The first works on the application of field theoretical methods and topological concepts in the physics of two-dimensional plasma and fluids started before the year 2000. Essentially they were connected with the functional integral approach for the calculation of the irreducible correlations of fluctuating potential in a magnetically confined plasma. It was our persistent conviction that these methods are well suited, probably the best adapted to the nature of turbulence in confined plasma. It was a time when the main procedure to reflect the turbulence effect in the linear dynamics of an instability was renormalization according to the Direct Interaction Approximation. For the drift wave instability the DIA method has actually permitted to calculate the spectral exponent which compared favorably with the numerical simulations. However there was a long series of approximation and it was not exactly clear why not to start a full application of the theory of Renormalization Group, instead of calculating the change of the propagator. We used path integral methods to calculate the generating functional of the correlation of a classical drift wave turbulence. The first application of this approach was however different: to calculate the effect of trapping of diffusing particles. It was question, in that application, of the extrinsic trappong, due to magnetic islands and stable vortical structures or transient structures. Later the intrinsic trapping has been investigated by the original method that is based on the Decorrelation Trajectory Method.

We have applied for the first time a topological method to show the strong stability of convective structures in confined plasma in a work presented at the "Festival de Theorie" in Aix-en-Provence (2001).

We have continued with the application of the field theoretical methods in the study of plasma, but this time we have directed our efforts to coherent structures. They are known to play an important role in the transport processes even if they are actually transient in a real plasma.

*We have noted that the most important particularity of the motion in fluids and plasmas is represented by the Chern-Simons term in a Lagrangian. The source of inspiration were the works on the Fractional Quantum Hall Effect with a dynamics in which many aspects of plasma and fluids are common. This alowed us to propose the Lagrangian and to derive the equation sinh-Poisson for the asymptotic states of the Euler 2D fluid*.

During a visit in Japan we have extended the field theoretical method, from the Euler fluid to the 2D planetary atmosphere and 2D magnetized plasma (both described by the same equation Charney - Hasegawa - Mima).

We invested several years in the study of this equation, although the self-duality was not attained and there was a residual energy in the asymptotic states. The results were:

- a strangely good description of the characteristics of the tropical cyclone. We have derived two algebraic equations, connecting the main parameters:
- (1) the maximum azimuthal wind velocity;
- (2) the radius of the "eye-wall";
- (3) the maximum radial extension of the tropical cyclone. These equations have been revised in 2013 but without essential changes, only better coefficients.

- good description of the convective structures of a magnetized plasma, well compared with observation.
- crystal of vortices in non-neutral plasma
- the structure of the function space around the extremum solution; this revealed an important aspect, the existence of a direction almost degenerate in the function space, which allows the system to slide almost effortless (small input of energy and vorticity) and access cuasi-singular states, a reflection of the vorticity concentration.

We have written an application for an European Competition ERC in 2011. The two marks obtained for the Project and for the Principal Investigator were not high enough to allow the access to the last phase of the competition. But the two marks were high enough to qualify for a special treatment set up by the Commission. It was demanded to the Member States to award a grant for support of the Projects that belonged to this cathegory. This was the origin of the Grant for the Contract ERC - Like nr.4/2012, the present Project.

The basis of the Project has in principle been adopted the Project submitted to the ERC competition of the Commission. However the duration of the ERC-Like grant has been established to two years (the original Project submitted to the Commission were elaborated for a duration of five years). Inevitably, part of the objectives of the initial (5 years) Project cannot be realized in the present (2 years) Project.

However we must express our gratitude for this extraordinary opportunity, to work on this subject and to have the occasion to make advancements

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