Numerical Calculations Related to the Rf Properties of the Plasma Sheath PDF Download
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Author: John Milan Pavkovich Publisher: ISBN: Category : Plasma (Ionized gases) Languages : en Pages : 206
Book Description
In many considerations of the rf properties of a finite plasma, the plasma is treated as a dielectric and the boundary conditions associated with an ordinary dielectric are applied. Although this approach works well at times, it is by no means a satisfactory approach to understanding the rf properties of the boundary. In this paper, a detailed rf theory of the sheath is presented. The complete collisionless Boltzmann equation is used to derive a linear integral equation for the rf electric field through the sheath. The analysis is one-dimensional. This integral equation is solved numerically for a semi-infinite uniform plasma bounded by a sheath defined by a parabolic dc potential. A Maxwellian distribution of velocities is assumed for all computations. The results show that it is reasonable to assume that the normal component of displacement is continuous but that extra waves are set up near the boundary which decay as one moves into the uniform plasma. These waves are somewhat like the cutoff waves excited in the neighborhood of a waveguide discontinuity and thus give rise to a sheath impedance. A pressure type theory is also presented. This theory is based on moments of the collisionless Boltzmann equation. The results do not agree very well with results of the more exact theory and thus it is concluded that this type of theory is rather unreliable. (Author).
Author: John Milan Pavkovich Publisher: ISBN: Category : Plasma (Ionized gases) Languages : en Pages : 206
Book Description
In many considerations of the rf properties of a finite plasma, the plasma is treated as a dielectric and the boundary conditions associated with an ordinary dielectric are applied. Although this approach works well at times, it is by no means a satisfactory approach to understanding the rf properties of the boundary. In this paper, a detailed rf theory of the sheath is presented. The complete collisionless Boltzmann equation is used to derive a linear integral equation for the rf electric field through the sheath. The analysis is one-dimensional. This integral equation is solved numerically for a semi-infinite uniform plasma bounded by a sheath defined by a parabolic dc potential. A Maxwellian distribution of velocities is assumed for all computations. The results show that it is reasonable to assume that the normal component of displacement is continuous but that extra waves are set up near the boundary which decay as one moves into the uniform plasma. These waves are somewhat like the cutoff waves excited in the neighborhood of a waveguide discontinuity and thus give rise to a sheath impedance. A pressure type theory is also presented. This theory is based on moments of the collisionless Boltzmann equation. The results do not agree very well with results of the more exact theory and thus it is concluded that this type of theory is rather unreliable. (Author).
Author: John Milan Pavkovich Publisher: ISBN: Category : Plasma sheaths Languages : en Pages : 22
Book Description
A theoretical treatment for the variation of rf fields within the sheath is given. The analysis is based on an integration of the collisionless Boltzmann equation, assuming that the static potential varies parabolically in the sheath. An effective impedance for the sheath can be defined, and that over the range in which the numerical results have been calculated, this impedance always has a real positive part. The real part of this impedance is associated with Landau damping. A set of curves is given of the field through the sheath. (Author).
Author: Haruhiko Kohno Publisher: ISBN: Category : Languages : en Pages : 191
Book Description
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 sheath plasma 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 self-consistent 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 wave-packet method, is developed for the purpose of solving for multiscale plasma waves in the tokamak poloidal plane accurately with reasonable computational cost. This method is established by combining the advantages of the finite element and spectral methods, so that important properties in the finite element method, such as the sparsity of the global matrix and the ease in satisfying the boundary conditions, are retained. The present scheme is applied to some illustrative 1D multiscale problems, and its accuracy improvement is demonstrated through comparisons with the conventional finite element method.
Author: John Milan Pavkovich
Author: John Milan Pavkovich
Author: John Milan Pavkovich
Author: John Milan Pavkovich
Author: 
Author: United States. National Bureau of Standards
Author: 
Author: 
Author: 
Author: Haruhiko Kohno
Author: Stanford University. Microwave Laboratory