Plasma boundary shape control and real-time equilibrium reconstruction on NSTX-U

Abstract

The upgrade to the National Spherical Torus eXperiment (NSTX-U) included two main improvements: a larger center-stack, enabling higher toroidal field and longer pulse duration, and the addition of three new tangentially aimed neutral beam sources, which increase available heating and current drive, and allow for flexibility in shaping power, torque, current, and particle deposition profiles. To best use these new capabilities and meet the high-performance operational goals of NSTX-U, major upgrades to the NSTX-U control system (NCS) hardware and software have been made. Several control algorithms, including those used for real-time equilibrium reconstruction and shape control, have been upgraded to improve and extend plasma control capabilities. As part of the commissioning phase of first plasma operations, the shape control system was tuned to control the boundary in both inner-wall limited and diverted discharges. It has been used to accurately track the requested evolution of the boundary (including the size of the inner gap between the plasma and central solenoid, which is a challenge for the ST configuration), X-point locations, and strike point locations, enabling repeatable discharge evolutions for scenario development and diagnostic commissioning.

Design and simulation of the snowflake divertor control for NSTX–U

“…For the purposes of SFD control validation, we artificially stabilized the system by negating the unstable eigenvalue. This procedure is consistent with the assumption that the plasma vertical position is stabilized by a separate control loop (as is done on NSTX-U [54]).…”

“…This time increment was found to yield an acceptable balance between controller performance and simulation execution time. Furthermore, 5 ms is approximately the time required for performing one cycle of the rtEFIT algorithm for real-time equilibrium reconstruction on NSTX-U [54]. Figure 6 displays a sequence of equilibria for each of the three simulation scenarios.…”

“…Both components are depicted in Figure 3. The rtEFIT algorithm, which was used extensively on both NSTX [53] and NSTX-U [54], computes an approximate solution to the plasma force-balance relation that is constrained by measurements of flux, field, and current from a variety of magnetic sensors on the device. In particular, rtEFIT provides a reasonably accurate estimate of the plasma boundary location to enable control of the boundary shape and divertor geometry.…”

“…The voltage commands for the PF1aL, PF1cL, and PF2L coils were computed by the SFD control algorithm as described in this paper, while the remaining PF coils were controlled by the Isoflux algorithm with the aim of maintaining the plasma boundary shape and upper Xpoint position while the SFD configuration was modified by the lower divertor coils. The Isoflux algorithm, which is the primary shape control algorithm used on NSTX-U [54], is a predominantly single-input-single-output algorithm that regulates the plasma boundary shape by minimizing the errors between the fluxes at several control points on the desired boundary, as shown in Figure 4, and the flux at the boundary-defining X-point. During simulations, the PF3U, PF5, and PF3L coils were allocated for control of the fluxes at the three control points, while the PF2U and PF1aU coils were assigned to directly control the radial and vertical coordinates of the upper X-point, respectively.…”

Neural net modeling of equilibria in NSTX-U

“…From the R OM P and Z CU R plots we observe multiple spikes in the traces and errors early on, especially within the first few hundred ms. For Z CU R the early errors are also more benign since they occur at low Ip. Z CU R is most important for vertical control, but the applied feedback is proportional to Z CU R I p [36]. These dynamic features are representative of the NSTX-U campaign and is in part due to the control difficulties of highly-elongated, unstable plasma, and short-pulse (vessel effects become important), machine, as well as EFIT01 reconstruction inaccuracy at very low Ip.…”