  In a previous paper, second- and fourth-order explicit symplectic integrators
were designed for a Hamiltonian of the Schwarzschild black hole. Following this
work, we continue to trace the possibility of the construction of explicit
symplectic integrators for a Hamiltonian of charged particles moving around a
Reissner-Nordstrom black hole with an external magnetic field. Such explicit
symplectic methods are still available when the Hamiltonian is separated into
five independently integrable parts with analytical solutions as explicit
functions of proper time. Numerical tests show that the proposed algorithms
share the desirable properties in their long-term stability, precision and
efficiency for appropriate choices of step sizes. For the applicability of one
of the new algorithms, the effects of the black hole's charge, the Coulomb part
of the electromagnetic potential and the magnetic parameter on the dynamical
behavior are surveyed. Under some circumstances, the extent of chaos gets
strong with an increase of the magnetic parameter from a global phase-space
structure. No the variation of the black hole's charge but the variation of the
Coulomb part is considerably sensitive to affect the regular and chaotic
dynamics of particles' orbits. A positive Coulomb part is easier to induce
chaos than a negative one.
