An implicit, scalable, relativistic nonlinear Fokker-Planck solver for runaway electrons

On the application of a sufficiently strong electric field, electrons break away from thermal equilibrium and approach relativistic speeds. These highly energetic `runaway' electrons (∼MeV) play a crucial role in understanding tokamak disruption events, and therefore their accurate simulation is essential to develop reliable mitigation technologies. For this purpose, we have developed a fully implicit, scalable relativistic Fokker-Planck kinetic electron solver. Energy and momentum conservation is  ensured for the electron-electron relativistic collisional interactions. Electron-ion interactions are modeled using the Lorentz operator, and synchrotron damping using the Abraham-Lorentz-Dirac reaction term. We use positivity preserving finite-difference schemes for both advection¹ and tensor diffusion² terms. This numerical treatment, combined with suitable preconditioning and multigrid strategies, allows us to accurately investigate phenomena that span a wide range of temporal scales. We demonstrate the scheme with numerical results ranging from small electric field electrical conductivity measurements, to accurate reproduction of runaway tail dynamics when strong electric fields are applied.

1) P Gaskell, A Lau Int J Num Meth Fluids 1988

2) W Hundsdorfer et al. J Comp Phys 1995