  In this work we consider a relativistic drift-kinetic model for runaway
electrons along with a Fokker-Planck operator for small-angle Coulomb
collisions, a radiation damping operator, and a secondary knock-on (Boltzmann)
collision source. We develop a new scalable fully implicit solver utilizing
finite volume and conservative finite difference schemes and dynamic mesh
adaptivity. A new data management framework in the PETSc library based on the
p4est library is developed to enable simulations with dynamic adaptive mesh
refinement (AMR), distributed memory parallelization, and dynamic load
balancing of computational work. This framework and the runaway electron solver
building on the framework are able to dynamically capture both bulk Maxwellian
at the low-energy region and a runaway tail at the high-energy region. To
effectively capture features via the AMR algorithm, a new AMR indicator
prediction strategy is proposed that is performed alongside the implicit time
evolution of the solution. This strategy is complemented by the introduction of
computationally cheap feature-based AMR indicators that are analyzed
theoretically. Numerical results quantify the advantages of the prediction
strategy in better capturing features compared with nonpredictive strategies;
and we demonstrate trade-offs regarding computational costs. The robustness
with respect to model parameters, algorithmic scalability, and parallel
scalability are demonstrated through several benchmark problems including
manufactured solutions and solutions of different physics models. We focus on
demonstrating the advantages of using implicit time stepping and AMR for
runaway electron simulations.
