Internal/External Magnetic Field Decomposition and the Dynamics of Mode Locking in DIII-D

The magnetic field on a closed surface external to the plasma contains enough information to distinguish the field of sources internal to the surface from the field of external sources [1]. This principle has several applications to axisymmetric and non-axisymmetric fields in tokamak experiments. For example, given two- or three-axis magnetic measurements with sufficient toroidal and poloidal resolution, the field of a rotating MHD mode can be distinguished from that of the wall currents that it induces, enabling a more accurate measurement of the mode amplitude. The same analysis provides a natural framework for measurement of the electromagnetic torque exchanged between the mode and the wall. Averaged over the rotation period, the torque measured during mode locking agrees well with a simple model. The presence of a static error field introduces variation of the torque balance during each rotation, leading to more complex dynamics. If calculated in real time, the evolution of the electromagnetic torque could aid in optimizing error field compensation, and provide advance warning of a mode-locking event. 

[1] R.M. Sweeney & E.J. Strait, Phys. Plasmas 26, 012509 (2019).