Electromagnetic plasma waves in the ion cyclotron range of frequencies (ICRF) are routinely used in magnetic fusion experiments to heat plasmas and drive currents. However, many experiments have revealed that wave energy losses in the plasma edge and at the wall are significant, and detected that the acceleration of ions into the walls due to the formation of radio-frequency (RF) sheaths is one of the root causes of this problem. Since the RF-enhanced sheaths have many undesirable effects, such as impurity production and hot spot generation, a predictive numerical tool is required to quantitatively evaluate these effects with complicated boundary shapes of tokamaks taken into account.In this thesis the numerical code that solves self-consistent RF sheath-plasma interactions in the scrape-off layer for ICRF heating is developed based on a nonlinear finite element technique and is applied to various problems in the one-dimensional (1D) and two-dimensional (2D) domains corresponding to simplified models for the poloidal plane of a tokamak. The present code solves for plasma waves based on the cold plasma model subject to the sheath boundary condition, in which the most important physics that happens in the sheath is captured without using the field quantities in the sheath.Using the developed finite element code, several new properties of the RF sheathplasma interactions are discovered. First, it is found in the 1D domain that multiple roots can be present due to the resonance of the propagating slow wave and its nonlinear interaction with the sheath. Second, sheath-plasma waves are identified in a 2D slab geometry, and it is proved in conjunction with an electrostatic 2D sheath mode analysis that the sheath-plasma wave only appears in the vicinity of the sheath surface if the plasma density is greater than the lower hybrid density, and its wavelength depends on various parameters. Third, as a consequence of the selfconsistent interaction between the propagating slow wave and the sheath, it is shown that the electric field distribution pattern in the plasma smoothly varies along the magnetic field lines between the conducting-wall and quasi-insulating limits.In the numerical analysis employing the 2D domain whose scale is equivalent to the Alcator C-Mod device, it is demonstrated that the calculated sheath potential can reach the order of kV, which is sufficient to yield enhanced sputtering at the wall. In addition, it is shown that the sheath potential in the close vicinity of the antenna current strap can be insensitive to the direction of the background magnetic field in the RF sheath dominated regime. Further, it is found from a series of nonlinear calculations that the sheath potential sensitively varies depending on the plasma density and electron temperature, which is consistent with the scaling derived from the Child-Langmuir law and the definition of the RF sheath potential.Lastly, a new finite element approach, which is named the finite element wavepacket method, is developed for the purpose of so...
SUMMARYA novel numerical scheme is developed by coupling the level set method with the adaptive mesh reÿnement in order to analyse moving interfaces economically and accurately. The ÿnite element method (FEM) is used to discretize the governing equations with the generalized simpliÿed marker and cell (GSMAC) scheme, and the cubic interpolated pseudo-particle (CIP) method is applied to the reinitialization of the level set function. The present adaptive mesh reÿnement is implemented in the quadrangular grid systems and easily embedded in the FEM-based algorithm. For the judgement on renewal of mesh, the level set function is adopted as an indicator, and the threshold is set at the boundary of the smoothing band. With this criterion, the variation of physical properties and the jump quantity on the free surface can be calculated accurately enough, while the computation cost is largely reduced as a whole. In order to prove the validity of the present scheme, two-dimensional numerical simulation is carried out in collapse of a water column, oscillation and movement of a drop under zero gravity. As a result, its e ectiveness and usefulness are clearly shown qualitatively and quantitatively. Among them, the movement of a drop due to the Marangoni e ect is ÿrst simulated e ciently with the present scheme.
SUMMARYA ow-condition-based interpolation ÿnite element scheme is presented for use of triangular grids in the solution of the incompressible Navier-Stokes equations. The method provides spatially isotropic discretizations for low and high Reynolds number ows. Various example solutions are given to illustrate the capabilities of the procedure.
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