Numerical analysis of radio-frequency sheath-plasma interactions in the ion cyclotron range of frequencies

Abstract

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...

Self consistent radio-frequency wave propagation and peripheral direct current plasma biasing: Simplified three dimensional non-linear treatment in the “wide sheath” asymptotic regime

“…It remains however to be experimented, with, e.g., the goal of "selecting" a specific solution out of potential multiple roots for the nonlinear coupled RF þ DC problem. 26,38 The convergence of this iterative scheme remains an open issue. Although it was presented in a simplified parallelepipedic geometry, the asymptotic method can be implemented numerically in its present form on more complex 3D simulation domains as long as lateral boundaries are kept normal to B 0 .…”

“…Numerical implementation with magnetized plasma was only achieved recently in still very simple geometry. 26 At the RF frequency, the RF current through the sheath is supposed to be mainly a displacement current. In this framework, the sheath is assimilated to a parallel plate capacitor of width d, filled with a dielectric material of dielectric constant e sh .…”

“…A minimal fluid approach is followed, inspired by earlier work on RF plasma discharges [22][23][24] and recently applied to tokamaks. 17,25,26 The RF and DC parts of the model are coupled by non-linear RF and DC sheath boundary conditions at both ends of open magnetic field lines. The approach, called SSWICH (self-consistent sheaths and waves for ion cyclotron heating 27 ) allows interaction between neighbouring flux tubes via the exchange of a) Author to whom correspondence should be addressed.…”

“…Multiple roots were evidenced in some circumstances. 26 In order to gain insight into the physical behaviour of the full non-linear DC þ RF model, and to provide a good "first guess" for its iterative resolution, the self-consistent system is solved explicitly in the asymptotic limit when the width of the sheaths gets very large. This simplified regime is reached as the RF power launched by the ICRF antenna tends to infinity.…”

20 years of research on the Alcator C-Mod tokamak

“…The sheath is produced by rectification of the RF waves due to the difference between electron and ion mobility. 332,333 The resulting potential accelerates ions, increasing their sputtering yield when they impact a material surface. An indirect evidence for an RF specific mechanism is from boron film erosion rates, estimated to be in the range of 15-20 nm/s, consistent with the eroding species having an energy far above the thermal background.…”