On the beta-drift of an initially circular vortex patch

The nonlinear inviscid evolution of a vortex patch in a single-layer quasi-geostrophic fluid and within a background planetary vorticity gradient is examined numerically at unprecedented spatial resolution. The evolution is governed by two dimensionless parameters: the initial size (radius) of the vortex compared to the Rossby deformation radius, and the initial strength of the vortex compared to the variation of the planetary vorticity across the vortex. It is found that the zonal speed of a vortex increases with its strength. However, the meridional speed reaches a maximum at intermediate vortex strengths. Both large and weak vortices are readily deformed, often into elliptical and tripolar shapes. This deformation is shown to be related to an instability of the instantaneous vorticity distribution in the absence of the planetary vorticity gradient β. The extremely high numerical resolution employed reveals a striking feature of the flow evolution, namely the generation of very sharp vorticity gradients surrounding the vortex and extending downstream of it in time. These gradients form as the vortex forces background planetary vorticity contours out of its way as it propagates. The contours close to the vortex swirl rapidly around the vortex and homogenize, but at some critical distance the swirl is not strong enough and, instead, a sharp vorticity gradient forms. The region inside this sharp gradient is called the ‘trapped zone’, though it shrinks slowly in time and leaks. This leaking occurs in a narrow wake called the ‘trailing front’, another zone of sharp vorticity gradients, extending behind the vortex

High-Resolution MHD Spectroscopy of External Kinks in a Tokamak Plasma

This thesis describes the first results of passive and active MHD spectroscopy experiments on the High Beta Tokamak-Extended Pulse (HBT-EP) device using a new array of magnetic diagnostics and coils. The capabilities of the HBT-EP experiment are significantly extended with the installation of a new adjustable conducting wall, high-power modular control coil arrays, and an extensive set of 216 magnetic sensors that allow simultaneous high-resolution detection of multimode MHD phenomena. The design, construction, and calibration of this system are described. The capability of this new magnetic diagnostic set is demonstrated by biorthogonal decomposition analysis of passive measurements of rotating resistive wall modes (RWMs). A strong multimode effect is detected for the first time in HBT-EP plasmas consisting of the simultaneous existence of m/n=3/1 and 6/2 RWMs which cause the plasma to evolve in a non-rigid multimode manner. Additional mode numbers as high as n=3 are also observed. Active MHD spectroscopy experiments using a "phase-flip" resonant magnetic perturbation (RMP) are able to excite a clear three-dimensional response. By adjusting the helicity of the magnetic field applied by the control coils, the driven plasma response is shown to be predominantly resonant field amplification. When the amplitude of the applied field is not too large, the driven resonant response appears linear, independent of the presence of background MHD phenomena and consistent with the predictions of single-helicity modeling of kink mode dynamics. The spatial structures of both the naturally rotating kink mode and the externally driven response are observed to be identical, while the temporal evolutions are approximately independent. The phase-flip driven plasma response is measured as a function of edge safety factor, plasma rotation, and the amplitude of the applied magnetic perturbation. As the RMP amplitude increases, the plasma response is shown to be linear, saturated, and ultimately, disruptive

Long-time discrete particle effects versus kinetic theory in the self-consistent single-wave model

The influence of the finite number N of particles coupled to a monochromatic wave in a collisionless plasma is investigated. For growth as well as damping of the wave, discrete particle numerical simulations show an N-dependent long time behavior resulting from the dynamics of individual particles. This behavior differs from the one due to the numerical errors incurred by Vlasov approaches. Trapping oscillations are crucial to long time dynamics, as the wave oscillations are controlled by the particle distribution inhomogeneities and the pulsating separatrix crossings drive the relaxation towards thermal equilibrium.Comment: 11 pages incl. 13 figs. Phys. Rev. E, in pres

Study of External Kink Modes in Shaped HBT-EP Plasmas

The first study of magnetohydrodynamic (MHD) equilibria and external kink modes in shaped plasmas on the High Beta Tokamak - Extended Pulse (HBT-EP) is described. A new poloidal field coil and high-current, low-voltage capacitive power supply was designed and installed. The new coil significantly modifies the shape of the plasma cross section and provides a new research tool for the study of kink mode structure and control. When fully energized, the coil creates a magnetic separatrix, which defines the boundary between confined and unconfined plasma. The separatrix is set by a poloidal field null called an “X-point”, which is on the inboard side of the torus, above the midplane. Several arrays of magnetic sensors observe and characterize the plasma equilibrium and the MHD fluctuations from kink modes. Free-boundary plasma equilibria are reconstructed using standard methods that minimize the mean-square error between the numerically reconstructed equilibria and various measurements. Reconstructions of shaped plasma equilibria show the creation of fully diverted plasmas with shaped outer boundaries. The reconstructions are confirmed by direct measurements using arrays of magnetic sensors and a moveable Langmuir probe to measure the outermost closed flux surface. Measurements of individual kink modes are obtained from the magnetic fluctuations using a technique known as biorthogonal decomposition. External kink modes that naturally arise in shaped plasmas are observed and described. The poloidal structure of modes in shaped plasmas are found to be similar to those that arise in circular plasmas, except near the X-point. The magnetic signature of kink modes on the surface of the plasma are calculated using the ideal MHD code DCON. For plasmas with an X-point, DCON shows a short-wavelength, low amplitude structure near the X-point. The code VALEN is used to calculate the perturbed magnetic field measured at the sensors due to the DCON mode at the plasma surface. VALEN includes the effects of sensor/plasma separation and eddy currents induced in conducting structures by rotation of the modes. Good agreement is found between the measured mode structures and the ideal kink mode structures calculated at the sensors by VALEN. A distributed array of forty active control coils was used to perturb the plasma equilibria, and for both shaped and circular equilibria, the structure of the response to the perturbation was found to be the same as the that of the dominant naturally occurring mode in that equilibrium. Finally, the magnitude of the plasma’s response to applied magnetic perturbations was found to be comparable between shaped and unshaped plasmas, even though separation between the sensors and the boundary of the shaped plasmas increases relative to circular plasmas with the same plasma current and radial positions. In addition to demonstrating a new research tool for study of kink modes on HBT-EP, this research demonstrates the importance of accurate electromagnetic calculations, including eddy currents, when comparing measured and predicted mode structure