Tearing modes play a key role in magnetically confined plasmas for thermonuclear interest. The nonlinear growth of these modes leads to the formation of the socalled magnetic islands. The study of magnetic islands is an important issue because they cause an increased radial heat and particle transport, thus compromising confinement, and they may also lead to major disruptions. In this thesis we addressed the study of magnetic island propagation and evolution in tokamaks, the main focus being on the drifttearing mode. We worked on two different issues, namely the analytical study of the propagation velocity of a freelyrotating island and the selfconsistent field profiles, and the numerical investigation of the regime of magnetic island propagation named "limit cycles", which has been recently observed in the Frascati tokamak FTU. On the first subject, we managed to include the neoclassical effects in a fourfield system of gyrofluid equations. To do that, we first computed the lowestorder Finite Larmor Radius (FLR) corrections to the poloidal flow damping by solving the gyrofluid equation for the ions under particular hypotheses and by using a procedure originally developed for the driftkinetic equation. Then we used a simplified version of the gyrofluid equations originally deduced by P. B. Snyder in his PhD thesis and we closed them by including the neoclassical effects mentioned above. This system of equations was then subject to further simplifications to find the radial profiles of the relevant plasma quantities in the presence of a magnetic island. Finally, we imposed the torquebalance condition on the freelyrotating magnetic island to compute the selfconsistent rotation velocity. The system of fourfield gyrofluid equations we have deduced generalizes the fourfield model adopted by Fitzpatrick & Waelbroeck in a series of dedicated papers and, in particular, the inclusion of the lowestorder FLR corrections to the poloidal flow damping leads to an additional term in the intermediatedamping case (which is relevant for realistic tokamak applications). The numerical resolution of the system of equations thus obtained, in principle, provides the island rotation velocity for different values of the plasma parameters entering the equations (within the limits of validity of the model). On the second subject, we investigated the nonlinear evolution of tearing modes in the presence of a large diamagnetic velocity to reproduce the dynamics observed in the regime of island propagation named "limit cycles”. The phenomenon consists in a quasiperiodic modulation of the amplitude and the rotation frequency of magnetic islands. This regime was named "limit cycles" because of the figure drawn by the trajectory of a point in the frequencyamplitude plane. To perform this task, we numerically integrated a simplified fourfield system of equations by using a finitedifference slab code developed by Daniela Grasso et al. from ISCCNR and Politecnico di Torino. To study this particular regime of island dynamics, we performed a series of simulations in the regime of large diamagnetic velocity, corresponding to a large equilibrium density gradient. We chose to try different values of the tearing mode stability parameter Δ' and of the plasma ß, which enters our expression for the diamagnetic velocity. For every choice of Δ' we observed a reversal of the amplitude growth in the nonlinear regime, for ß large enough. For particular values of these parameters, we managed to reproduce qualitatively the amplitude evolution of the islands in the “limit cycles” regime. We also observed a significant deformation of the island and a large component of the second harmonic, in agreement with the experimental observations. We ascribed this set of peculiar features to a stabilizing effect of the diamagnetic velocity in the nonlinear regime, caused by the flattening of the density profile inside the separatrix, which is also responsible for the island deformation.
Study of magnetic island propagation and evolution in tokamak plasmas
2017
Abstract
Tearing modes play a key role in magnetically confined plasmas for thermonuclear interest. The nonlinear growth of these modes leads to the formation of the socalled magnetic islands. The study of magnetic islands is an important issue because they cause an increased radial heat and particle transport, thus compromising confinement, and they may also lead to major disruptions. In this thesis we addressed the study of magnetic island propagation and evolution in tokamaks, the main focus being on the drifttearing mode. We worked on two different issues, namely the analytical study of the propagation velocity of a freelyrotating island and the selfconsistent field profiles, and the numerical investigation of the regime of magnetic island propagation named "limit cycles", which has been recently observed in the Frascati tokamak FTU. On the first subject, we managed to include the neoclassical effects in a fourfield system of gyrofluid equations. To do that, we first computed the lowestorder Finite Larmor Radius (FLR) corrections to the poloidal flow damping by solving the gyrofluid equation for the ions under particular hypotheses and by using a procedure originally developed for the driftkinetic equation. Then we used a simplified version of the gyrofluid equations originally deduced by P. B. Snyder in his PhD thesis and we closed them by including the neoclassical effects mentioned above. This system of equations was then subject to further simplifications to find the radial profiles of the relevant plasma quantities in the presence of a magnetic island. Finally, we imposed the torquebalance condition on the freelyrotating magnetic island to compute the selfconsistent rotation velocity. The system of fourfield gyrofluid equations we have deduced generalizes the fourfield model adopted by Fitzpatrick & Waelbroeck in a series of dedicated papers and, in particular, the inclusion of the lowestorder FLR corrections to the poloidal flow damping leads to an additional term in the intermediatedamping case (which is relevant for realistic tokamak applications). The numerical resolution of the system of equations thus obtained, in principle, provides the island rotation velocity for different values of the plasma parameters entering the equations (within the limits of validity of the model). On the second subject, we investigated the nonlinear evolution of tearing modes in the presence of a large diamagnetic velocity to reproduce the dynamics observed in the regime of island propagation named "limit cycles”. The phenomenon consists in a quasiperiodic modulation of the amplitude and the rotation frequency of magnetic islands. This regime was named "limit cycles" because of the figure drawn by the trajectory of a point in the frequencyamplitude plane. To perform this task, we numerically integrated a simplified fourfield system of equations by using a finitedifference slab code developed by Daniela Grasso et al. from ISCCNR and Politecnico di Torino. To study this particular regime of island dynamics, we performed a series of simulations in the regime of large diamagnetic velocity, corresponding to a large equilibrium density gradient. We chose to try different values of the tearing mode stability parameter Δ' and of the plasma ß, which enters our expression for the diamagnetic velocity. For every choice of Δ' we observed a reversal of the amplitude growth in the nonlinear regime, for ß large enough. For particular values of these parameters, we managed to reproduce qualitatively the amplitude evolution of the islands in the “limit cycles” regime. We also observed a significant deformation of the island and a large component of the second harmonic, in agreement with the experimental observations. We ascribed this set of peculiar features to a stabilizing effect of the diamagnetic velocity in the nonlinear regime, caused by the flattening of the density profile inside the separatrix, which is also responsible for the island deformation.File  Dimensione  Formato  

Casolari_Activity.pdf
accesso aperto
Tipologia:
Altro materiale allegato
Dimensione
33.57 kB
Formato
Adobe PDF

33.57 kB  Adobe PDF  Visualizza/Apri 
Casolari_PhDthesis.pdf
accesso aperto
Tipologia:
Altro materiale allegato
Dimensione
6.93 MB
Formato
Adobe PDF

6.93 MB  Adobe PDF  Visualizza/Apri 
I documenti in UNITESI sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/20.500.14242/142966
URN:NBN:IT:UNIPI142966