Adaptive energy-preserving algorithms for guiding center system

We develop two types of adaptive energy preserving algorithms based on the averaged vector field for the guiding center dynamics, which plays a key role in magnetized plasmas. The adaptive scheme is applied to the Gauss Legendre's quadrature rules and time stepsize respectively to overcome the energy drift problem in traditional energy-preserving algorithms. These new adaptive algorithms are second order, and their algebraic order is carefully studied. Numerical results show that the global energy errors are bounded to the machine precision over long time using these adaptive algorithms without massive extra computation cost.