIC wave growth due to the ion cyclotron instability in Earth’s magnetosphere. The presented theoretical analysis shows that energy cascade from the Pc 4–5 frequency range (2–22 mHz) into the range of Pc 1–2 pulsations (0.1–5 Hz), i.e. into the frequency range of EMIC waves, is able to supply the needed level of seed fluctuations that guarantees growth of EMIC waves up to the observable level during one pass through the near equatorial region where the ion cyclotron instability takes place. We also analyze the magnetic field data from the Polar and Van Allen Probes spacecraft to test the suggested nonlinear mechanism. In this initial study we restrict our analysis to magnetic fluctuation spectra only. We do not analyze the third-order structure function, but judge whether a nonlinear energy cascade is present or whether it is not by only analyzing the appearance of power-law distributions in the low-frequency part of the magnetic field spectra. While the power-law spectrum alone does not guarantee that a nonlinear cascade is present, the power-law distribution is a strong indication of the possible development of a nonlinear cascade. Our analysis shows that a nonlinear energy cascade is indeed observed in both the outer and inner magnetosphere data, and EMIC waves are growing from this nonthermal background. All the analyzed data are in good agreement with the theoretical model presented in this study. Overall, the results of this study support a nonlinear energy cascade in Earth’s magnetosphere as a mechanism which is responsible for supplying seed fluctuating energy in the higher frequency domain where EMIC waves grow due to the ion cyclotron instability.