  We investigate the dynamics of polymer translocation through a nanopore under
an externally applied field using the 2D fluctuating bond model with
single-segment Monte Carlo moves. We concentrate on the influence of the field
strength $E$, length of the chain $N$, and length of the pore $L$ on forced
translocation. As our main result, we find a crossover scaling for the
translocation time $\tau $ with the chain length from $\tau \sim N^{2\nu}$ for
relatively short polymers to $\tau \sim N^{1 + \nu}$ for longer chains, where
$\nu $ is the Flory exponent. We demonstrate that this crossover is due to the
change in the dependence of the translocation velocity v on the chain length.
For relatively short chains $v \sim N^{- \nu}$, which crosses over to $v \sim
N^{- 1}$ for long polymers. The reason for this is that with increasing $N$
there is a high density of segments near the exit of the pore, which slows down
the translocation process due to slow relaxation of the chain. For the case of
a long nanopore for which $R_\parallel $, the radius of gyration $R_{g}$ along
the pore, is smaller than the pore length, we find no clear scaling of the
translocation time with the chain length. For large $N$, however, the
asymptotic scaling $\tau \sim N^{1 + \nu}$ is recovered. In this regime, $\tau
$ is almost independent of $L$. We have previously found that for a polymer,
which is initially placed in the middle of the pore, there is a minimum in the
escape time for $R_\parallel \approx L$. We show here that this minimum
persists for a weak fields $E$ such that $EL$ is less than some critical value,
but vanishes for large values of $EL$.
