Title: Study of External Kink Modes in Shaped HBT-EP Plasmas
Description: 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.