  The equations of motion of a single particle subject to an arbitrary electric
and a static magnetic field form a Poisson system. We present a second-order
time integration method which preserves well the Poisson structure and compare
it to commonly used algorithms, such as the Boris scheme. All the methods are
represented in a general framework of splitting methods. We use the so-called
$\phi$ functions, which give efficient ways for both analyzing and implementing
the algorithms. Numerical experiments show an excellent long term stability for
the new method considered.
