Dov Rhodes

High resolution detection and excitation of resonant magnetic perturbations in a wall-stabilized tokamaka)

We report high-resolution detection of the 3D plasma magnetic response of wall-stabilized tokamak discharges in the High Beta Tokamak-Extended Pulse [T. H. Ivers et al., Phys. Plasmas 3, 1926 (1996)] device. A new adjustable conducting wall has been installed on HBT-EP made up of 20 independent, movable, wall segments instrumented with three distinct sets of 40 modular coils that can be independently driven to generate a wide variety of magnetic perturbations. High-resolution detection of the plasma response is made with 216 poloidal and radial magnetic sensors that have been located and calibrated with high-accuracy. Static and dynamic plasma responses to resonant and non-resonant magnetic perturbations are observed through measurement of the step-response following a rapid change in the toroidal phase of the applied perturbations. Biorthogonal decomposition of the full set of magnetic sensors clearly defines the structures of naturally occurring external kinks as being composed of independent m/n = 3/1 and 6/2 modes. Resonant magnetic perturbations were applied to discharges with pre-existing, saturated m/n = 3/1 external kink mode activity. This m/n = 3/1 kink mode was observed to lock to the applied perturbation field. During this kink mode locked period, the plasma resonant response is characterized by a linear, a saturated, and a disruptive plasma regime dependent on the magnitude of the applied field and value of the edge safety factor and plasma rotation.We report high-resolution detection of the 3D plasma magnetic response of wall-stabilized tokamak discharges in the High Beta Tokamak-Extended Pulse [T. H. Ivers et al., Phys. Plasmas 3, 1926 (1996)] device. A new adjustable conducting wall has been installed on HBT-EP made up of 20 independent, movable, wall segments instrumented with three distinct sets of 40 modular coils that can be independently driven to generate a wide variety of magnetic perturbations. High-resolution detection of the plasma response is made with 216 poloidal and radial magnetic sensors that have been located and calibrated with high-accuracy. Static and dynamic plasma responses to resonant and non-resonant magnetic perturbations are observed through measurement of the step-response following a rapid change in the toroidal phase of the applied perturbations. Biorthogonal decomposition of the full set of magnetic sensors clearly defines the structures of naturally occurring external kinks as being composed of independent m/n = 3/1 ...

Electrohydrodynamic Drop Deformation by Strong Electric Fields: Slender-Body Analysis

Slender-body approximations are utilized to analyze drop elongation by a uniformly applied electric field. The Taylor--Melcher model of leaky-dielectric liquids is employed, with electrohydrodynamic flow animation by electrical shear stresses at the free surface. Using the drop slenderness as the small asymptotic parameter, separate asymptotic expansions of the pertinent fields are presented in “inner” and “outer” regions, respectively, corresponding to the drop cross-sectional and longitudinal scales, as well as an additional expansion in the drop phase. For a given shape, both the electric potential and flow field are calculated. Asymptotic matching is possible only for low drop viscosity. The normal-stress condition on the free surface provides a scaling relation between the slenderness parameter and the dimensionless electric field, expressed as a capillary number. The predicted slenderness scaling, inversely with the

The elongated shape of a dielectric drop deformed by a strong electric field

6/7

Shaping Effects on Resistive-Plasma Resistive-Wall Mode Stability in a Tokamak

-power of the electric field, is the same as that appropriate for dielectric li...

The effects of differential flow between rational surfaces on toroidal resistive MHD modes

A dielectric drop is suspended within a dielectric liquid and is exposed to a uniform electric field. Due to polarization forces, the drop deforms from its initial spherical shape, becoming prolate in the field direction. At strong electric fields, the drop elongates significantly, becoming long and slender. For moderate ratios of the permittivities of the drop and surrounding liquid, the drop ends remain rounded. The slender limit was originally analysed by Sherwood ( J. Phys . A, vol. 24, 1991, p. 4047) using a singularity representation of the electric field. Here, we revisit it using matched asymptotic expansions. The electric field within the drop is continued into a comparable solution in the ‘inner’ region, at the drop cross-sectional scale, which is itself matched into the singularity representation in the ‘outer’ region, at the drop longitudinal scale. The expansion parameter of the problem is the elongated drop slenderness. In contrast to familiar slender-body analysis, this parameter is not provided by the problem formulation, and must be found throughout the course of the solution. The drop aspect-ratio scaling, with the 6/7-power of the electric field, is identical to that found by Sherwood ( J. Phys . A, vol. 24, 1991, p. 4047). The predicted drop shape is compared with the boundary-integral solutions of Sherwood ( J. Fluid Mech ., vol. 188, 1988, p. 133). While the agreement is better than that found by Sherwood ( J. Phys . A, vol. 24, 1991, p. 4047), the weak logarithmic decay of the error terms still hinders an accurate calculation. We obtain the leading-order correction to the drop shape, improving the asymptotic approximation.