Several problems in magnetically confined fusion, such as the computation of exterior vacuum fields or the decomposition of the total magnetic field into separate contributions from the plasma and the external sources, are best formulated in terms of integral equation expressions. Based on Biot-Savart-like formulae, these integrals contain singular integrands. The regularization method commonly used to address the computation of various singular surface integrals along general toroidal surfaces is low-order accurate, and therefore requires a dense computational mesh in order to obtain sufficient accuracy. In this work, we present a fast, high-order quadrature scheme for the efficient computation of these integrals. Several numerical examples are provided demonstrating the computational efficiency and the high-order accurate convergence. A corresponding code for use in the community has been publicly released 1 . *

Many applications in magnetic confinement fusion require the efficient calculation of surface integrals with singular integrands. The singularity subtraction approaches typically used to handle such singularities are complicated to implement and low-order accurate. In contrast, we demonstrate that the Kapur–Rokhlin quadrature scheme is well-suited for the logarithmically singular integrals encountered for a toroidally axisymmetric confinement system, is easy to implement and is high-order accurate. As an illustration, we show how to apply this quadrature scheme for the efficient and accurate calculation of the normal component of the magnetic field due to the plasma current on the plasma boundary, via the virtual-casing principle.