  The Langevin equation is ubiquitously employed to numerically simulate
plasmas and dusty plasmas. However, the usual assumption of white noise becomes
untenable when the system is subject to an external AC electric field. This is
because the charged particles in the plasma, which provide the thermal bath for
the particle transport, become themselves responsive to the AC field and the
thermal noise is field-dependent and non-Markovian. We theoretically study the
particle diffusivity in a Langevin transport model for a tagged charged
particle immersed in a dense plasma of charged particles that act as the
thermal bath, under an external AC electric field, by properly accounting for
the effects of the AC field on the thermal bath statistics. We analytically
derive the time-dependent generalized diffusivity $D(t)$ for different initial
conditions. The generalized diffusivity exhibits damped oscillatory-like
behaviour with initial very large peaks, where the generalized diffusion
coefficient is enhanced by orders of magnitude with respect to the
infinite-time steady-state value. The latter coincides with the Stokes-Einstein
diffusivity in the absence of external field. For initial conditions where the
external field is already on at $t=0$ and the system is thermalized under DC
conditions for $t \leq 0$, the short-time behaviour is hyperballistic, $MSD
\sim t^4$ (where MSD is the mean-squared displacement), leading to giant
enhancement of the particle transport. Finally, the theory elucidates the role
of medium polarization on the local Lorentz field, and allows for estimates of
the effective electric charge due to polarization by the surrounding charges.
