Exact expression for the hot plasma conductivity kernel in configuration space

Electromagnetic perturbations of a magnetized plasma cause induced charges and currents, collectively known as the plasma response. In the frequency domain, this response is a non-local functional of the electric field. The associated integral kernel, known as the conductivity kernel, is well known in wave-number space, assuming the special case of a homogeneous plasma with a given Maxwellian background distribution function. It is used in this form by many full-wave codes. However, it may be more advantageous to solve the wave problem using a finite element model because of its attractive meshing flexibility. In this paper an exact solution for the conductivity kernel is derived in configuration space, to our knowledge for the first time in 3D. It is valid to all orders in Larmor radius, and up to arbitrary cyclotron harmonic. Future finite element models can be easily constructed using this kernel, which is shown in two simple examples. The model includes mode conversion as well, demonstrated by the second example.