  The Maxwell time is a typical time scale for the screening of an electric
field in a medium with a given conductivity. We introduce a generalization of
the Maxwell time that is valid for gas discharges: the \emph{ionization
screening time}, that takes the growth of the conductivity due to impact
ionization into account. We present an analytic estimate for this time scale,
assuming a planar geometry, and evaluate its accuracy by comparing with
numerical simulations in 1D and 3D. We investigate the minimum plasma density
required to prevent the growth of streamers with local field enhancement, and
we discuss the effects of photoionization and electron detachment on ionization
screening. Our results can help to understand the development of pulsed
discharges, for example nanosecond pulsed discharges at atmospheric pressure or
halo discharges in the lower ionosphere.
