ETD

Archivio digitale delle tesi discusse presso l'Università di Pisa

Tesi etd-03272018-104209


Tipo di tesi
Tesi di laurea magistrale
Autore
SCOTTO D'ABUSCO, MANUEL
URN
etd-03272018-104209
Titolo
Development of a genetic algorithm for transport studies in high-temperature laboratory plasmas
Dipartimento
FISICA
Corso di studi
FISICA
Relatori
relatore Prof. Pegoraro, Francesco
relatore Dott. Sattin, Fabio
correlatore Dott.ssa Carraro, Lorella
Parole chiave
  • transport
  • laboratory plasmas
  • global optimization
Data inizio appello
18/04/2018
Consultabilità
Completa
Riassunto
Getting nuclear fusion reactions on Earth is one of the most ambitious technological challenges of the last 60 years. In stars light nuclei can melt thanks to the force of gravity that compresses the matter up to density and temperatures such to trigger these reactions. On the contrary, strong magnetic fields are used on the Earth to confine the plasma until reaching the temperatures necessary for the triggering. These experiments have revealed over the years a fascinating but extremely complex physics. During my thesis work I approached a machine for experiments of this type, in particular a machine of the RFP type (Reverse Field Pinch) managed by the RFX laboratory and located in Padua. Its plasma is characterized by two somewhat different plasma confinement regimes. The first, called "multiple helicity" (MH), is prevalent in experiments at low plasma current. This scenario is characterized by a low level of confinement of matter and energy. The second regime is primarily identified by high plasma currents and called "quasi-single helicity" (QSH), and it is characterized by significantly better properties in terms of plasma temperature, confinement time, etc.

A laboratory plasma is inevitably constituted, alongside the main element, normally hydrogen or its isotopes, even by small percentages of heavier elements called "impurities", coming from contamination from the external atmosphere, the solid walls that enclose the volume of plasma and, in some cases, also from voluntary contaminations for diagnostic purposes made by the experimenters.
A significant presence of impurities is noxious to the performance of a plasma, since atoms with a high degree of ionization are efficient radiators, and consequently they cool the plasma in which they are immersed. The degradation of the fusion performance is naturally different depending on whether the impurities are localized in the core of the plasma, at a higher temperature and therefore more "valuable", or in the on-board area, already cold and therefore of lesser interest. On the contrary, the possibility of maintaining a relatively cold interface between the plasma and the material walls, decreasing the thermal load on them, possibly exploiting the radiative properties of the impurities, represents an interesting line of research.

For these reasons, the study of the dynamics of impurities within a laboratory fusion plasma is of extreme interest.
By treating impurities as a fluid, their dynamics can be described in good approximation by a diffusive motion. In cylindrical geometry, appropriate for the shape of magnetic confinement machines, it is formalized by the equation

\begin{equation}\label{impurity continuity}
\frac{\partial n_{z}}{\partial t} = -\frac{1}{r}\frac{\partial}{\partial r}\bigg[r \bigg(- D(r)\frac{\partial n_{z}}{\partial r} + v(r)n_{z} \bigg) \bigg]+S_{z}(r) \\
\end{equation}

Within this equation $n_{z}$ represents the spatial density of the generic ion with charge $z$ while $S_{z}$ collectively embraces all the terms of source or loss (ionization from states with different charge, recombination, absorption or release from the walls, etc .... Finally, the diffusion coefficients D (r) and convection V (r) (potentially also dependent on the ionic species) summarize the interactions between the ions and the main plasma that determine their transport. They assume the main role for the determination of the impurity dynamics.

Although there are several theories (some of them summarized in the thesis) that provide estimates for D, V, at present no one satisfactorily reproduces the experimental evidences. As a consequence, the current preferred approach is inverse: we start with measures that - in an indirect way - provide an estimate of $n (r, t)$ to infer a plausible pair of $D, V.$ This knowledge of transport coefficients, however partial and hardly extrapolated outside the experimental contexts from which they were extracted, still provides minimal information essential for each subsequent theoretical-modeling elaboration. From a mathematical point of view, the process considered is an optimization problem, in which a set of parameters is searched that minimizes some distance between a set of experimental data and the reconstructed numerical analogues, in our case, based on the transport model of equation above.

The need to manage an optimization problem with a potentially large number of degrees of freedom immediately induces to devise, if possible, automated methods of solution.
This thesis proposes to develop and use such an instrument in some reference cases. I have integrated three distinct elements within a single software tool:

(A) a database of experimental measurements of RFX. These are measures that, indirectly, are due to the spatial and temporal densities $n (r, t)$ of the ionic species of carbon and oxygen, the impurities present with greater abundance within RFX. Specifically, I considered plasma X-ray spectroscopy measurements, spectral line measurements emitted by specific C and O ion states, and plasma temperature measurements.

(B) A pre-existing transport code that solves a more sophisticated version of the equations (1) for the density of C and O for given data profiles of D and V and that, in the post-processing phase, produces the synthetic equivalents of the quantities measured at point (A).

(C) Finally, an optimization module compares the experimental data set (A) with the synthetic signals (B) and looks for the profiles $ D, V $ that minimize the difference between the two. The optimization algorithm is based on Genetic Algorithms, a consolidated tool in optimization problems.

During the thesis some examples of use of this tool are presented, with a wide discussion dedicated to the problems encountered and which had to be overcome.
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