  Dynamics of a charged particle in the canonical coordinates is a Hamiltonian
system, and the well-known symplectic algorithm has been regarded as the de
facto method for numerical integration of Hamiltonian systems due to its
long-term accuracy and fidelity. For long-term simulations with high
efficiency, explicit symplectic algorithms are desirable. However, it is widely
accepted that explicit symplectic algorithms are only available for
sum-separable Hamiltonians, and that this restriction severely limits the
application of explicit symplectic algorithms to charged particle dynamics. To
overcome this difficulty, we combine the familiar sum-split method and a
generating function method to construct second and third order explicit
symplectic algorithms for dynamics of charged particle. The generating function
method is designed to generate explicit symplectic algorithms for
product-separable Hamiltonian with form of
$H(\mathbf{p},\mathbf{q})=\mathbf{p}_{i}f(\mathbf{q})$ or
$H(\mathbf{p},\mathbf{q})=\mathbf{q}_{i}f(\mathbf{p})$. Applied to the
simulations of charged particle dynamics, the explicit symplectic algorithms
based on generating functions demonstrate superiorities in conservation and
efficiency.
