  In this paper, we present an efficient algorithm for the long time behavior
of plasma simulations. We will focus on 4D drift-kinetic model, where the
plasma's motion occurs in the plane perpendicular to the magnetic field and can
be governed by the 2D guiding-center model.
  Hermite WENO reconstructions, already proposed in \cite{YF15}, are applied
for solving the Vlasov equation. Here we consider an arbitrary computational
domain with an appropriate numerical method for the treatment of boundary
conditions.
  Then we apply this algorithm for plasma turbulence simulations. We first
solve the 2D guiding-center model in a D-shape domain and investigate the
numerical stability of the steady state. Then, the 4D drift-kinetic model is
studied with a mixed method, i.e. the semi-Lagrangian method in linear phase
and finite difference method during the nonlinear phase. Numerical results show
that the mixed method is efficient and accurate in linear phase and it is much
stable during the nonlinear phase. Moreover, in practice it has better
conservation properties.
