Intermittency and coherent structures in ionospheric and magnetospheric turbulence a nonperturbative: a nonperturbative approach to space plasma transport

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Batchelor and Townsend (1949) were probably the first ones to report that small scales of high-Reynolds number Navier-Stokes turbulence were intermittent. We now strongly believe that intermittency might be the cause behind the existence of non-Gaussian tails in the PDFs. The conventional  approach has consisted of treating the turbulence problems perturbatively. The conventional models have failed to catch the essence of intermittency. Indeed, many phenomena, in various fields of physics and in plasma physics in particular, manifest themselves through a tail in the PDFs. The challenge is to develop mathematical models that enable the extraction of PDFs from nonlinear partial differential equations. One such model is the "Instanton" model first developed in Quantum Mechanics and Quantum Field Theory (t'Hooft). We propose to apply the "Instanton" formalism to the problem of ionospheric turbulence as it occurs in the auroral E and F regions and to the problem of ion acoustic turbulence as it occurs in the auroral acceleration region. We propose to apply and develop suitable nonperturbative techniques to first look at ionospheric turbulence, described by PDEs very similar to the Hasegawa-Wakatani equations. Our first step will be to apply the Instanton formalism to the non-dissipative case, where exact nonlinear coherent structures are known to exist. The second step will consist of including the dissipation mechanisms and assessing their impacts on the nondisspative solution. The third step will consist of extracting the PDFs and calculating the needed moments to establish a base for comparison with ionsopheric and auroral acceleration observations.