Sensitivity of Energetic Particle Transport in 3D Toroidal Magnetic Confinement Configurations to Changes in Boundary Shape

Cross-field transport of energetic particles in 3D magnetic field configurations due to magnetic drifts depends sensitively on the spatial dependence of the confining magnetic field. In optimizing a configuration, it is desirable to know how changes in the shape of the outermost flux surface will impact the transport. We present here a method for determining this sensitivity for arbitrary displacements of the outer flux surface based on adjoint methods. The method compares the value of a transport metric for two neighboring MHD equilibria that differ by a small displacement of the magnetic field, but have the same flux dependent pressure profile and rotational transform. The method involves a single solution of the linearized MHD equations for fixed boundary shape but subject to the addition of a judiciously chosen bulk force. The method can be implemented in a standard MHD stability code. Examples will be presented.