Streamlined calculations of the neoclassical bootstrap current and ambipolar radial electric field for stellarator optimization

Accurate and fast calculations of the neoclassical bootstrap current and ambipolar radial electric fields are essential for finite-beta stellarator optimization. The bootstrap current is a self-generated current, parallel to B, which arises due to momentum transfer from bouncing (trapped) particles to passing particles on a flux surface. The bootstrap current and its transient response can alter the rotational transform throughout the plasma which can impact core transport properties and modify the expected edge geometry properties outside of the plasma column which will influence the divertor design. Accurate estimates of the bootstrap current are critical for modeling the plasma response. Typical methods to calculate the bootstrap current can be both time-consuming and memory-intensive which presents a challenge for an optimization loop. This work presents a set of equations for a streamlined version of a drift-kinetic equation solver, sufficient for calculating the bootstrap current and neoclassical transport in many situations. Comparisons will be shown between the streamlined calculations and a more comprehensive model that includes additional physics.