Equatorial magnetosonic waves observed by Cluster satellites: The Chirikov resonance overlap criterion

Magnetosonic waves play an important role on the overall dynamics of relativistic radiation belt electrons. Numerical codes modelling the evolution of the radiation belts often account for wave-particle interaction with magnetosonic waves. The diffusion coefficients incorporated in these codes are generally estimated based on the results of statistical surveys of the occurrence and amplitude of these waves. These statistical models assume that the spectrum of the magnetosonic waves can be considered as continuous in frequency space. This assumption can only be valid if the discrete nature of the waves satisfy the Chirikov overlap criterion. Otherwise the assumption of a continuous frequency spectrum could produce erroneous results in wave models and hence estimates of the electron diffusion coefficients used in numerical models of the inner magnetosphere. Recently it was demonstrated, through a case study conducted on a single short (10~s) period snapshot within a longer wave event, that the discrete nature of the equatorial magnetosonic waves do satisfy the Chirikov overlap criterion and so the assumption of a continuous frequency spectrum is valid for the calculation of diffusion coefficients. This paper expands this study to a broader range of time with many magnetosonic wave events to determine whether the discrete nature of the waves always satisfy the Chirikov overlap criterion. The results show that most, but not all, discrete magnetosonic emissions satisfy the Chirikov overlap criterion. Therefore the use of the continuous spectrum, employed in quasi-linear theory, may not always be justified.