The present work is motivated by the importance of r.f. sheaths in determining the antenna-plasma interaction and the sensitivity of the sheaths to the complicated three-dimensional structure of modern ion cyclotron range of frequency (ICRF) antennas. To analyze r.f. sheaths on the plasma facing regions of the launcher, we first calculate the contact points of the tokamak magnetic field lines on the surface of the antenna Faraday screen and nearby limiters for realistic three-dimensional magnetic flux surface and antenna geometries. Next, the r.f. voltage that can drive sheaths at the contact points is determined and used to assess the resulting sheath power dissipation, r.f.-driven sputtering, and r.f.-induced convective cells (which produce edge profile modification). The calculations are embodied in a computer code, ansat (Antenna Sheath Analysis Tool), and sample ansat runs are shown to highlight the physics and geometry-dependent characteristics of the r.f. sheaths and their relationship to the antenna design. One use of ansat is therefore as a design tool, to assess the strengths and weaknesses of a given design with respect to critical voltage handling and edge plasma interaction issues. Additionally, examples are presented where ansat has been useful in the analysis and interpretation of ICRF experiments

A computer code, ANSAT (Antenna Sheath Analysis Tool) has been developed which allows an analysis of rf sheaths on the plasma facing regions of ICRF antennas. ANSAT, a post‐processor for the ARGUS code, calculates the contact points of the tokamak magnetic field lines on the surface of the antenna Faraday screen and nearby limiters for realistic three dimensional magnetic flux surface and antenna geometries, and determines the rf voltage that can drive sheaths at the contact points. The code then assesses the resulting rf‐induced convective cells, rf‐driven sputtering, and sheath power dissipation. Diagnostics for ‘‘hot spots’’ on the Faraday screen, convective cell flow patterns, locations of sheaths, and classes of sheaths are available. The effect on the sheath voltages of bumper tiles, antenna skew and misalignment, error and ripple fields and plasma are addressed. It is shown by some examples that ANSAT is a useful tool for antenna design and for interpretation of ICRF experiments.

The design, analysis, and performance evaluation of rf power systems ultimately requires accurate modeling of a chain of subsystems starting with the rf transmitter and ending with the power absorption in the plasma. A collection of computer codes is used at ORNL to calculate the plasma loading and wave spectrum for a three‐dimensional rf antenna, the transmission/reflection properties of the Faraday shield and its effect on the electrical characteristics and phase velocity of the antenna, the internal coupling among antenna array components and the incorporation of the antenna array into a transmission line model of the phase control, tuning, matching, and power distribution system. Some codes and techniques are more suited for the rapid evaluation of system design progressions, while others are more applicable to the detailed analysis of final designs or existing hardware. The interaction of codes and the accuracy of calculations will be illustrated by the process of determining the plasma loading as a function of phasing and density profiles for the TFTR ICRH antennas and comparing the results to measurements. An example of modeling a complex antenna geometry will be the comparison of calculations with the measured electrical response of a four‐strap mockup of the JET A2 antenna array which was loaned to ORNL by the JET ICRH team.

The effect of aspect ratio on magnetic field fluctuations in reversed-field pinches is investigated using a three-dimensional magnetohydrodynamic code. Configurations with aspect ratios of 1.1, 2.2, and 4.4 are modeled. The results are extrapolated to aspect ratio 8.8 for comparison with the Extrap T1 experiment [Nucl. Fusion 34, 427 (1994)]. It is found that the average modal amplitudes decrease with aspect ratio. However, the spectrum broadens correspondingly, resulting in negligible effect on the magnetic fluctuation level. The computed spectrum dynamics are found to be in good agreement with experimental observations on the T1 experiment. Quantitative evaluations of the field line stochasticity indicate no dependence of the mean magnetic field diffusion rate on aspect ratio.

A new solver has been developed for the ARGUS electromagnetic field solver package to analyze the ICRH antenna coupling problem. The key advantages are that complex 3‐D structures, e.g., Faraday screen, side walls..., are represented realistically, and that all currents flowing in the structures are solved self‐consistently. Plasma response is included as a surface impedance in Fourier‐space while the field solution around the antenna [satisfying ∇×(∇×E)=(ω/c2E] is computed in real space. The plasma impedance matrix is calculated separately, e.g., analytically or from a full‐wave code such as ORION.

Magnetohydrodynamic computation demonstrates that feedback can sustain reversal and reduce the loop voltage in resistive shell reversed field pinch (RFP) plasmas. Edge feedback on approximately 2R/a tearing modes resonant near the axis is found to restore plasma parameters to nearly their levels obtained with a close fitting conducting shell. When original dynamo modes are stabilized, neighbouring tearing modes grow to maintain the RFP dynamo more efficiently. This suggests that the experimentally observed limits on RFP pulse lengths to the order of the shell time can be overcome by applying feedback to a few helical modes.

MHD computation demonstrates that feedback can sustain reversal and reduce loop voltage in resistive-shell reversed field pinch (RFP) plasmas. Edge feedback on {approximately}2R/a tearing modes resonant near axis is found to restore plasma parameters to nearly their levels with a close-fitting conducting shell. When original dynamo modes are stabilized, neighboring tearing modes grow to maintain the RFP dynamo more efficiently. This suggests that experimentally observed limits on RFP pulselengths to the order of the shell time can be overcome by applying feedback to a few helical modes.

A general purpose 3D electromagnetic field solver code, ARGUS, is being used to analyze the TFTR Antennas. To data, the vacuum radiation patterns produced by the bay M and L antennas have been obtained and reported. Recent work has concentrated on antenna performance comparison and understanding the role of geometry on performance (e.g., the impact of end‐effects on current 2D models). Additional diagnostics such as evaluation of phase velocity and strap inductance are being implemented to enhance our understanding and to better compare with measurements.

The detailed dynamics underlying the self-generation of magnetic flux (‘‘dynamo’’) in reversed-field pinches (RFPs) is investigated with a three-dimensional magnetohydrodynamic code. A novel energy diagnostic is used to identify the path taken in Fourier space by the poloidal magnetic field energy as it is converted to axial magnetic field energy by the dynamo. At high values of the pinch parameter, Θ, and Lundquist number, S, the dynamo can be alternatingly dominated by quasilinear and nonlinear processes in a quasiperiodic fashion. Quasilinearly, the m=1 modes can reverse the axial field by themselves. However, m=0 modes are crucial to produce the nonlinear dynamo that triggers quasiperiodic relaxations. The same causal mechanism is likely to be responsible for the experimentally observed sawteeth.

The linear magnetohydrodynamic stability of current-driven modes is evaluated for a reversed field pinch in which the plasma is bounded by a thin resistive shell surrounded by a vacuum region out to a radius at which a perfectly conducting wall is situated. The effects of variation of the shell resistivity and wall proximity are investigated. Growth rates of tearing modes and kink modes are calculated by analytical solution based on the modified Bessel function model for the equilibrium. Relevance to experiments is discussed.

The nonlinear behavior of the reversed-field pinch bounded by a resistive shell or a distant conducting wall is investigated with a three-dimensional magnetohydrodynamic code. Nonlinear interaction between modes enhances fluctuation levels as the conducting wall is removed. The enhanced fluctuation induced v×b electric field, which produces the dynamo effect, suppresses toroidal current, and enhances surface helicity dissipation. Thus, loop voltage must increase to sustain the current and maintain helicity balance.