Section: New Results

Ionospheric plasma

Participants : Didier Auroux, Sebastian Minjeaud.

In order to guarantee the integrity of the european positionning system Galileo, it is fundamental to identify all the potential sources of system unavailability. One of the main sources that has been identified is the phenomenon of ionospheric scintillations which causes radio frequency signal amplitude and phase variations when satellite signals pass through the ionosphere. Scintillations appear as the turbulent aspect of a larger disturbance of the ionospheric plasma density, which has the shape of a plasma bubble. In this context and in the framework of the ANR IODISSEE, a model hierarchy aimed at representing the evolution of the ionospheric plasma was proposed (Besse and al., 2004). It is based on an asymptotic analysis of the Euler-Maxwell system thanks to typical scales of the physical parameters involved in this framework. Among these models the simplest, referred to as the Striation model, describes the evolution of the quasineutral plasma in a plane perpendicular to the earth magnetic field. The magnetic field is assumed constant, and both electron and ions inertia are neglected. In this model the mobility of charge particles is assumed infinite along the magnetic field lines so that they constitute equipotential for the electric field. This property allows the computation of the electric field by means of a two dimensional elliptic equation with coefficients integrated along the magnetic field lines. This equation is coupled to either a two or a three dimensional transport equation for the evolution of the plasma density.

Data assimilation

We worked on data-models coupling method to identify the parameters of the Striation model (especially, the initial data for the electronic density and the ion/neutral collision frequency). Some measurements acquired during the mission of satellite DEMETER will constitute the set of observed data. We consider this problem from an optimal control point of view. We define a cost function measuring the misfit between the observed data and the corresponding model states. This function can be seen as a function of only the input model parameters. The previous inverse problem is then equivalent to minimizing this cost function. Of course, this problem can be ill posed (over or under-determined, non convex...) and we need to add some regularization terms (mainly Tikhonov terms), using some a priori estimation of the model parameters. The effective minimization of the cost function (in order to estimate the best possible set of model parameters) relies on the computation of the adjoint state. Thanks to the help of L. Hascoet, the adjoint of the Striation code was derived and validated with the automatic differentiation tool TAPENADE. We obtained the first results of coefficients identification in very simple situations.

Wave Propagation

The electronic density fluctuations of the ionospheric plasma have been identified as the main causes of the scintillation phenomena since they induce some variations of the amplitudes and phases of the signals passing through the ionosphere. These fluctuations have indeed a direct influence on the refractive index of the medium. A code was developed to simulate the propagation of wave signals in the perturbed ionosphere (whose representation is obtained thanks to the Striation code). We chose to use the method of the Rytov approximations which allow to obtain sufficiently accurate results (since, e.g., it takes into account the diffraction due to the small structures) whithin a reasonable computational time (contrary to the resolution of the whole Maxwell system). This work was carried out during the Master 2 internship of Gonzalo José Carracedo Carballal (advised with P. Lafitte, Ecole Centrale Paris).