The Toroidal Flow Effect In Axisymmetric Fusion Device

Toroidal rotation plays significant roles in many tokamak plasma processes.This thesis focuses on the effect of strong localized toroidal flow on tokamak equilibrium and the effect of three dimension on vertical displacement events(VDE).At first,we develop the toroidal rotational equilibrium code to prepare for the fol-lowing study.The Grad-Shafranov equation is solved using spectral elements for toka-mak equilibrium with toroidal rotation.The Grad-Shafranov solver builds upon and extends the NIMEQ code[Howell and Sovinec,Comput.Phys.Commun.185(2014)1415]previously developed for static tokamak equilibria.Both geometric and alge-braic convergence are achieved as the polynomial degree of the spectral-element basis increases.A new analytical solution to the Grad-Shafranov equation is obtained for Solov'ev equilibrium in presence of rigid toroidal rotation,in addition to a previously obtained analytical solution for a different set of equilibrium and rotation profiles.The numerical solutions from the extended NIMEQ are benchmarked with the analytical solutions,with good agreements.Besides,the extended NIMEQ code is benchmarked with the FLOW code[L.Guazzotto,R.Betti,et al.,Phys.Plasma 11(2004)604].The modification of pressure profile induced by toroidal flow is investigated.The relative change of pressure profile is found significant around the edge.Toroidal rotation is well known to play significant roles in the edge transport and L-H transition dynamics of tokamaks.Our recent calculation finds that a sufficiently strong localized toroidal rotation can directly bring out the formation of edge pressure pedestal with reversed magnetic shear that is reminiscent of an H-mode plasma,purely through the effects of toroidal rotation on the tokamak MHD equilibrium itself.In particular,the enhanced edge toroidal rotation enables a substantial peaking of the parallel current profile near edge in higher ? regimes,which leads to the flattening or reversal of the local q(safety factor)profile.Here the formation of pressure pedestal along with the reversed magnetic shear region is shown to be the natural outcome of the MHD tokamak equilibrium in a self-consistent response to the presence of a localized toroidal rotation typically observed in H-mode or QH-mode.VDE is so dangerous for tokamak devices that the feedback control system is ap-plied to most tokamak devices.However,the physics model of the feedback control system is the two dimension theory for VDE.The three dimension effects accelerate the VDE process.High n modes in three dimension VDE(3D-VDE)is growing as first and derive the magnetic island with high m.Then the magnetic islands are growing and overlapped by each other,leading to the destruction of magnetic flux surface,which induces and accelerates thermal quench(TQ)and the reduction of the safety factor at magnetic axis q0.The(1,1)magnetic island is formed when q0<1,which accelerates TQ.Meanwhile,the magnetic flux surface can re-form after it is destroyed completely.Besides,the plasma acts like the ballooning mode with finger and filament structures.