Vertical stability and its implications for the SPARC tokamak

The SPARC tokamak will operate with a highly shaped equilibrium (κa ~ 1.75, δ = 0.54) to achieve its performance goals, and thus be subject to vertical instability. However, the vertical instability growth rate, γ, is slower than comparably sized tokamaks due to the relatively thick vacuum vessel walls needed to withstand disruption forces at high field and current. Using the Toksys suite of tools, a survey of possible accessible shapes near the SPARC primary reference discharge indicates a maximum γ < 100 s-1. Steel vertical stability plates, which are positioned near the diverter shaping coils, have a modest (~25%) effect of reducing the vertical growth rate. Using a "max Z" analysis, we set the required power supply voltage and current to account for a vertical displacement of 10% of the minor radius a, defined as robust vertical control. Requirements for power supply energy and vertical stability coil heating are obtained from the expected spectra of plasma disturbances and diagnostic noise. Furthermore, this work suggests a small modification of the outboard limiter location to allow for an unmitigated vertical disturbance of 5% of the minor radius and subsequent additional vertical motion due to finite control system response without allowing the plasma to become limited.