  We study the enhancement of tunneling through a potential barrier $V(x)$ by a
time-dependent electric field with special emphasis on pulse-shaped vector
potentials such as $A_x(t)=A_0/\cosh^2(\omega t)$. In addition to the known
effects of pre-acceleration and potential deformation already present in the
adiabatic regime, as well as energy mixing in analogy to the Franz-Keldysh
effect in the non-adiabatic (impulse) regime, the pulse $A_x(t)$ can enhance
tunneling by ``pushing'' part of the wave-function out of the rear end of the
barrier. Besides the natural applications in condensed matter and atomic
physics, these findings could be relevant for nuclear fusion, where pulses
$A_x(t)$ with $\omega=1~\rm keV$ and peak field strengths of $10^{16}~\rm V/m$
might enhance tunneling rates significantly.
