Paraxial expansion of the wave kinetic equation for electron cyclotron beams in turbulent plasmas

The paraxial WKB (beam tracing) method has proven to be very powerful for the computation of electron cyclotron (EC) beams for heating, current-drive and diagnostics applications in smooth plasma equilibria. However, fluctuation-induced beam broadening with possible concerns for ITER application has raised interest on the effect of edge density fluctuations. This issue was recently tackled through a new approach based on the wave kinetic equation (WKE) and a representation of the beam in phase-space. This method has been implemented in the WKBeam code and employed to assess the impact of fluctuations under ITER conditions. In this work we propose to apply the paraxial technique to the wave kinetic equation. On the one hand this allows a comparison to the pWKB approach on the level of equations, clarifying the physical meaning of the WKE in phase-space and the limitations of a standard Gaussian beam in physical pace. On the other hand, we achieve a remarkable speed-up compared to WKBeam: Evolution of the beam is a direct result of a system of 11 ordinary differential equations whereas in WKBeam typically 10(5) rays are traced (Monte-Carlo approach). In its present formulation the paraxial method applies to situations in which turbulence conserves the Gaussian beam shape, which is the case in the diffusive scattering regime. For beam and turbulence parameters chosen in accordance with this requirement we achieve good agreement with the well-benchmarked WKBeam code.